LQG Control with an H-infinity / Performance Bound: A Riccati Equation Approach

Authors

D.S. Bernstein, W.M. Haddad

Year

1989

Journal Paper

Algorithm

H-infinity LQG Control

Source

IEEE Transactions on Automatic Control

Identifiers

DOI 10.1109/9.16419

Abstract¶

An LQG (linear quadratic Gaussian) control-design problem involving a constraint on H-infinity / disturbance attenuation is considered. The H-infinity / performance constraint is embedded within the optimization process by replacing the covariance Lyapunov equation by a Riccati equation whose solution leads to an upper bound on L2/ performance. In contrast to the pair of separated Riccati equations of standard LQG theory, the H-infinity /-constrained gains are given by a coupled system of three modified Riccati equations. The coupling illustrates the breakdown of the separation principle for the H-infinity / -constrained problem. Both full-order and reduced-order design problems are considered with an H-infinity / attenuation constraint involving both state and control variables. An algorithm is developed for the full-order design problem and illustrative numerical results are given.

Summary¶

Bernstein and Haddad study LQG controllers subject to an H-infinity-style performance bound, deriving Riccati-equation conditions that connect stochastic optimal control with robust performance guarantees. The paper is part of the bridge between LQG design and robust control analysis.