LAUSR

This paper proposes a controller that gives guaranteed optimal performance in terms of the relative cost for a class of discrete-time nonlinear systems with uncertainties. In some systems, the absolute optimal cost values may be highly dependent on the disturbances. It is desirable to design a controller bounding the relative cost, which is defined as the ratio between the actual cost and the posteriori calculated optimal cost. In this paper, a novel worst-case relative cost optimal control method is developed, assuming that the disturbance sequence belongs to a known finite admissible set. The control policy uses the current states, current accumulated cost, and all current and past disturbance values as feedback. Then the problem is extended to a stochastic case, and the worst-case expected relative cost is minimised. A numerical example on linear systems and a numerical example on the nonlinear hybrid electric vehicle energy management problem are provided.