Robust Model Based Control of Constrained Systems.

Abstract

This dissertation is concerned with control of systems subject to input and state constraints. Model Predictive Control (MPC) is one promising control technique that is capable of dealing with constraints. Its flexible formulation also provides mechanisms to tune the closed loop system for desired performance. However, due to computational complexity and its dependency on accurate models of the system, the MPC applications for systems with fast dynamics or with model uncertainties are not wide spread. The focus of this dissertation is to develop methodologies and tools that can enhance the computational efficiency and address robustness issues of constrained dynamic systems. The core contribution of this dissertation is that it provides a computational efficient MPC solver, referred to as InPA-SQP (Integrated Perturbation Analysis and Sequential Quadratic Programming).

The main results include four major components. First, a neighboring extremal control method is proposed for discrete-time optimal control problems subject to a general class of inequality constraints. A closed form solution for the neighboring extremal (NE) control is provided and a sufficient condition for existence of the neighboring extremal solution is specified. Second, the NE method is integrated with sequential quadratic programming that leads to InPA-SQP. Third, a robust control method is introduced for linear discrete-time systems subject to mixed input-state constraints. Unlike conventional MPC, the method does not require repeatedly solving an optimization problem online while guarantees states convergence to a minimal invariant set. Fourth, it is shown that if the dynamics of disturbances are incorporated, the attractor set associated with the proposed constrained robust control methods can be considerably smaller, leading to a much less conservative design.

Applications of the InPA-SQP and proposed constrained robust control constitute the other key element of the study. The InPA-SQP is employed in two experimental applications: one for voltage regulation of a DC/DC converter and another for path following of a model ship. Both applications show effectiveness of the method in terms of computation and constraints handling. These applications not only serve as validation platforms but also motivate new research topics for further investigation.