An Algorithm for the Computation of Polyhedral Invariant Sets for Closed-Loop Linear MPC Systems

نویسندگان

  • A. Alessio
  • A. Bemporad
  • M. Lazar
  • W.P.M.H. Heemels
چکیده

Given an asymptotically stabilizing linear MPC controller, this paper proposes an algorithm to construct invariant polyhedral sets for the closed-loop system. The approach exploits a recently developed DC (Difference of Convex functions) programming technique developed by the authors to construct a polyhedral set in between two convex sets. Here, the inner convex set is any given level set V (x) = γ of the MPC value function, while the outer convex set is the level set of a the value function of a modified multiparametric quadratic program. The level gamma acts as a tuning knob for deciding the size of the polyhedral invariant containing the inner set, ranging from the origin (γ = 0) to the maximum invariant set around the origin where the unconstrained MPC solution remains feasible, up to the feasibility domain (possibly the whole state space Rn) provided by the multiparametric QP solver (γ = inf). Potential applications of the technique include reachability analysis of MPC systems and generation of constraints to supervisory decision algorithms on top of MPC loops. During the interactive session the numerical behavior of the proposed algorithm in Matlab will be demonstrated, based on a software implementation on top of the Hybrid Toolbox for MPC setup, simulation, and multiparametric programming solutions.

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تاریخ انتشار 2006