an:05926098
Zbl 1240.90345
Kumar, Ajeet; Vladimirsky, Alexander
An efficient method for multiobjective optimal control and optimal control subject to integral constraints
EN
J. Comput. Math. 28, No. 4, 517-551 (2010).
00282644
2010
j
90C29 49J30 49L25 65K05
optimal control; multiobjective optimization; Hamilton-Jacobi equation; discontinuous viscosity solution
Summary: We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a ``budget'' remaining to satisfy each constraint; the augmented Hamilton-Jacobi-Bellman PDE is then solved numerically. The efficiency of our approach hinges on the causality in that PDE, i.e., the monotonicity of characteristic curves in one of the newly added dimensions. A semi-Lagrangian ``marching'' method is used to approximate the discontinuous viscosity solution efficiently. We compare this to a recently introduced ``weighted sum'' based algorithm for the same problem. We illustrate our method using examples from flight path planning and robotic navigation in the presence of friendly and adversarial observers.