Guaranteed Steering Control

The problem of steering the state of a dynamic system to a target set while avoiding specified regions of state space is considered. Sufficient conditions for attaining the target are given in terms of a Lyapunov-type attraction test function, while avoidance of forbidden regions is guaranteed by a relationship between the state trajectory and a set of barrier functions. These sufficient conditions may be useful for establishing analytically properties of certain pointwise optimal feedback control schemes which have been demonstrated previously only by simluations. As an example, the sufficient conditions are used to establish a region of efficacy for a feedback control for obstacle avoidance in the plane.