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Performance Analysis of Piecewise Linear Systems and Model Predictive Control Systems


A. Bemporad, F.D. Torrisi, M. Morari

vol. AUT00-14

In their recent paper, Bemporad et al. provided a tool for obtaining the explicit solution of constrained model predictive control (MPC) problems by showing that the control law is a continuous piecewise affine (PWA) function of the state vector. Therefore, the feedback interconnection between the MPC controller and a linear system, or a PWA system (e.g., a PWA approximation of a nonlinear system), is a PWA system. For discrete-time PWA and hybrid systems, Bemporad and Torrisi presented an algorithm for verification/reachability analysis. In this paper, we formulate the performance analysis problem of closed-loop PWA systems (including MPC feedback loops where the prediction model and the plant model could be different) as a reachability analysis problem, and use the verification algorithm to obtain a tool for characterizing (i) the set of states for which the evolution is feasible, (ii) the domain of stability, (iii) the performance of the closed-loop.

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% Autogenerated BibTeX entry
@TechReport { BemTor:2000:IFA_37,
    author={A. Bemporad and F.D. Torrisi and M. Morari},
    title={{Performance Analysis of Piecewise Linear Systems and Model
	  Predictive Control Systems}},
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