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Constrained Robust Model Predictive Control Based on Polyhedral Invariant Sets by Off-line Optimization

This paper proposes a fast robust model predictive control using polyhedral invariant sets for uncertain polytopic discrete-time systems. A sequence of nested polyhedral invariant sets corresponding to a sequence of state feedback gains is constructed off-line. Thus, most of the computational burdens are moved off-line. At each sampling time, when the measured state lies between two adjacent polyhedral invariant sets, a state feedback gain is calculated by solving a linear programming based on linear interpolation between two pre-computed state feedback gains. The controller design is illustrated with an example. The simulation results showed that the proposed algorithm provides a better control performance while on-line computation is still tractable as compared to previously reported algorithms.