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After defending my PhD thesis in January 2016 I have joined the inspire IfA group part-time as a postdoctoral researcher. Additionally, I joined embotech to make optimization the most pervasive decision making technology out there.

Please contact me at hempel@embotech.ch if you have questions about how optimization methods can transform your approach to autonomous decision making, help make your business more efficient, and provide ideal solutions for your products and customers. I am also happy to discuss the individual merits of embotech's products: FORCES Pro for generation of efficient, embeddable solvers for structured decision problems or ECOS for solving general optimization problems on any platform.

Research Interests

All things optimization

I am interested in optimization in its various forms. Topics of particular interest include (but are not limited to)

  • large-scale convex optimization algorithms for conic optimization problems (LP, SOCP, SDP),
  • the inverse parametric programming problem, i.e. can we construct an optimization problem that has a particular solution,
  • remodelling constraints to move an optimization problem from one problem class to another,
  • bilevel optimization problems,
  • mathematical programs with equilibrium / complementarity constraints.

Related Publications
  • A.B. Hempel, P.J. Goulart, J. Lygeros, "A Necessary Optimality Condition for Constrained Optimal Control of Hybrid Systems", Proceedings of the IEEE Conference on Decision and Control (CDC) 2015, Osaka, Japan.
    • Abstract: Using the fact that continuous piecewise affine systems can be written as special inverse optimization models, we present necessary optimality conditions for constrained optimal control problems for hybrid dynamical systems. The modeling approach is based on the fact that piecewise affine functions can be written as the difference of two convex functions and has been described in previous publications. The inverse optimization model resulting from this approach can be replaced by its Karush-Kuhn-Tucker conditions to yield a linear complementarity model. An optimal control problem for this model class is an instance of a mathematical program with complementarity constraints for which classical Karush-Kuhn-Tucker optimality conditions may not hold. Exploiting the regularity properties of the inverse optimization model, we show why for the class of control problems under consideration this is not the case and the classical optimality conditions also characterize optimal input trajectories.
  • A.B. Hempel, P.J. Goulart, J. Lygeros, "Strong Stationarity Conditions for Optimal Control of Hybrid Systems", arXiv:1507.02878.
    • Abstract:

      We present necessary and sufficient optimality conditions for finite time optimal control problems for a class of hybrid systems described by linear complementarity models. Although these optimal control problems are difficult in general due to the presence of complementarity constraints, we provide a set of structural assumptions ensuring that the tangent cone of the constraints possesses geometric regularity properties. These imply that the classical Karush-Kuhn-Tucker conditions of nonlinear programming theory are both necessary and sufficient for local optimality, which is not the case for general mathematical programs with complementarity constraints. We also present sufficient conditions for global optimality.

      We proceed to show that every continuous piecewise affine system can be written as an optimizing process which results in a linear complementarity model satisfying our structural assumptions. Hence, our stationarity results apply to a large class of hybrid systems with piecewise affine dynamics. We present simulation results illustrating the potentially substantial benefits possible from using a nonlinear programming approach to the optimal control problem with complementarity constraints instead of a more traditional mixed-integer formulation.


