Stefan Richter
Ph.D. Student in the Hybrid Systems Group
Supervisor: Prof. Manfred Morari
Address: Automatic Control Laboratory
ETH Zurich
Physikstrasse 3
ETL I11
8092 Zurich, Switzerland
Email: richters@ee.ethz.ch
Phone: +41 44 632 0373
Fax: +41 44 632 1211
Research Interests
Computational Complexity Certification of Linear Model Predictive Control (MPC)
We aim at providing an a priori bound on the number of iterations of iterative optimization methods applied to linear MPC problems with quadratic costs (constrained LQR). This allows the control engineer to select appropriate control hardware and reduce testing time but also ensures a safe operation of the control system.
Challenges include
- practicality and tightness of bounds,
- scalability of both the optimization method and the certification procedure,
- numerical robustness of the method,
- linking system properties with certified bounds to understand when the certified method is also fast.
This is the topic of my Ph.D. thesis and is joint work with Colin N. Jones (EPFL Lausanne).
- Related Publications
- S. Richter, C. N. Jones, and M. Morari,
"Certifcation Aspects of the Fast Gradient Method for Solving the Dual of Parametric Convex Programs,"
submitted to Mathematical Methods of Operations Research, Springer, 2011.
- Abstract This paper examines the challenges of certifying the computational complexity of the fast gradient method for the solution of the dual of a parametric convex program. To this end, a lower iteration bound is derived such that for all parameters from a compact set a solution with a specified level of suboptimality will be obtained. For its practical importance, the derivation of the smallest lower iteration bound is considered. In order to determine it, we investigate both the computation of the worst case minimal Euclidean distance between an initial iterate and a Lagrange multiplier and the issue of finding the largest step size for the fast gradient method. In addition, we argue that optimal preconditioning of the dual problem can not be proven to decrease the smallest lower iteration bound. The findings of this paper are of importance in embedded optimization, for instance, in model predictive control.
- Y. Ma, S. Richter, and F. Borrelli,
"Distributed Model Predictive Control for Building Temperature Regulation," in
Control and Optimization with Differential-Algebraic Constraints, SIAM, 2012 (accepted).
- Abstract We study the problem of temperature regulation in a network of building thermal zones. The control objective is to keep zone temperatures within a comfort range while consuming the least energy by using predictive knowledge of weather and occupancy. First, we present a simplified two-mass nonlinear system for modeling thermal zone dynamics. Model identification and validation based on historical measured data are presented. Second, a distributed model-based predictive control (DMPC) is designed for optimal heating and cooling. The DMPC is implemented using sequential quadratic program, dual decomposition, and the fast gradient method. Simulation results show good performance and computational tractability of the resulting scheme.
- S. Richter, M. Morari, and C. N. Jones,
"Towards Computational Complexity Certification for Constrained MPC
Based on Lagrange Relaxation and the Fast Gradient Method,"
Proceedings of the 50th IEEE Conference on Decision and Control (CDC)
and European Control Conference (ECC), Orlando, FL, USA, 2011, pp. 5223-5229.
- Abstract
This paper discusses the certification of Nesterov's fast gradient method
for problems with a strongly convex quadratic objective and a feasible set
given as the intersection of a parametrized affine set and a convex set.
For this, we derive a lower iteration bound for the solution of the dual
problem that is obtained from a partial Lagrange Relaxation and propose
a new constant step-size rule that we prove to be optimal under mild
assumptions. Finally, we apply the certification procedure to a
constrained MPC problem and show that the new step-size rule
improves performance significantly.
- Abstract
This paper discusses the certification of Nesterov's fast gradient method
for problems with a strongly convex quadratic objective and a feasible set
given as the intersection of a parametrized affine set and a convex set.
For this, we derive a lower iteration bound for the solution of the dual
problem that is obtained from a partial Lagrange Relaxation and propose
a new constant step-size rule that we prove to be optimal under mild
assumptions. Finally, we apply the certification procedure to a
constrained MPC problem and show that the new step-size rule
improves performance significantly.
- S. Richter, C. N. Jones, and M. Morari,
"Computational Complexity Certification for Real-Time MPC with Input Constraints
Based on the Fast Gradient Method," in IEEE Transactions on Automatic
Control 57(6), 2012 (tentative).
- Abstract This paper proposes to use Nesterov's fast gradient method for the solution of linear quadratic model predictive control (MPC) problems with input constraints. The main focus is on the method's a priori computational complexity certification which consists of deriving lower iteration bounds such that a solution of pre-specified suboptimality is obtained for any possible state of the system. We investigate cold- and warm-starting strategies and provide an easily computable lower iteration bound for cold-starting and an asymptotic characterization of the bounds for warm-starting. Moreover, we characterize the set of MPC problems for which small iteration bounds and thus short solution times are expected. The theoretical findings and the practical relevance of the obtained lower iteration bounds are underpinned by various numerical examples and compared to certification results for a primal-dual interior point method.
