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Robust memory state feedback model predictive control for discrete-time uncertain state delayed systems. (English) Zbl 1194.93071

Summary: We propose a memory state feedback Model Predictive Control (MPC) law for a discrete-time uncertain state delayed system with input constraints. The model uncertainty is assumed to be polytopic, and the delay is assumed to be unknown, but with a known upper bound. We derive a sufficient condition for cost monotonicity in terms of Linear Matrix Inequality (LMI), which can be easily solved by an efficient convex optimization algorithm. A delayed state dependent quadratic function with an estimated delay index is considered for incorporating MPC problem formulation. The MPC problem is formulated to minimize the upper bound of infinite horizon cost that satisfies the sufficient condition. Therefore, a less conservative sufficient condition in terms of LMI can be derived to design a more robust MPC algorithm. A numerical example is included to illustrate the effectiveness of the proposed method.

MSC:

93B52 Feedback control
93B40 Computational methods in systems theory (MSC2010)
93C55 Discrete-time control/observation systems
93C41 Control/observation systems with incomplete information
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