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Efficient software tools for control and analysis of hybrid systems


M. Kvasnica

no. 17662

This thesis deals with the topic of control and analysis of constrained dynamical systems.

Specifically, we consider the class of hybrid dynamical systems, i.e. systems which combine continuous dynamics with discrete logic. Such systems can efficiently describe the dynamical behavior of systems with on/off switches, gear shifts, or can be used to approximate nonlinearities by utilizing the concept of multiple linearizations.

It is well known that the task of deriving stabilizing controllers for dynamical systems subject to constraints on states and inputs can be attacked by utilizing the concept of Receding Horizon Control (RHC). In RHC, the sequence of manipulated variables is obtained by optimizing a given performance function subject to specified constraints. Subsequently, only the first input of that sequence is applied to the system. At the next time step, the state is measured again and the procedure is repeated. However, the computational complexity involved in solving each optimization problem significantly limits the minimal admissible sampling rate at which RHC can be applied on-line.

This problem has been alleviated to some degree by the recent introduction of multi-parametric programming to control theory. In this approach the given RHC optimization problem is solved off-line for all admissible initial conditions which satisfy system constraints. By solving the problem in a parametric fashion, the solution can be shown to take the form of a look-up table, which describes a piecewise affine state feedback law defined over a polyhedral partition. The on-line implementation of such feedback laws then reduces to a simple set-membership set, which can be performed very efficiently on-line, thus allowing to apply the concept of RHC to processes with fast dynamics. The main drawback of the multi-parametric technique, however, is the growing complexity of the look-up table as the problem size increases. One of the aims of this thesis is therefore to mitigate this problem.

Specifically, various schemes to speed up the calculation of the parametric solutions to RHC problems are presented in this thesis. A combination of reachability-based methods along with efficient polytope reduction techniques yields new computation algorithms which are substantially faster than other known schemes. Moreover, new algorithms are given which serve to speed up the task of finding a correct entry in the look-up table on-line.

Large part of this thesis is devoted to a description of the Multi-Parametric Toolbox (MPT), which is a novel software tool for modeling, control, and analysis of constrained dynamical systems. The main strong point of MPT is that it simplifies and automates many tasks a control engineer has to go through when designing and validating optimal control laws based on the RHC principle. The toolbox offers a broad spectrum of algorithms compiled in a user friendly and accessible format starting from different performance objectives (linear, quadratic, minimum-time) to the handling of systems with persistent additive and polytopic uncertainties. Users can add custom constraints, such as polytopic, contraction or collision avoidance constraints, or create custom objective functions. Resulting optimal control laws can either be embedded into target applications in the form of the C code, or deployed to control platforms using the Real Time Workshop.

The MPT toolbox contains all of the algorithms presented in this thesis as well as a wide range of additional algorithms and tools developed by the academic community.


Type of Publication:

(03)Ph.D. Thesis

M. Morari

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% Autogenerated BibTeX entry
@PhDThesis { Xxx:2008:IFA_3046,
    author={M. Kvasnica},
    title={{Efficient software tools for control and analysis of hybrid
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