- S. Richter, S. Mariéthoz, and M. Morari,
"High-Speed Online MPC Based on a Fast Gradient
Method Applied to Power Converter Control," in American Control Conference (ACC),
2010, pp. 4737-4743.
- Abstract
Bounding the computational complexity of an online optimization method
in a real-time environment with hard time constraints is a challenging problem.
This paper investigates a new solution approach based on a fast gradient
method in the context of model predictive control (MPC) of power converters.
Different from other solution methods that either provide bounds that are
far off from the practically observed ones or do not allow for bounding the
computational effort at all this method enables easy to compute and meaningful
bounds that can further be decreased by means of a preconditioning technique.
We report an implementation of the fast gradient method on an industrial-type
digital signal processor with integer arithmetics and show that worst case
runtimes are in the order of tens of microseconds using less than one kByte
of memory while being numerically robust. Moreover, this method also
improves the control performance compared to explicit MPC.
- Abstract
Bounding the computational complexity of an online optimization method
in a real-time environment with hard time constraints is a challenging problem.
This paper investigates a new solution approach based on a fast gradient
method in the context of model predictive control (MPC) of power converters.
Different from other solution methods that either provide bounds that are
far off from the practically observed ones or do not allow for bounding the
computational effort at all this method enables easy to compute and meaningful
bounds that can further be decreased by means of a preconditioning technique.
We report an implementation of the fast gradient method on an industrial-type
digital signal processor with integer arithmetics and show that worst case
runtimes are in the order of tens of microseconds using less than one kByte
of memory while being numerically robust. Moreover, this method also
improves the control performance compared to explicit MPC.
- S. Richter, C. N. Jones, and M. Morari,
"Real-time input-constrained MPC using fast gradient methods,"
Proceedings of the 48th IEEE Conference on Decision and Control (CDC)
held jointly with 2009 28th Chinese Control Conference, Shanghai, China, 2009, pp. 7387-7393.
- Abstract
Linear quadratic model predictive control (MPC) with input constraints leads to an optimization
problem that has to be solved at every instant in time. Although there exists computational complexity
analysis for current online optimization methods dedicated to MPC, the worst case complexity bound is
either hard to compute or far off from the practically observed bound. In this paper we introduce fast
gradient methods that allow one to compute a priori the worst case bound required to find a solution
with pre-specified accuracy. Both warm- and cold-starting techniques are analyzed and an
illustrative example confirms that small, practical bounds can be obtained that together with the
algorithmic and numerical simplicity of fast gradient methods allow online optimization at high rates.
- Abstract
Linear quadratic model predictive control (MPC) with input constraints leads to an optimization
problem that has to be solved at every instant in time. Although there exists computational complexity
analysis for current online optimization methods dedicated to MPC, the worst case complexity bound is
either hard to compute or far off from the practically observed bound. In this paper we introduce fast
gradient methods that allow one to compute a priori the worst case bound required to find a solution
with pre-specified accuracy. Both warm- and cold-starting techniques are analyzed and an
illustrative example confirms that small, practical bounds can be obtained that together with the
algorithmic and numerical simplicity of fast gradient methods allow online optimization at high rates.
- S. Richter, C. N. Jones, and M. Morari,
"Certifcation Aspects of the Fast Gradient Method for Solving the Dual of Parametric Convex Programs,"
submitted to Mathematical Methods of Operations Research, Springer, 2011.
- Related Technical Reports
- S. Richter, M. Morari and C. N. Jones,
"A Complexity-Based Review on Proximal Gradient Methods for Convex Composite Optimization,"
IfA Technical Report vol. AUT12-01, 2012.
- Abstract
The proximal gradient method and its accelerated variants represent recent generalizations
of the gradient and fast gradient methods for convex composite minimization where the objective
is represented as the sum of a smooth and a potentially nonsmooth function. These methods can
be understood as exploiting the additive structure of the composite problem and hence are able
to break the black box lower complexity bounds of first-order methods for nonsmooth
convex optimization. This tutorial-style paper aims at highlighting the necessary background
in complexity theory such that thereafter both the strength and significance of the proximal
gradient method and its accelerated variants can be assessed from a complexity point of view.
- Abstract
The proximal gradient method and its accelerated variants represent recent generalizations
of the gradient and fast gradient methods for convex composite minimization where the objective
is represented as the sum of a smooth and a potentially nonsmooth function. These methods can
be understood as exploiting the additive structure of the composite problem and hence are able
to break the black box lower complexity bounds of first-order methods for nonsmooth
convex optimization. This tutorial-style paper aims at highlighting the necessary background
in complexity theory such that thereafter both the strength and significance of the proximal
gradient method and its accelerated variants can be assessed from a complexity point of view.
