Novel Method to Control Linear Systems of Acceleration Constrained Dynamics

A linear time-dependent controlled system with given time-dependent acceleration state constraints is considered. Due to such constraints, this system becomes inherently nonlinear. For constant acceleration constraints this difficulty can be circumvented by replacing state constraints with control constraints at the expense of reduced control performance. For time-dependent acceleration constraints this method may fail. In this paper a novel replacing rule is proposed and its success in respecting the constraints and enhancing control performance is illustrated by examples of pursuit-evasion problems.