Closed-form H-infinity Optimal Control for a Class of Infinite-Dimensional Systems

TL;DR

This paper derives explicit, closed-form solutions for H-infinity optimal control and estimation in certain infinite-dimensional systems, notably those governed by PDEs, simplifying synthesis without iterative procedures.

Contribution

It provides explicit formulas for optimal controllers and estimators for PDE systems, avoiding traditional iterative H-infinity synthesis methods.

Findings

Explicit formulas for optimal control and estimation are derived.

Optimal performance levels are explicitly calculated.

Results are applicable to finite-dimensional systems and useful for benchmarking.

Abstract

H-infinity optimal control and estimation are addressed for a class of systems governed by partial differential equations with bounded input and output operators. Diffusion equations are an important example in this class. Explicit formulas for the optimal state feedback controller as well as the optimal state estimator are given. Unlike traditional methods for H-infinity synthesis, no iteration is needed to obtain the optimal solution. Moreover, the optimal performance for both the state feedback and state estimation problems are explicitly calculated. This is shown to be useful for problems of H-infinity optimal actuator and sensor location. Furthermore, the results can be used in testing and bench-marking of general purpose algorithms for H-infinity synthesis. The results also apply to finite-dimensional systems.