Control of extremes and level-crossings in stationary Gaussian random processes

Abstract

An optimal stochastic control problem that minimizes the intensity for a signal to cross a level in the upward direction is solved. The optimal controller also approximately minimizes the probability that the signal is above the level. The latter problem has previously been solved approximately by minimum variance control, which is known to have a badly behaved control signal. To overcome this, weighting on the control signal-LQG-design-has been proposed, but there has been no good criterion on how to choose the weighting. The problem is rewritten as a one-parametric optimization problem over a set of LQG-problem solutions, and the solution can sometimes be thought of as finding optimal weightings in an LQG-problem.<>