Stabilizing low complexity feedback control of constrained piecewise affine systems

Piecewise affine (PWA) systems are powerful models for describing both non-linear and hybrid systems. One of the key problems in controlling these systems is the inherent computational complexity of controller synthesis and analysis, especially if constraints on states and inputs are present. In add...

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Bibliographic Details
Published in:Automatica (Oxford) 2005-10, Vol.41 (10), p.1683-1694
Main Authors: Grieder, Pascal, Kvasnica, Michal, Baotić, Mato, Morari, Manfred
Format: Article
Language:English
Subjects:
Applied sciences
Computer science
control theory
systems
Control system analysis
Control system synthesis
Control theory. Systems
Exact sciences and technology
Model predictive control
Multi-parametric programming
Optimal control
Piecewise affine system
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Summary:Piecewise affine (PWA) systems are powerful models for describing both non-linear and hybrid systems. One of the key problems in controlling these systems is the inherent computational complexity of controller synthesis and analysis, especially if constraints on states and inputs are present. In addition, few results are available which address the issue of computing stabilizing controllers for PWA systems without placing constraints on the location of the origin. This paper first introduces a method to obtain stability guarantees for receding horizon control of discrete-time PWA systems. Based on this result, two algorithms which provide low complexity state feedback controllers are introduced. Specifically, we demonstrate how multi-parametric programming can be used to obtain minimum-time controllers, i.e., controllers which drive the state into a pre-specified target set in minimum time. In a second segment, we show how controllers of even lower complexity can be obtained by separately dealing with constraint satisfaction and stability properties. To this end, we introduce a method to compute PWA Lyapunov functions for discrete-time PWA systems via linear programming. Finally, we report results of an extensive case study which justify our claims of complexity reduction.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2005.04.016