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.

%B Hybrid Systems: Computation and Control %S Lecture Notes in Computer Science %I Springer-Verlag %C Heidelberg, Germany %V LNCS 2289 %P 351-363 %G eng %0 Book Section %B Hybrid Systems: Computation and Control %D 2002 %T Synthesis of robust control systems under resource constraints %A L. Palopoli %A C. Pinello %A A. L. Sangiovanni-Vincentelli %A L. El-Ghaoui %A A. Bicchi %E M. Greenstreet %E C. Tomlin %K Embedded Control %K Robotics %B Hybrid Systems: Computation and Control %S Lecture Notes in Computer Science %I Springer-Verlag %C Heidelberg, Germany %V LNCS 2289 %P 337-350 %G eng %0 Conference Paper %B Proc. IFAC Workshop on Motion Control %D 1998 %T Decentralized Air Traffic Management Systems: Performance and Fault Tolerance %A A. Bicchi %A A. Marigo %A G. Pappas %A M. Pardini %A G. Parlangeli %A C. Tomlin %A S. Sastry %K Air Traffic Management Systems %K Autonomous Vehicles %K Hybrid and Embedded Control Systems %K Nonlinear Control Systems %B Proc. IFAC Workshop on Motion Control %G eng