This thesis is in the field of Optimal Control. It addresses research questions concerning both the properties of optimal controls and also schemes for control system stabilization based on the solution of optimal control problems.
The first part is concerned with the derivation of necessary conditions of optimality for two classes of optimal control problems not covered by earlier theory. The first is the class of optimal control problems with a combination of mixed control-state constraints and pure state constraints in which the dynamics are described by a differential inclusion under weaker hypotheses than have previously been considered. The second is the class of optimal control problems in which the dynamics take the form of a non-smooth differential equation with delays, and where the end-time is included in the decision variables. We shall demonstrate that these new optimality conditions lead to algorithms for solution of certain optimal control problems not amenable to earlier theory.
Model Predictive Control (MPC) is an approach to control system design based on solving, at each control update time, an optimal control problem. This is the subject matter of the second part of the thesis. We derive new MPC algorithms for constrained linear and nonlinear systems which, in certain significant respect, are simpler to implement than standard schemes, and which achieve performance specification under more general conditions than has previously been demonstrated. These include stability and feasibility.