Input‐to‐state stability of min‐max MPC scheme for nonlinear time‐varying delay systems

This paper studies the robustness problem of the min–max model predictive control (MPC) scheme for constrained nonlinear time-varying delay systems subject to bounded disturbances. The notion of the input-to-state stability (ISS) of nonlinear time-delay systems is introduced. Then by using the Lyapunov–Krasovskii method, a delay-dependent sufficient condition is derived to guarantee input-to-state practical stability (ISpS) of the closed-loop system by way of nonlinear matrix inequalities (NLMI). In order to lessen the online computational demand, the non-convex min-max optimization problem is then converted to a minimization problem with linear matrix inequality (LMI) constraints and a suboptimal MPC algorithm is provided. Finally, an example of a truck-trailer is used to illustrate the effectiveness of the proposed results. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

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