A Robust Control Design for FIR Plants with Parameter Set Uncertainty

This paper proposes a method of computing the finite-horizon control inputs for FIR plants whose parameters are only known to lie in a set. The parameter set is assumed to be described by an ellipsoidal bound, which could be provided by some identification scheme with a parameter set estimator. The finite-horizon control obtained minimizes the maximum LQR cost from all plants with parameters in the given set. The computation of this robust control is shown to be a convex optimization problem, thus global minimization is guaranteed and many efficient methods are available to compute the minimizing control. In addition, the method can also be used to compute the control for the dual problem in which the plant parameters are known but the initial states of the plant are assumed to lie in a set.