Mathematics – Optimization and Control
Scientific paper
2009-01-26
Mathematics
Optimization and Control
The final version accepted by J. Comp. Math. : 41 pages, 14 figures. Since the previous version: typos fixed, formatting impro
Scientific paper
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.
Kumar Ajeet
Vladimirsky Alexander
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