P.: Symbolic approximate time-optimal control

Abstract. There is an increasing demand for controller design techniques ca-pable of addressing the complex requirements of todays embedded applications. This demand has sparked the interest in symbolic control where lower complex-ity models of control systems are used to cater for complex specifications given by temporal logics, regular languages, or automata. These specification mech-anisms can be regarded as qualitative since they divide the trajectories of the plant into bad trajectories (those that need to be avoided) and good trajecto-ries. However, many applications require also the optimization of quantitative measures of the trajectories retained by the controller, as specified by a cost or utility function. As a first step towards the synthesis of controllers reconciling both qualitative and quantitative specifications, we investigate in this paper the use of symbolic models for time-optimal controller synthesis. We con-sider systems related by approximate (alternating) simulation relations and show how such relations enable the transfer of time-optimality information between the systems. We then use this insight to synthesize approximately time-optimal controllers for a control system by working with a lower com-plexity symbolic model. The resulting approximately time-optimal controllers are equipped with upper and lower bounds for the time to reach a target, describing the quality of the controller. The results described in this paper were implemented in the Matlab Toolbox Pessoa [1] which we used to workout several illustrative examples reported in this paper. 1