- S. Richter, C. N. Jones, and M. Morari,
"Real-Time MPC with Input Constraints Using the Fast Gradient Method,"
IfA Technical Report vol. AUT10-05, 2010.
- Abstract
This paper considers the application of Nesterov's fast gradient method in the context of
linear quadratic model predictive control (MPC) with input constraints. The main focus is
on the method's a priori computational complexity certification which consists of deriving
lower iteration bounds such that a solution of pre-specified suboptimality is obtained for
any possible state of the dynamic system. Cold- and warm-starting strategies for MPC are
defined and the corresponding problems to obtain the bounds are discussed. Moreover, an
easy to compute upper bound for cold-starting is given and an asymptotic characterization
for warm-starting is presented. We also investigate the choice of the suboptimality level
in the context of MPC and propose an optimal preconditioning technique to increase the
convergence rate of the method. Finally, we characterize the set of MPC problems for
which small iteration bounds and thus short solution times are expected in terms of
the system and weight matrices and underpin the theoretical investigations as well as
the practical applicability by various numerical examples, which indicate that
extremely short certified solution times can be obtained.
- Abstract
This paper considers the application of Nesterov's fast gradient method in the context of
linear quadratic model predictive control (MPC) with input constraints. The main focus is
on the method's a priori computational complexity certification which consists of deriving
lower iteration bounds such that a solution of pre-specified suboptimality is obtained for
any possible state of the dynamic system. Cold- and warm-starting strategies for MPC are
defined and the corresponding problems to obtain the bounds are discussed. Moreover, an
easy to compute upper bound for cold-starting is given and an asymptotic characterization
for warm-starting is presented. We also investigate the choice of the suboptimality level
in the context of MPC and propose an optimal preconditioning technique to increase the
convergence rate of the method. Finally, we characterize the set of MPC problems for
which small iteration bounds and thus short solution times are expected in terms of
the system and weight matrices and underpin the theoretical investigations as well as
the practical applicability by various numerical examples, which indicate that
extremely short certified solution times can be obtained.
- S. Richter, M. Morari and C. N. Jones,
"A Complexity-Based Review on Proximal Gradient Methods for Convex Composite Optimization,"
IfA Technical Report vol. AUT12-01, 2012.
- Related Talks
-
"Towards Computational Complexity Certification for Constrained MPC
Based on Lagrange Relaxation and the Fast Gradient Method,"
50th IEEE Conference on Decision and Control (CDC)
and European Control Conference (ECC), Orlando, FL, USA, December 2011.
- Abstract
This paper discusses the certification of Nesterov's fast gradient method
for problems with a strongly convex quadratic objective and a feasible set
given as the intersection of a parametrized affine set and a convex set.
For this, we derive a lower iteration bound for the solution of the dual
problem that is obtained from a partial Lagrange Relaxation and propose
a new constant step-size rule that we prove to be optimal under mild
assumptions. Finally, we apply the certification procedure to a
constrained MPC problem and show that the new step-size rule
improves performance significantly.
- Abstract
This paper discusses the certification of Nesterov's fast gradient method
for problems with a strongly convex quadratic objective and a feasible set
given as the intersection of a parametrized affine set and a convex set.
For this, we derive a lower iteration bound for the solution of the dual
problem that is obtained from a partial Lagrange Relaxation and propose
a new constant step-size rule that we prove to be optimal under mild
assumptions. Finally, we apply the certification procedure to a
constrained MPC problem and show that the new step-size rule
improves performance significantly.
-
"Certification of the Fast Gradient Method in Model Predictive Control,"
International Conference on Operations Research OR2011, Zurich, Switzerland, September 2011.
- Abstract
Model predictive control (MPC) requires the solution of a constrained finite
horizon optimal control problem in a receding horizon fashion. Consequently,
the solution to this optimization problem has to be obtained within one
sampling period of the control loop. But guaranteeing deterministic
termination of an iterative solution method is a challenging problem in
general. This talk focuses on certifying the fast gradient method for both
input-only constrained and input/state constrained linear quadratic MPC.
We establish links between problem data and convergence speed and emphasize
the practicability of the certification results by several examples and
real-world applications.
- Abstract
Model predictive control (MPC) requires the solution of a constrained finite
horizon optimal control problem in a receding horizon fashion. Consequently,
the solution to this optimization problem has to be obtained within one
sampling period of the control loop. But guaranteeing deterministic
termination of an iterative solution method is a challenging problem in
general. This talk focuses on certifying the fast gradient method for both
input-only constrained and input/state constrained linear quadratic MPC.
