Discrete-time optimal preview control

The field of Preview Control is concerned with using advanced knowledge of disturbances or references in order to improve tracking quality or disturbance rejection. Areas of application include guidance of autonomous vehicles, robotics and process control. This thesis studies Optimal Discrete-Time Preview Control, in which the controlled plant is assumed to be unconstrained, linear and discrete-time, with a preview horizon that extends for a fixed time into the future. Controller optimality is determined using either the H2 or H∞ norms. The central objective of this thesis is to produce a generic set of tools for solving a wide class of H2 and H∞ Preview Control problems. To this end, a very general preview problem is introduced, which captures fixed-lag smoothing, tracking with robust performance specifications, and also preview-based mixed-sensitivity design. In principle, whilst this problem can be solved using standard generalised regulator synthesis results, such an approach is found to require the solution of unacceptably large Discrete Algebraic Riccati Equations (DAREs). A core theme of this thesis involves the efficient solution of the H2 and H∞ versions of such DAREs, and also the order reduction of the resulting controllers. It is found that the dimension of all matrix equations required for controller synthesis, and also the order of the resulting controllers, is no higher than the degree of the plant plus weighting functions. Additional results are presented concerning the norm reduction that is achievable through preview action, and a discussion of the generic properties of preview controllers is provided. Preview Control appears to be well suited for application to autonomous vehicles. However, a class of nonlinearities generically associated with vehicle models prevents its immediate use. Fortunately, this nonlinearity may be accurately represented by a parameterised set of linear systems, from which a simple controller may be derived. This control scheme is successfully demonstrated on a nonlinear bicycle model.