TY - GEN

T1 - Stability and invariance analysis of approximate explicit MPC based on PWA Lyapunov functions

AU - Rubagotti, Matteo

AU - Trimboli, Sergio

AU - Bernardini, Daniele

AU - Bemporad, Alberto

N1 - Funding Information:
★This work was partially supported by the European Commission under project FP7-INFSO-ICT-248858 “MOBY-DIC – Model-based synthesis of digital electronic circuits for embedded control”.

PY - 2011/1/1

Y1 - 2011/1/1

N2 - For piecewise affine (PWA) systems whose dynamics are only defined in a bounded and possibly non-invariant set χ, 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 χ and on synthesizing a piecewise affine and possibly discontinuous Lyapunov function on a larger bounded set containing χ 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 χ. 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 χ 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.

AB - For piecewise affine (PWA) systems whose dynamics are only defined in a bounded and possibly non-invariant set χ, 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 χ and on synthesizing a piecewise affine and possibly discontinuous Lyapunov function on a larger bounded set containing χ 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 χ. 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 χ 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.

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U2 - 10.3182/20110828-6-IT-1002.00539

DO - 10.3182/20110828-6-IT-1002.00539

M3 - Conference contribution

AN - SCOPUS:84866749126

SN - 9783902661937

VL - 44

T3 - IFAC Proceedings Volumes (IFAC-PapersOnline)

SP - 5712

EP - 5717

BT - Proceedings of the 18th IFAC World Congress

PB - IFAC Secretariat

ER -