We establish links between problem data and convergence speed and emphasize
the practicability of the certification results by several examples and
real-world applications.
-
"First Order Methods for MPC: Certification & Code Generation,"
UC Berkeley, US, July 2011.
- Abstract
In this talk we review certification issues in linear MPC with quadratic costs.
We first discuss first order methods for smooth convex optimization and hint at the fast gradient method
as an optimal first order method. Thereafter we apply it to input-only and input-and-state constrained MPC
and provide some certification results for examples and real-world applications.
Finally, we summarize the key features of FiOrdOs, a first order optimization code generator.
- Abstract
In this talk we review certification issues in linear MPC with quadratic costs.
We first discuss first order methods for smooth convex optimization and hint at the fast gradient method
as an optimal first order method. Thereafter we apply it to input-only and input-and-state constrained MPC
and provide some certification results for examples and real-world applications.
Finally, we summarize the key features of FiOrdOs, a first order optimization code generator.
-
"Computational Complexity Certification for MPC Based on the Fast Gradient Method,"
SIAM Conference on Optimization, Darmstadt, Germany, SIOPT 2011.
- Abstract
MPC requires the solution of a constrained finite horizon optimal control
problem in a receding horizon fashion. Consequently, the solution to this
optimization problem has to be obtained within one sampling period of the
con- trol loop. But guaranteeing deterministic termination of iterative
solution methods is a challenging problem in general. This talk focuses
on certifying Nesterov's fast gradient method for constrained linear
quadratic MPC and points out links between problem data and convergence
speed.
- Abstract
MPC requires the solution of a constrained finite horizon optimal control
problem in a receding horizon fashion. Consequently, the solution to this
optimization problem has to be obtained within one sampling period of the
con- trol loop. But guaranteeing deterministic termination of iterative
solution methods is a challenging problem in general. This talk focuses
on certifying Nesterov's fast gradient method for constrained linear
quadratic MPC and points out links between problem data and convergence
speed.
-
"High-Speed Online MPC Based on a Fast Gradient Method Applied to Power Converter Control,"
American Control Conference, Baltimore, US, 2010.
- Abstract
Bounding the computational complexity of an online optimization method in a
real-time environment with hard time constraints is a challenging problem.
This paper considers a new solution approach based on a fast gradient
method in the context of Model Predictive Control (MPC) of power converters.
Different from other solution methods that either do not allow for bounding
the computational effort at all or provide bounds that are far off from
practically observed bounds, the fast gradient method is shown to provide
easy to compute and meaningful bounds that can further be decreased by means
of a pre-conditioning technique. We report an implementation of this method
on an industrial-type digital signal processor with integer arithmetics and
show that runtimes are in the order of tens of us using less than one kByte
of memory. Finally, we not only prove feasibility of the new method but also
show that we outperform control approaches that are based on explicit MPC.
- Abstract
Bounding the computational complexity of an online optimization method in a
real-time environment with hard time constraints is a challenging problem.
This paper considers a new solution approach based on a fast gradient
method in the context of Model Predictive Control (MPC) of power converters.
Different from other solution methods that either do not allow for bounding
the computational effort at all or provide bounds that are far off from
practically observed bounds, the fast gradient method is shown to provide
easy to compute and meaningful bounds that can further be decreased by means
of a pre-conditioning technique. We report an implementation of this method
on an industrial-type digital signal processor with integer arithmetics and
show that runtimes are in the order of tens of us using less than one kByte
of memory. Finally, we not only prove feasibility of the new method but also
show that we outperform control approaches that are based on explicit MPC.
-
"Real-Time Input-Constrained MPC Using Fast Gradient Methods,"
Conference on Decision and Control (CDC), Shanghai, China, 2009.
- Abstract
Linear quadratic model predictive control (MPC) with input constraints leads
to an optimization problem that has to be solved at every instant in time.
Although there exists computational complexity analysis for current online
optimization methods dedicated to MPC, the worst case complexity bound is
either hard to compute or far off from the practically observed bound. In
this paper we introduce fast gradient methods that allow one to compute a
priori the worst case bound required to find a solution with
pre-specified accuracy. Both warmand cold-starting techniques are
analyzed and an illustrative example confirms that small, practical
bounds can be obtained that together with the algorithmic and numerical
simplicity of fast gradient methods allow online optimization at high
rates.
- Abstract
Linear quadratic model predictive control (MPC) with input constraints leads
to an optimization problem that has to be solved at every instant in time.
