Adaptive robust model predictive control

Model Predictive Control (MPC) repeatedly solves a finite horizon optimal control problem subject to input and state constraints. The performance of MPC algorithms depends crucially on the quality of the model that is used to optimize the predicted future performance. To reduce system model uncertainties, adaptive controllers have been proposed for MPC enabling model parameters to be identified online. Adaptive robust MPC, combining adaptive control and robust MPC, therefore has the potential to estimate system parameters while satisfying operating constraints and providing stability guarantees. However, although adaptive robust MPC algorithms have been considered for several decades, robust, computationally tractable adaptive MPC remains a topic under research. This thesis proposes several adaptive robust Model Predictive Control strategies for linear and nonlinear systems with constant unknown model uncertainties and bounded additive disturbances. By combining set membership parameter identification with robust tube MPC, the proposed algorithms guarantee robust constraint satisfaction and recursive feasibility. Computational tractability is ensured by using polytopic sets of fixed complexity to bound parameter sets and predicted states. The closed-loop system is proven to be input-to-state stable under a nominal cost. For parameter identification, the thesis proposes various approaches that incorporate persistence of excitation conditions as computationally tractable constraints with feasibility guarantees within adaptive MPC. Methods of ensuring persistence of excitation include augmenting the cost function, exploiting the random nature of disturbance inputs inherent in the model, introducing additional excitation into the control inputs, and including both disturbance and additional input excitation in the algorithm. The performance of various approaches is compared in terms of parameter convergence and tracking or regulation performance. In addition, the thesis relates the probabilistic rates of parameter set convergence to persistence of excitation conditions and proves convergence of the estimated parameter sets to the true parameter values using the proposed algorithms.