Optimal control with state-space constraint II
SIAM Journal on Control and Optimization
An approximation scheme for the minimum time function
SIAM Journal on Control and Optimization
Numerical methods for stochastic control problems in continuous time
Numerical methods for stochastic control problems in continuous time
SIAM Review
Ordered Upwind Methods for Hybrid Control
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
Ordered Upwind Methods for Hybrid Control
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
A Fast Sweeping Method for Static Convex Hamilton-Jacobi Equations
Journal of Scientific Computing
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Elliptical distance transforms and applications
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Fast Two-scale Methods for Eikonal Equations
SIAM Journal on Scientific Computing
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We introduce a family of highly efficient (non-iterative) numerical methods for a wide class of hybrid control systems. The application of Dijkstra's classical method to a discrete optimal trajectory problem on a network obtains the solution in O(M log M) operations. The key idea behind the method is a careful use of the direction of information propagation, stemming from the optimality principle. In a series of recent papers, we have introduced a number of Ordered Upwind Methods (OUMs) to efficiently solve the fully anisotropic continuous optimal control problems. These techniques rely on using a partial information on the characteristic directions of the Hamilton-Jacobi-Bellman PDE, stemming from the continuous variant of the optimality principle. The resulting non-iterative algorithms have the computational complexity of O(M log M), where M is the total number of grid points where the solution is computed, regardless of the dimension of the control/state variables. In this paper, we showho wOrde red Upwind Methods may be extended to efficiently solve the hybrid (discrete/continuous) control problems. We illustrate our methods by solving a series of hybrid optimal trajectory problems with and without time-dependence of anisotropic speed functions.