Although there exists computational complexity analysis for current online
optimization methods dedicated to MPC, the worst case complexity bound is
either hard to compute or far off from the practically observed bound. In
this paper we introduce fast gradient methods that allow one to compute a
priori the worst case bound required to find a solution with
pre-specified accuracy. Both warmand cold-starting techniques are
analyzed and an illustrative example confirms that small, practical
bounds can be obtained that together with the algorithmic and numerical
simplicity of fast gradient methods allow online optimization at high
rates.
-
"Extreme MPC - Optimization in the Microsecond World,"
IfA Internal Seminar Series, 2009.
- Abstract
In this talk I will discuss how to solve the linear MPC problem with quadratic costs and
constraints on the control inputs online at every time-step and how to upper-bound
the computational efforts a priori. It will be shown, that for a specified performance
level meaningful bounds (e.g. flops, number of iterations) can be derived.
The solution method of choice is a fast gradient method - developed by Y. Nesterov
in 1983 - which seems to be less well-known in the community. Through its
algorithmic simplicity the fast gradient method is well-suited for inexpensive
computational devices. A practical implementation of the method for the control
of an AC-DC power converter gets presented showing that solution times of
50 microseconds at less than 1kBytes memory usage are possible for a low-cost DSP.
- Abstract
In this talk I will discuss how to solve the linear MPC problem with quadratic costs and
constraints on the control inputs online at every time-step and how to upper-bound
the computational efforts a priori. It will be shown, that for a specified performance
level meaningful bounds (e.g. flops, number of iterations) can be derived.
The solution method of choice is a fast gradient method - developed by Y. Nesterov
in 1983 - which seems to be less well-known in the community. Through its
algorithmic simplicity the fast gradient method is well-suited for inexpensive
computational devices. A practical implementation of the method for the control
of an AC-DC power converter gets presented showing that solution times of
50 microseconds at less than 1kBytes memory usage are possible for a low-cost DSP.
-
"Towards Computational Complexity Certification for Constrained MPC
Based on Lagrange Relaxation and the Fast Gradient Method,"
50th IEEE Conference on Decision and Control (CDC)
and European Control Conference (ECC), Orlando, FL, USA, December 2011.
(Convex) Optimization
I am interested in all aspects of optimization, with strong emphasis on convex optimization. Topics of personal interest include
- theory, complexity and implementation of optimization methods, such as optimal first order methods, interior point methods and active set methods,
- dual methods, e.g. Lagrange Relaxation, Augmented Lagrangians,
- cone programming (LP, SOCP, SDP),
- modeling for convex programming,
- (non-convex) optimal control problems,
- convex analysis.
Control
My interest and experience are mainly in the field of linear (constrained) control, e.g.
- theory, formulation and efficient solution of model predictive control problems,
- observers for hybrid systems,
- particle filters,
- classical control methods (frequency domain).
- Related Talk
-
"
Optimality of Affine Policies in Multi-Stage Robust Optimization," CDC 2009 Review, IfA Internal Seminar Series, 2010.
- Abstract
This is a CDC 2009 review presentation of the paper
"Optimality of Affine Policies in Multi-stage Robust Optimization"
by Dimitris Bertsimas, Dan A. Iancu, and Pablo A. Parrilo (MIT).
- Abstract
This is a CDC 2009 review presentation of the paper
"Optimality of Affine Policies in Multi-stage Robust Optimization"
by Dimitris Bertsimas, Dan A. Iancu, and Pablo A. Parrilo (MIT).
-
"
Optimality of Affine Policies in Multi-Stage Robust Optimization," CDC 2009 Review, IfA Internal Seminar Series, 2010.
- Master's Thesis
-
S. Richter, "
Probabilistic Hybrid State Estimation of Piecewise Affine Systems Through Qualitative Approximation,"
supervised by Prof. Manfred Morari and
Prof. Michael Hofbaur (UMIT), 2007.
- Abstract
Piecewise affine (PWA) systems are an important hybrid modelling class for dynamical systems
which have an implicit interaction between the continuous state and their behaviorial mode.
This work introduces a novel hybrid estimation approach for PWA systems subject to
non-negligible state disturbance and measurement noise. In this case, the number of
possible evolutions of the system grows without bounds as time proceeds. Current estimation
approaches do not explicitly account for this and thus their application is restricted to
PWA systems with a fairly small number of modes. In order to make estimation also applicable
to systems with a large number of modes, our main idea is to put emphasis on most probable
evolutions of the system and reframe hybrid estimation as a discrete search problem. For this
purpose, we introduce a likelihood measure for mode transitions which can be efficiently
approximated by means of a qualitative abstraction of the underlying PWA dynamics. We prove
that this approximation obeys an asymptotic argument, so that it is indeed an admissible
approximation. Once we have found the most probable evolutions of the system, we apply
standard continuous filtering techniques (e.g. Kalman Filters), to obtain continuous state
estimates. Simulation results show that our approach concentrates computational resources
on most likely evolutions of the system and thus significantly speeds up the estimation
task while still maintaining sufficient estimation accuracy.
