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Article Dans Une Revue Modeling, Identification and Control Année : 2010

Piecewise quadratic Lyapunov functions for stability verification of approximate explicit MPC

Morten Hovd
  • Fonction : Auteur
Sorin Olaru

Résumé

Explicit MPC of constrained linear systems is known to result in a piecewise affine controller and therefore also piecewise affine closed loop dynamics. The complexity of such analytic formulations of the control law can grow exponentially with the prediction horizon. The suboptimal solutions offer a trade-off in terms of complexity and several approaches can be found in the literature for the construction of approximate MPC laws. In the present paper a piecewise quadratic (PWQ) Lyapunov function is used for the stability verification of an of approximate explicit Model Predictive Control (MPC). A novel relaxation method is proposed for the LMI criteria on the Lyapunov function design. This relaxation is applicable to the design of PWQ Lyapunov functions for discrete-time piecewise affine systems in general.

Dates et versions

hal-00524537 , version 1 (08-10-2010)

Identifiants

Citer

Morten Hovd, Sorin Olaru. Piecewise quadratic Lyapunov functions for stability verification of approximate explicit MPC. Modeling, Identification and Control, 2010, 31 (2), pp.45-53. ⟨10.4173/mic.2010.2.1⟩. ⟨hal-00524537⟩
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