Modified State Predictive Control Aiming at Improving Robust Stability

Abstract

Finite spectrum assignment, also known as state predictive control, is an effective control method for systems with time delay in the input. This paper considers introducing some modification on the control law of state predictive control, where the modification can be interpreted, roughly speaking, as suitably taking account of the (intentionally introduced) deviation of the past input from what is desired in the sense of the conventional state predictive control. The motivation for introducing such modification lies in an attempt to modify the dynamics of the controller while maintaining a feature of the conventional state predictive control to a certain extent. In particular, we aim at improving robust stability for non-parametric uncertainties of the plant. We first derive the characteristic equation of the modified state predictive control systems, and give a necessary and sufficient condition for stability. We then derive an explicit representation of the complementary sensitivity function associated with the robust stability analysis problem for multiplicative uncertainties. Finally, we demonstrate through a numerical example that modified state predictive control can indeed be useful for improving robust stability if the modification is introduced suitably.