- Abstract
Piecewise affine (PWA) systems are an important hybrid modelling class for dynamical systems
which have an implicit interaction between the continuous state and their behaviorial mode.
This work introduces a novel hybrid estimation approach for PWA systems subject to
non-negligible state disturbance and measurement noise. In this case, the number of
possible evolutions of the system grows without bounds as time proceeds. Current estimation
approaches do not explicitly account for this and thus their application is restricted to
PWA systems with a fairly small number of modes. In order to make estimation also applicable
to systems with a large number of modes, our main idea is to put emphasis on most probable
evolutions of the system and reframe hybrid estimation as a discrete search problem. For this
purpose, we introduce a likelihood measure for mode transitions which can be efficiently
approximated by means of a qualitative abstraction of the underlying PWA dynamics. We prove
that this approximation obeys an asymptotic argument, so that it is indeed an admissible
approximation. Once we have found the most probable evolutions of the system, we apply
standard continuous filtering techniques (e.g. Kalman Filters), to obtain continuous state
estimates. Simulation results show that our approach concentrates computational resources
on most likely evolutions of the system and thus significantly speeds up the estimation
task while still maintaining sufficient estimation accuracy.
-
S. Richter, "
Probabilistic Hybrid State Estimation of Piecewise Affine Systems Through Qualitative Approximation,"
supervised by Prof. Manfred Morari and
Prof. Michael Hofbaur (UMIT), 2007.
Student Projects
These are student projects that I have been supervising/co-supervising during my Ph.D.:
- Master's Theses
-
"
FiOrdOs: A Matlab Toolbox for C-Code Generation for First Order Methods," Fabian Ullmann, 2011.
- Abstract
This master thesis deals with the development of a Matlab toolbox, called
FiOrdOs, that implements provably efficient first order optimization methods,
for instance, Nesterov's fast gradient method. The toolbox allows one
to generate tailored solver code for parametric convex quadratic programs
with a feasible set being the intersection of a simple set and an affine set.
From the optimization problem's description in Matlab, portable C code is
generated. This code can be used directly in C or also in Matlab through a
MEX-interface. For a subclass of problems, additional functionalities such
as optimal preconditioning and certification of the iteration count are
provided. As a first proof of concept, the toolbox was successfully used to
generate code for the trajectory tracking controller of a quadrotor.
- Abstract
This master thesis deals with the development of a Matlab toolbox, called
FiOrdOs, that implements provably efficient first order optimization methods,
for instance, Nesterov's fast gradient method. The toolbox allows one
to generate tailored solver code for parametric convex quadratic programs
with a feasible set being the intersection of a simple set and an affine set.
From the optimization problem's description in Matlab, portable C code is
generated. This code can be used directly in C or also in Matlab through a
MEX-interface. For a subclass of problems, additional functionalities such
as optimal preconditioning and certification of the iteration count are
provided. As a first proof of concept, the toolbox was successfully used to
generate code for the trajectory tracking controller of a quadrotor.
-
"
MPC Control of a Ball on Plate System: Theory and Implementation," René Waldvogel, 2010.
- Abstract
This thesis considers all the building blocks, from theory to practical implementation, required
to make a ball on plate system run. To achieve the goal of controlling and regulating the ball
on the plate, a cascaded control strategy is used. For the outer loop, being the ball system,
different controllers such as a PID, an LQR and an MPC controller that takes input
constraints into account are implemented. The main focus is on the state feedback controllers
though, for which we use a multi - rate extended Kalman Filter to estimate the states of
the ball. This is necessary since we can only detect the position of the ball by a Cognex
In - Sight 1050 vision system. The inner loop, being the motor/plate system, is controlled
by a PID controller with two degrees of freedom. To handle the signals of the sensors and to
implement the control strategies of the ball on plate system we use a B&R industrial
control unit from the X20 system range. As a supplement, a haptic interface is realized by
a DC motor and a rotary encoder of austriamicrosystems to allow humans to control the
system manually. The DC motor is thereby used to give feedback.
See the ball on plate in action:
- Abstract
This thesis considers all the building blocks, from theory to practical implementation, required
to make a ball on plate system run. To achieve the goal of controlling and regulating the ball
on the plate, a cascaded control strategy is used. For the outer loop, being the ball system,
different controllers such as a PID, an LQR and an MPC controller that takes input
constraints into account are implemented. The main focus is on the state feedback controllers
though, for which we use a multi - rate extended Kalman Filter to estimate the states of
the ball. This is necessary since we can only detect the position of the ball by a Cognex
In - Sight 1050 vision system. The inner loop, being the motor/plate system, is controlled
by a PID controller with two degrees of freedom. To handle the signals of the sensors and to
implement the control strategies of the ball on plate system we use a B&R industrial
control unit from the X20 system range. As a supplement, a haptic interface is realized by
a DC motor and a rotary encoder of austriamicrosystems to allow humans to control the
system manually. The DC motor is thereby used to give feedback.
