In this paper we consider the problem of optimal control (specifically, minimum-time steering) for systems with quantized inputs. In particular, we propose a new approach to the solution of the optimal control problem for an important class of nonlinear systems, i.e. chained-form systems. By exploiting results on the structure of the reachability set of these systems under quantized control, the optimal solution is determined solving an integer linear programming problem. Our algorithm represents an improvement with respect to classical approaches in terms of exactness, as it does not resort to any a priori state-space discretization. Although the computational complexity of the problem in our formulation is still formally exponential, it lends itself to application of Branch and Bound techniques, which substantially cuts down computations in many cases, as it has been experimentally observed.

JF - Hybrid Systems: Computation and Control T3 - Lecture Notes in Computer Science PB - Springer-Verlag CY - Heidelberg, Germany VL - LNCS 2289 ER - TY - CHAP T1 - Synthesis of robust control systems under resource constraints T2 - Hybrid Systems: Computation and Control Y1 - 2002 A1 - L. Palopoli A1 - C. Pinello A1 - A. L. Sangiovanni-Vincentelli A1 - L. El-Ghaoui A1 - A. Bicchi ED - M. Greenstreet ED - C. Tomlin KW - Embedded Control KW - Robotics JF - Hybrid Systems: Computation and Control T3 - Lecture Notes in Computer Science PB - Springer-Verlag CY - Heidelberg, Germany VL - LNCS 2289 ER - TY - CONF T1 - Decentralized Air Traffic Management Systems: Performance and Fault Tolerance T2 - Proc. IFAC Workshop on Motion Control Y1 - 1998 A1 - A. Bicchi A1 - A. Marigo A1 - G. Pappas A1 - M. Pardini A1 - G. Parlangeli A1 - C. Tomlin A1 - S. Sastry KW - Air Traffic Management Systems KW - Autonomous Vehicles KW - Hybrid and Embedded Control Systems KW - Nonlinear Control Systems JF - Proc. IFAC Workshop on Motion Control ER -