P Arametric P Rogramming in C Ontrol

The main contributions in this thesis are advances in parametric programming. The thesis is divided into two parts; theoretical advances and application areas for parametric programming. The first part deals with continuity properties and the structure of solutions to convex parametric quadratic and linear programs. The second part focuses on applications of parametric quadratic and linear programming in control theory. This thesis is mainly a collection of articles where each article has been slightly modified. Note that several definitions differ from paper to paper (chapter to chapter). Chapter 2 presents a novel method for obtaining a unique polyhedral representation of a continuous selection for convex parametric quadratic programs (which includes parametric linear programs). The main contribution is to utilize a two-level optimization method to obtain the minimum norm solution. Chapter 3 introduces the so-called facet-to-facet property for parametric programs. It is pointed out that the correctness of several existing algorithms depend upon this property being satisfied. However, it is exemplified that the facet-to-facet property does not hold for strictly convex parametric quadratic programs. A new exploration strategy is proposed to remedy this problem. In Chapter 4 a method for obtaining explicit solutions to inf – sup control of constrained discrete–time discontinuous piecewise affine system subject to state-and input-dependent disturbances is presented. For this problem a solution is not guaranteed to exist. When a solution does not exist, a sub-optimal solution is obtained and a bound on the sub-optimality is given. The method allows for the degree of sub-optimality to be specified a priori. Chapter 5 presents a method that utilizes the dynamics of a discrete-time system to reduce the computational effort needed to evaluate the piecewise affine control law. The explicit control law and structure of the dynamic system makes it possible to map a polyhedral set one step forward in time. We demonstrate how this one-step forward reach set can be utilized to speed up the evaluation of the control law at the next sample instant. Chapter 6 presents a case study and experimental results for constrained control allocation for a scale model of a thruster-controlled floating platform. An explicit solution to a convexified problem is computed and the experimental results document the performance. ii problems is presented. The problem is divided into a master and a set of sub-problems for the purpose of obtaining a feasible, but possibly sub-optimal, solution. The decomposition strategy provides flexibility for the designer, …