Amplitude‐constrained adaptive lqg control of first‐order systems

Abstract

This paper considers the problem of adaptive LQG control design when the system control input is subject to an amplitude constraint. A first-order stochastic system is considered mainly because its output can be satisfactorily described by a Gaussian probability density function (PDF) or can be calculated numerically. In this light, two algorithms are proposed. In the first algorithm an approach given by Toivonen has been adopted where the PDF of the output is approximated by the Gaussian density in order to develop a suboptimal adaptive feedback controller. The approach in the second algorithm is based on the numerically calculated PDF of the system output yielding a near-optimal feedback gain. The proposed algorithms are compared with existing ones via simulations.

Adaptive LQG Control With Loop Transfer Recovery

“…Adaptive LQG control has been discussed e.g. in (Bitmead et al, 1990;Tay and Moore, 1991;Krolikowski, 1995;Mäkilä et al, 1984), where in (Tay and Moore, 1991) an adaptive LQG/LTR problem was solved augmenting the basic estimator-based controller with a stable proper linear system feeding back the estimation residuals. This idea was also used for non-adaptive continuous-time systems in (Tay and More, 1989) using the H ∞ /H 2 optimization technique.…”