EXTENSION OF LINEAR QUADRATIC OPTIMAL-CONTROL THEORY FOR MIXED BACKGROUNDS

Abstract

The problem of finding an optimal controller, while both deterministic and stochastic signals are present in the feedback system, is addressed. A general framework is developed to solve the above problem and to unify conventional frequency domain LQ and LQG optimal control theories. Both the system transient and steady-state behaviours are considered and the exact tracking of the arbitrary reference signal is guaranteed. The decomposition of a mixed signal into the deterministic and stochastic parts gives a chance to investigate the effect of the weighting factors, which were specified in the cost function, on the compromise between transient and steady-state system performance. The solution, which characterizes the structure of the optimal controller, results in a set of independent diophantine equations, instead of a set of coupled ones. Moreover, the number of equations can be reduced under weak conditions. Finally, both transient command tracking and steady-state noise rejection capabilities can be optimized simultaneously by using a two-parameter control scheme.