-
"
FiOrdOs: A Matlab Toolbox for C-Code Generation for First Order Methods," Fabian Ullmann, 2011.
- Semester Theses
-
"
Integration of New Control Hardware for the Flexible Shaft Experiment,"
Paul Brunner, 2012.
- Abstract The Fachpraktikum experiment "Flexible Shaft II LQR" provides students a hands-on introduction to LQR control. The current setup should now be updated using industrial control hardware from B&R automation.
-
"
Control Design for the Traloc Serpentine Robot ,"
Tobias Bleiker, 2011 (co-supervised with Roy Smith).
- Abstract
This Semester Thesis addresses the design of an appropriate joint control for the Traloc
serpentine robot which was developed at the Autonomous Systems Lab at ETH Zurich.
The scope of this report covers the study of the mechanical system, the derivation of
its mathematical description and the design of different control concepts for the joint
actuation.
The understanding of the mechanical aspects such as the joint mechanism, the forces acting on the system and other mechanical effects, like backlash in the chain-drivers, is crucial for the development of a mathematical model. Afterwards, the main focus is laid on the derivation of a mathematical description which captures the dynamics of the system and the implementation of a corresponding simulation framework in Simulink. Taking all crucial forces and mechanical effects into account turned out to be the main challenge. Several tests were run on the robot in order to validate and improve the mathematical model. Based on the model, control concepts were finally addressed, discussed and compared where a hybrid controller showed the best performance.
The results and the gained insights of the Semester Thesis can be used to either further improve the control performance or to implement high level control algorithms for the Traloc snakelike robot.
Further information about this project can be found on the Traloc website.
See the robot moving (Videos taken from the Traloc website!):
- Abstract
This Semester Thesis addresses the design of an appropriate joint control for the Traloc
serpentine robot which was developed at the Autonomous Systems Lab at ETH Zurich.
The scope of this report covers the study of the mechanical system, the derivation of
its mathematical description and the design of different control concepts for the joint
actuation.
-
"
Control of an Autonomous Sailing Catamaran on the Concept of Hydrofoils,"
Pascal Gohl, Fadri Furrer, 2010.
- Abstract
The goal of the focus project Hyraii is the design, construction and autonomous control
of an unmanned
hydrofoil sailing catamaran. The boat was designed from the team last semester and will be
built by the team this semester. A mathematical model has been developed
last semester based on the boat design. Our goal is to develop the control of the hydrofoils,
rudder and sail as well as designing and building the actuator and sensor hardware with the team.
To master this goal we need to model the sensors and actuators and implement them.
Fast and smooth flight is achieved by selecting a robustly stabilizing controller for the
flaps of the hydrofoils. The different control algorithms have to be evaluated beforehand
and after the implementation we have to calibrate and test the system on the water.
The navigation of the boat has no primary role since the goal is to develop a fast sailing
boat on the concept of hydrofoils.
Further information about this project can be found on the Hyraii website.
See the boat flying:
- Abstract
The goal of the focus project Hyraii is the design, construction and autonomous control
of an unmanned
hydrofoil sailing catamaran. The boat was designed from the team last semester and will be
built by the team this semester. A mathematical model has been developed
last semester based on the boat design. Our goal is to develop the control of the hydrofoils,
rudder and sail as well as designing and building the actuator and sensor hardware with the team.
To master this goal we need to model the sensors and actuators and implement them.
Fast and smooth flight is achieved by selecting a robustly stabilizing controller for the
flaps of the hydrofoils. The different control algorithms have to be evaluated beforehand
and after the implementation we have to calibrate and test the system on the water.
The navigation of the boat has no primary role since the goal is to develop a fast sailing
boat on the concept of hydrofoils.
-
"
Robustness Analysis for Hybrid Control of a Mechanical System with Backlash,"
Kimberly Chung, 2008 (co-supervised with Thomas Besselmann).
- Abstract
The goal of this semester thesis was to solve robustness problems previously en-
countered during a study in Model Predictive Control (MPC) of a mechanical system
with backlash conducted at the Automatic Control Laboratory of ETH Zurich.
Control strategies were developed to mitigate the effects of backlash such as control
performance degradation and reduced life of mechanical components due to wearing.
