Wiener-Hopf Approaches to Regulator, Filter/Observer, and Optimal Coupler Problems

摘要

Most approaches to optimal linear stochastic control problems depend on time domain techniques for both their theoretical foundations and for computational algorithms. In contrast, this paper discusses innovations based on classical transform domain Wiener-Hopf theory. These innovations avoid several difficulties occurring in time domain solutions (e.g., those which arise in connection with singular regulator and filter problems). Emphasis will be upon solution techniques and properties in distinction to derivations. The following points will be demonstrated: linear regulator, filter/observer problems can be solved using linear algebraic equations (in distinction to solving nonlinear Riccati equations); the R weighting matrix need not be positive definite nor is it necessary that 1/R exists; singular regulator and filter/observer problems (e.g., the cheap control problem) can be handled neatly; the weighting matrices, R and Q, can be explicit functions of frequency; and there are some advantages in using non-diagonal Q and R matrices.