  • A.B. Hempel, P.J. Goulart, J. Lygeros, "Inverse Parametric Optimization with an Application to Hybrid System Control", IEEE Transactions on Automatic Control, vol. 60, no.4, pp. 1064-1069, April 2015, available on Optimization Online.
    • Abstract: We present a number of results on inverse parametric optimization and its application to hybrid system control. We show that any function that can be written as the difference of two convex functions can also be written as a linear mapping of the solution to a convex parametric optimization problem. We exploit these results in application to the control of systems with piecewise affine dynamics, and show that it is possible to model such systems as optimizing processes. Optimal control problems for such systems can be remodeled as bilevel optimization problems and solved with existing techniques.
  • A.B. Hempel, P.J. Goulart, "A novel method for modelling cardinality and rank constraints", Proceedings of the IEEE Conference on Decision and Control (CDC) 2014, Los Angeles, USA, pp. 4322-4327.
    • Abstract: Constraints on the cardinality or rank of decision variables in optimization problems are generally modelled separately from algebraic constraints. In this paper we show that cardinality constraints on vectors and rank constraints on matrices can be represented using purely algebraic constraints on continuous variables, by exploiting classical results on the Ky Fan norm for matrices and its analogous norm for vectors. Using this technique, a vector cardinality constraint can be modelled via introduction of a small number of additional variables and linear constraints, in conjunction with a single bilinear inequality. Analogously, a matrix rank constraint can be modelled via introduction of additional matrix variables and linear matrix inequalities, in conjunction with a single bilinear matrix inequality. We discuss a number of variations on cardinality and rank constraints that can be modelled in a similar way.
  • A.B. Hempel, P.J. Goulart, J. Lygeros, "Every continuous piecewise affine function can be obtained by solving a parametric linear program", Proceedings of the 13th European Control Conference, Zurich, Switzerland, 2013, pp. 2657-2662.
    • Abstract: It is well-known that solutions to parametric linear or quadratic programs are continuous piecewise affine functions of the parameter. In this paper we prove the converse, i.e. that every continuous piecewise affine function can be identified with the solution to a parametric linear program. In particular, we provide a constructive proof that every piecewise affine function can be expressed as the linear mapping of the solution to a parametric linear program with at most twice as many variables as the dimension of the domain of the piecewise affine function. Our method is illustrated via two small numerical examples.
  • A.B. Hempel, P.J. Goulart, J. Lygeros, "Inverse Parametric Quadratic Programming and an Application to Hybrid Control", Nonlinear Model Predictive Control Conference, Noordwijkerhout, The Netherlands, 2012, pp. 68-73.
    • Abstract: We present the complete solution to the inverse parametric quadratic programming problem: from a given continuous piecewise affine function we construct both the constraints and objective function of a parametric quadratic program, such that the supplied function is the unique parametric minimizer for the constructed problem data. In contrast to past approaches to this problem, our method does not rely on prior knowledge of the constraint set or sufficient sampling of the optimizer function, and is guaranteed to solve the inverse optimization problem exactly if a solution exists. We then apply this inverse optimization technique to the control of piecewise affine systems. By recasting the hybrid system dynamics as the parametric solution to a quadratic program obtained from our inverse optimization technique, we derive an equivalent linear complementarity model via the Karush-Kuhn-Tucker conditions of the identified optimization problem. This approach allows one to solve an optimal control problem for a piecewise affine system by solving a mathematical program with equilibrium constraints. Simulation results suggest that the computational effort required to solve such problems can be significantly smaller than that required for conventional mixed-integer quadratic programming approaches for systems with piecewise affine dynamics. We demonstrate via two numerical examples that globally optimal points can be identified using this approach.

Control Systems

I am interested in control systems and theory, in particular in the context of optimization theory. Some topics I am particularly interested in are

  • hybrid system models, particularly piecewise affine discrete-time models,
  • remodelling dynamical systems in terms of optimizing processes,
  • optimal and model predictive control of linear, nonlinear, and hybrid systems.

Related Publications
  • A.B. Hempel, P.J. Goulart, J. Lygeros, "A Necessary Optimality Condition for Constrained Optimal Control of Hybrid Systems", Proceedings of the IEEE Conference on Decision and Control (CDC) 2015, Osaka, Japan.
    • Abstract: Using the fact that continuous piecewise affine systems can be written as special inverse optimization models, we present necessary optimality conditions for constrained optimal control problems for hybrid dynamical systems. The modeling approach is based on the fact that piecewise affine functions can be written as the difference of two convex functions and has been described in previous publications. The inverse optimization model resulting from this approach can be replaced by its Karush-Kuhn-Tucker conditions to yield a linear complementarity model. An optimal control problem for this model class is an instance of a mathematical program with complementarity constraints for which classical Karush-Kuhn-Tucker optimality conditions may not hold. Exploiting the regularity properties of the inverse optimization model, we show why for the class of control problems under consideration this is not the case and the classical optimality conditions also characterize optimal input trajectories.
  • A.B. Hempel, P.J. Goulart, J. Lygeros, "Strong Stationarity Conditions for Optimal Control of Hybrid Systems", arXiv:1507.02878.
    • Abstract:

