Theory of linear and integer programming
Theory of linear and integer programming
Extracting state information form a quantized output record
Systems & Control Letters
Dynamic Programming: Models and Applications
Dynamic Programming: Models and Applications
Approximate simulation relations and finite abstractions of quantized control systems
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Sensor/actuator abstractions for symbolic embedded control design
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
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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.