Previous studies involved speed control of a rotary system consisting of a drive shaft
and a load shaft with a backlash element between the two. Linear and hybrid MPC
controllers were designed to control the speed of the load shaft under constraints.
The controllers were tested on a testbed where the hybrid MPC controller exhibited
unrobust behavior. A detailed review of the modeling and implementation procedures
revealed that the unrobust behavior was due to an incorrect implementation strategy.
This paper further describes the results obtained from an investigation of a hybrid
MPC controller without constraints.
- Abstract
The goal of this semester thesis was to solve robustness problems previously en-
countered during a study in Model Predictive Control (MPC) of a mechanical system
with backlash conducted at the Automatic Control Laboratory of ETH Zurich.
Control strategies were developed to mitigate the effects of backlash such as control
performance degradation and reduced life of mechanical components due to wearing.
Previous studies involved speed control of a rotary system consisting of a drive shaft
and a load shaft with a backlash element between the two. Linear and hybrid MPC
controllers were designed to control the speed of the load shaft under constraints.
The controllers were tested on a testbed where the hybrid MPC controller exhibited
unrobust behavior. A detailed review of the modeling and implementation procedures
revealed that the unrobust behavior was due to an incorrect implementation strategy.
This paper further describes the results obtained from an investigation of a hybrid
MPC controller without constraints.
-
"
Hybrid Estimation for a Mechanical System with Backlash,"
Thomas Loser, 2007 (co-supervised with Thomas Besselmann).
- Abstract
Backlash is a common problem in mechanical systems. It can cause control
performance degradation and decrease the life expectancy of the mechanical
components. Therefore a benchmark system consisting of a flexible shaft
with backlash has been developed at the ETH Zurich. It is used to test and
develop hybrid models and control strategies. Recent work contains the
identification of this benchmark system, the implementation of a controller
as well as the design of a state observer. However, experimental data has
returned unsatisfactory results and led to the assumption that the model
is not accurate enough. More precisely, one believed that the poor
performance was due to an offset between the motor and load sensors.
Therefore the observer has been extended by one state taking into
account this offset. In this semester thesis, the influence of the
observer extension on control performance is investigated in
simulations.
- Abstract
Backlash is a common problem in mechanical systems. It can cause control
performance degradation and decrease the life expectancy of the mechanical
components. Therefore a benchmark system consisting of a flexible shaft
with backlash has been developed at the ETH Zurich. It is used to test and
develop hybrid models and control strategies. Recent work contains the
identification of this benchmark system, the implementation of a controller
as well as the design of a state observer. However, experimental data has
returned unsatisfactory results and led to the assumption that the model
is not accurate enough. More precisely, one believed that the poor
performance was due to an offset between the motor and load sensors.
Therefore the observer has been extended by one state taking into
account this offset. In this semester thesis, the influence of the
observer extension on control performance is investigated in
simulations.
-
"
Integration of New Control Hardware for the Flexible Shaft Experiment,"
Paul Brunner, 2012.
- Other Student Projects
-
"
Ball on Plate Demo,"
Christian Saner, Thomas Willi, 2011 (co-supervised with Aldo Zgraggen).
- Abstract The goal of this project is to develop a graphical user interface on a mobile control panel for an easy and intuitive operation of the ball on plate system. Additionally, a basic game should be developed so that users can challenge the automatic controller. This will allow one to use the ball on plate system for demos.
-
"
New Control Hardware for the Speed Control Experiment,"
Tobias Grämer, 2009.
- Abstract
The aim of the project is to implement industrial control hardware of B&R on the
speed control experiment in the student's lab ("Fachpraktikum"). Also, a graphical user interface
should be programmed such that students can operate the experiment intuitively.
Further information about this project can be found on the Fachpraktikum website.
- Abstract
The aim of the project is to implement industrial control hardware of B&R on the
speed control experiment in the student's lab ("Fachpraktikum"). Also, a graphical user interface
should be programmed such that students can operate the experiment intuitively.
-
"
New Control Hardware for the 2DOF Lead-Lag Helicopter,"
Marc Osswald, 2009.
- Abstract
The aim of the project is to implement industrial control hardware of B&R on the
2DOF Helicopter experiment in the student's lab ("Fachpraktikum"). Also, a graphical user interface
should be programmed such that students can operate the experiment intuitively.
Further information about this project can be found on the Fachpraktikum website.
- Abstract
The aim of the project is to implement industrial control hardware of B&R on the
2DOF Helicopter experiment in the student's lab ("Fachpraktikum"). Also, a graphical user interface
should be programmed such that students can operate the experiment intuitively.
-
"
Ball on Plate Demo,"
Christian Saner, Thomas Willi, 2011 (co-supervised with Aldo Zgraggen).
Last update: 22/12/2011