      We present necessary and sufficient optimality conditions for finite time optimal control problems for a class of hybrid systems described by linear complementarity models. Although these optimal control problems are difficult in general due to the presence of complementarity constraints, we provide a set of structural assumptions ensuring that the tangent cone of the constraints possesses geometric regularity properties. These imply that the classical Karush-Kuhn-Tucker conditions of nonlinear programming theory are both necessary and sufficient for local optimality, which is not the case for general mathematical programs with complementarity constraints. We also present sufficient conditions for global optimality.

      We proceed to show that every continuous piecewise affine system can be written as an optimizing process which results in a linear complementarity model satisfying our structural assumptions. Hence, our stationarity results apply to a large class of hybrid systems with piecewise affine dynamics. We present simulation results illustrating the potentially substantial benefits possible from using a nonlinear programming approach to the optimal control problem with complementarity constraints instead of a more traditional mixed-integer formulation.


  • A. Filieri, M. Maggio, K. Angelopoulos, N. D’Ippolito, I. Gerostathopoulos, A.B. Hempel, H. Hoffmann, P. Jamshidi, E. Kalyvianaki, C. Klein, F. Krikava, S. Misailovic, A.V. Papadopoulos, S. Ray, A.M. Sharifloo, S. Shevtsov, M. Ujma, T. Vogel, "Software Engineering Meets Control Theory", Proceedings of 10th International Symposium on Software Engineering for Adaptive and Self-Managing Systems, May 2015, Firenze, Italy.
    • Abstract:

      The software engineering community has proposed numerous approaches for making software self-adaptive. These approaches take inspiration from machine learning and control theory, constructing software that monitors and modifies its own behavior to meet goals. Control theory, in particular, has received considerable attention as it represents a general methodology for creating adaptive systems. Control-theoretical software implementations, however, tend to be ad hoc. While such solutions often work in practice, it is difficult to understand and reason about the desired properties and behavior of the resulting adaptive software and its controller.

      This paper discusses a control design process for software systems which enables automatic analysis and synthesis of a controller that is guaranteed to have the desired properties and behavior. The paper documents the process and illustrates its use in an example that walks through all necessary steps for self-adaptive controller synthesis.


