OPTIMAL AND ROBUST PARAMETERIZATION OF LINEAR CONTROLLER AND ESTIMATOR GAINS (MINIMAX, COMPUTERS)

The problems of selecting the parameters of controllers and estimators for optimal performance or minimax-optimal performance are considered. The structures of the optimal solutions to linear quadratic control and estimation problems for any linear functions of the observations are assumed. However, the linear functions of the observations are assumed to be parameterized.;Optimal parameterization is considered to obtain the best performance with a reduced on-line computational and/or storage burden. Optimal parameterization may also be used to design systems which do not satisfy some of the assumptions of the standard theory. The solutions to optimal parameterization problems are compared to those of the corresponding optimal nonparameterized problems.;Minimax-optimal parameterization is considered to obtain the best performance when inadequate a priori knowledge is available for optimal parameterization. The parameters are selected to minimize the worst case value of a cost criterion which reflects the system's performance over the domain of the unspecified properties of the plant or its environment. These designs are referred to as robust parameterizations. Although the second-order statistics of the process and measurement noise are assumed to be known precisely in the standard optimal design approach to minimum variance estimators; e.g., the Kalman Filter, this information is rarely available. Robust parameterization can provide a better approach to such problems.;The various approaches to optimal and robust design of parameterized regulators, filters and smoothers are summarized in the specification of a comprehensive computer program. The practicality of such a program is demonstrated by a consideration of the amount of memory and computer time required for the off-line solution for the parameters to be used on-line.