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On input-to-state stability of min-max nonlinear model predictive control. (English) Zbl 1129.93433

Summary: We consider discrete-time nonlinear systems that are affected, possibly simultaneously, by parametric uncertainties and other disturbance inputs. The min-max model predictive control (MPC) methodology is employed to obtain a controller that robustly steers the state of the system towards a desired equilibrium. The aim is to provide a priori sufficient conditions for robust stability of the resulting closed-loop system using the input-to-state stability (ISS) framework. First, we show that only input-to-state practical stability can be ensured in general for closed-loop min-max MPC systems; and we provide explicit bounds on the evolution of the closed-loop system state. Then, we derive new conditions for guaranteeing ISS of min-max MPC closed-loop systems, using a dual-mode approach. An example illustrates the presented theory.

MSC:

93C55 Discrete-time control/observation systems
93C10 Nonlinear systems in control theory
93C41 Control/observation systems with incomplete information
93D25 Input-output approaches in control theory
93D09 Robust stability
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