  • M. Colombino, A.B. Hempel, R. Smith, "Robust Stability of a Class of Interconnected Nonlinear Positive Systems", Proceedings of the American Control Conference, Chicago, USA, 2015.
    • Abstract: We present conditions for robust stability of a class of linear systems interconnected by uncertain nonlinear, norm-bounded functions. We show that such conditions can be reformulated as classical small gain like conditions for a related linear system. Under further assumptions that render such related linear system positive, we show that we can achieve sharp tractable conditions for robust stability of the original nonlinear system.
  • A.B. Hempel, P.J. Goulart, J. Lygeros, "Inverse Parametric Optimization with an Application to Hybrid System Control", IEEE Transactions on Automatic Control, vol. 60, no.4, pp. 1064-1069, April 2015, available on Optimization Online.
    • Abstract: We present a number of results on inverse parametric optimization and its application to hybrid system control. We show that any function that can be written as the difference of two convex functions can also be written as a linear mapping of the solution to a convex parametric optimization problem. We exploit these results in application to the control of systems with piecewise affine dynamics, and show that it is possible to model such systems as optimizing processes. Optimal control problems for such systems can be remodeled as bilevel optimization problems and solved with existing techniques.
  • D. Bohl, N. Kariotoglou, A.B. Hempel, P.J. Goulart, J. Lygeros, "Model-based current limiting for traction control of an electric four-wheel drive race car", Proceedings of the 14th European Control Conference, Strasbourg, France, 2014, pp. 1981-1986.
    • Abstract: This paper describes a novel traction control method and its application to an electric four-wheel driven race car. The proposed control method is based on a detailed model of tire dynamics and is designed for hardware with limited memory and computational power. We derive a linear parameter-varying model from first principles and validate it against a full nonlinear vehicle model. We then use the model to design a gain-scheduled LQRI controller, parametric on the measured vehicle velocity and lateral acceleration. We show that when incorporating additional information about the tire state, a gain scheduled LQRI controller is capable of minimizing excessive wheel spin by limiting the maximum torque available to the driver. This leads to a performance gain in acceleration while improving the handling characteristics of the race car. The proposed controller is thoroughly tested for its sensitivity to sensor noise and changes in system parameters in simulation and then implemented on a prototype race car competing in Formula Student. Experiments indicate satisfactory experimental performance from the initial control design without additional tuning of the controller parameters. This illustrates the simplicity of the design and ease of implementation.
  • A.B. Hempel, P.J. Goulart, J. Lygeros, "Inverse Parametric Quadratic Programming and an Application to Hybrid Control", Nonlinear Model Predictive Control Conference, Noordwijkerhout, The Netherlands, 2012, pp. 68-73.
    • Abstract: We present the complete solution to the inverse parametric quadratic programming problem: from a given continuous piecewise affine function we construct both the constraints and objective function of a parametric quadratic program, such that the supplied function is the unique parametric minimizer for the constructed problem data. In contrast to past approaches to this problem, our method does not rely on prior knowledge of the constraint set or sufficient sampling of the optimizer function, and is guaranteed to solve the inverse optimization problem exactly if a solution exists. We then apply this inverse optimization technique to the control of piecewise affine systems. By recasting the hybrid system dynamics as the parametric solution to a quadratic program obtained from our inverse optimization technique, we derive an equivalent linear complementarity model via the Karush-Kuhn-Tucker conditions of the identified optimization problem. This approach allows one to solve an optimal control problem for a piecewise affine system by solving a mathematical program with equilibrium constraints. Simulation results suggest that the computational effort required to solve such problems can be significantly smaller than that required for conventional mixed-integer quadratic programming approaches for systems with piecewise affine dynamics. We demonstrate via two numerical examples that globally optimal points can be identified using this approach.
  • A.B. Hempel, A.B. Kominek, H. Werner, "Output-Feedback Controlled-Invariant Sets for Systems with Linear Parameter-Varying State Transition Matrix", Proceedings of the joint IEEE Conference on Decision and Control and European Control Conference, Orlando, USA, 2011, pp. 3422-3427.
    • Abstract: The notion of output-feedback controlled-invariant sets is extended from LTI systems to systems with linear parameter-varying state transition matrix. A theorem is presented that can be used to verify whether a given polytope can be made invariant under output-feedback. The theorem also provides the constraints a control input has to fulfill to make the candidate set invariant. Predictive output-feedback controllers based on such a set can satisfy hard constraints on both the plant state and the control inputs in the presence of process disturbances and measurement noise. Simulation results demonstrate the strength of such a controller that can guarantee constraints for a subset of the state space without requiring state information or estimation.

Personal Information

Education

  • PhD student in the Automatic Control Laboratory at ETH Zurich since 2011
  • Master of Science in Mechatronics from Hamburg University of Technology, 2010
  • Master of Business Administraion in Technology Management from Northern Institute of Technology, Hamburg, 2009
  • Bachelor of Science in General Engineering Science (Systems Egnineering) from Hamburg University of Technology, 2007
  • Abitur (high-school diploma) from Gymnasium Othmarschen, Hamburg, 2003

Work "experience"

  • Extended employments with Microsoft (development of intranet tools and server administration) and SterniPark Hamburg e.V. (civil service in childcare)
  • Several employments in university level education (TA for Mathematics and Electrical Engineering classes, RA for a textbook publication)
  • Internships with Rolls-Royce (Oberursel, Germany) and Airbus (Hamburg, Germany)
Obligatory links to my publications, talks, and open student projects:

Design inspired by Stefan Richter. Last update: 04/06/2015