Publications - Book Chapter

This paper deals with the stabilization problem for a particular class of hybrid systems, namely discrete-time linear systems subject to a uniform (a priori fixed) quantization of the control set. Results of our previous work on the subject provided a description of minimal (in a specific sense) invariant sets that could be rendered maximally attractive under any quantized feedback strategy. In this paper, we consider the design of stabilizing laws that optimize a given cost index on the state and input evolution on a finite, receding horizon. Application of Model Predictive Control techniques for the solution of similar hybrid control problems through Mixed Logical Dynamical reformulations can provide a stabilizing control law, provided that the feasibility hypotheses are met. In this paper, we discuss precisely what are the shortest horizon length and the minimal invariant terminal set for which it can be guaranteed a stabilizing MPC scheme. The final paper will provide an example and simulations of the application of the control scheme to a practical quantized control problem.

In this paper the problem of stabilizing a wheeled vehicle of unicycle type to a set point, using only visual feedback, is considered. The practically most relevant problem of keeping the tracked features in sight of the camera while maneuvering to park the vehicle is taken into account. This constraint, often neglected in the literature, combines with the nonholonomic nature of the vehicle kinematics in a challenging controller design problem. We provide an effective solution to such problem by using a combination of previous results on non-smooth control synthesis, and recently developed hybrid control techniques. Simulations and experimental results on a laboratory vehicle are reported, showing the practicality of the proposed approach.