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.