Towards Non-conservative Robust Control of Constrained Dynamic Systems

This work is concerned with robust stabilization and robust invariance of constrained uncertain systems that are represented by Linear Difference Inclusions (LDI). Novel frameworks for obtaining robust static Linear Time Invariant (LTI) controllers, periodic interpolating controllers, Model Predictive Controllers (MPC), and (periodic) invariant sets are introduced. The aim of the proposed methods is to obtain controllers that provide an enlarged feasible domain while maintaining an acceptable online computational complexity. A novel framework for obtaining robust periodic invariant ellipsoidal sets is developed. These sets prove useful for enlarging the feasible domain of MPC. For robust MPC, the focus is on scenario tree formulations which are often called multi-stage MPC. An efficient offline synthesis method that guarantees recursive feasibility of multi-stage MPC while reducing the online computational complexity is developed. A rigorous analysis for the theoretical properties of multi-stage MPC is performed, which shows intrinsic stability problems in such formulations of MPC. A novel method for solving these intrinsic problems is proposed. The developed method is then extended for use with the developed periodic invariant ellipsoids to enlarge the feasible domain of the multi-stage MPC. Moreover, an optimization problem for determining if a given set of vertex matrices, represent a LDI for a nonlinear system is presented. From this, periodic invariant ellipsoids can be computed for the nonlinear system. A nonlinear MPC is then introduced, which has a periodic prediction horizon and periodic terminal sets.