Abstract
For a linear performance index the solution to the CFTOC problem is a time-varying piecewise affine function of the state. However, when a receding horizon control strategy is used, stability and/or feasibility for all time of the closed-loop system is not guaranteed a priori. In this chapter an algorithm is presented that by analyzing the CFTOC solution a posteriori extracts regions of the state space for which closed-loop stability and feasibility for all time can be guaranteed. The algorithm computes the maximal positively invariant set and stability region of a piecewise affine system by combining reachability analysis with some basic polyhedral manipulation. The simplicity of the overall computation stems from the fact that in all steps of the algorithm only linear programs need to be solved.
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© 2007 Springer-Verlag Berlin Heidelberg
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(2007). Stability Analysis. In: Optimal Control of Constrained Piecewise Affine Systems. Lecture Notes in Control and Information Sciences, vol 359. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72701-9_9
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DOI: https://doi.org/10.1007/978-3-540-72701-9_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72700-2
Online ISBN: 978-3-540-72701-9
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