Constrained control of uncertain linear time-invariant systems: an interpolation based approach

In this talk, a novel approach to control uncertain discrete-time linear time-invariant systems with polytopic state and control constraints is proposed. The main idea is to use interpolation. The control law has an implicit and explicit form. In the implicit form, at each time instant, at most two linear programming problems are solved on-line. In the explicit form, the control law is given as a piece-wise affine and continuous function of the state. The design method can be seen as a computationally favorable alternative to optimization-based control schemes such as Model Predictive Control. Proofs of recursive feasibility and asymptotic stability are given. Several simulations demonstrate the performance, also in comparison with MPC. Extensions include output feedback, LPV and time-varying systems, and ellipsoidal constraint sets. Some problems with the new approach are pointed out, and simplifying solutions suggested. Main reference: Hoai-Nam Nguyen, Constrained control of uncertain, time-varying systems: an interpolation based approach, Springer Lecture Notes in Control and Information Sciences, 2014.