Rubagotti, Matteo and Trimboli, Sergio and Bernardini, Daniele and Bemporad, Alberto Stability and invariance analysis of approximate explicit MPC based on PWA Lyapunov functions. In: Proceedings of the 18th IFAC World Congress. IFAC. ISBN 978-3-902661-93-7 (2011)Full text not available from this repository.
For piecewise affine (PWA) systems whose dynamics are only defined in a bounded and possibly non-invariant set X, this paper proposes a numerical approach to analyze the stability of the origin and to find a region of attraction. The approach relies on introducing fake dynamics outside X and on synthesizing a piecewise affine and possibly discontinuous Lyapunov function on a larger bounded set containing X by solving a linear program. The existence of a solution proves that the origin is an asymptotically stable equilibrium of the original PWA system and determines a region of attraction contained in X. The procedure is particularly useful in practical applications for analyzing a posteriori the stability properties of approximate explicit model predictive control laws defined over a bounded set X of states, and to determine whether, for a given set of initial states, the closed-loop system evolves within the domain X where the control law is defined.
|Item Type:||Book Section|
|Uncontrolled Keywords:||Hybrid systems stability|
|Subjects:||Q Science > QA Mathematics
T Technology > TJ Mechanical engineering and machinery
|Research Area:||Computer Science and Applications|
|Depositing User:||Users 37 not found.|
|Date Deposited:||29 Jul 2011 10:52|
|Last Modified:||30 Sep 2013 12:29|
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