Constrained H[infinity]-optimization for discrete-time control systems

Citation

Rotstein, Hector P. (1993) Constrained H[infinity]-optimization for discrete-time control systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/51VE-9H34. https://resolver.caltech.edu/CaltechETD:etd-11282007-130457

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. In order to formulate a problem in the [...]-optimal control framework, all specifications have to be combined in a single [...]-norm objective, by an appropriate selection of weighting functions. If some of the specifications have the form of hard time domain constraints, the task of finding weighting functions that achieve a satisfactory design can become arduous. In this thesis, a theory for constrained [...]-control is presented, that can deal with the standard [...] objective and time domain constraints. Specifically, the following time domain constrained problem is solved: given a number [...], and a set of fixed inputs [...], find a controller such that the closed loop transfer matrix has an [...]-norm less than [...], and the time response [...] to the signal [...] belongs to some pre-specified set [...] for each [...]. Constraints are only imposed over a finite horizon, and this allows the formulation of a two step procedure. In the first step, the optimal way of clearing the constraints is found by computing a solution to a convex non differentiable problem. In the second, a standard unconstrained [...]-problem is solved. The final controller results from putting together the solution to both subproblems. The objective function for the minimization, and the solution to the whole problem are constructed using state-space formulas. The ellipsoid algorithm is argued to be a convenient procedure for performing the optimization since, if carefully implemented, it can deal with the two main characteristics of the problem, i.e., nondifferentiability and large-scale. The validity of assuming constraints over a finite horizon is justified by presenting a procedure for computing a solution that gives an overall satisfactory behavior. For clarity of exposition, this thesis starts by discussing a very special instance of the problem, and then proceeds to give the solution to the general case. Also, a benchmark problem for robust control is solved to illustrate the applicability of the theory.

Thesis Files