Tube-enhanced Multi-stage Model Predictive Control

The principal theme of the thesis is addressing the challenge of the trade-off between optimality and complexity in the field of robust Model Predictive Control (MPC). Different robust MPC formulations are proposed that guarantee rigorous constraint satisfaction, recursive feasibility, and robust asymptotic stability for linear and nonlinear systems with additive and parametric uncertainties under standard assumptions. For linear systems with full-state feedback, a basic formulation and an advanced formulation of Tube-Enhanced Multi-Stage (TEMS) MPC are presented. The basic formulation avoids the problem of growth in problem complexity concerning less significant uncertainties by computing a constant feedback law offline and improves the performance of the controller by calculating a sequence of control policies for significant uncertainties modeled on a scenario-tree. The advanced formulation provides users with additional options to limit the rapid growth of problem complexity beyond a certain prediction step called robust horizon with the help of affine feedback policies. It results in a linear increase in problem complexity with respect to the prediction horizon beyond the robust horizon. For nonlinear systems, the proposed TEMS Nonlinear MPC (NMPC) scheme implements two multi-stage controllers hierarchically to achieve robustness against uncertainties. Novel robust output feedback formulations are proposed that can work with any estimation scheme that can provide an estimate along with an error bound. The concept of substitute estimates is introduced to obtain control policies for the linear output feedback case using the multi-stage, the tube-based, and the TEMS MPC schemes. The advantages of the proposed schemes are demonstrated using two case studies.