An Efficient Method for Multiobjective Optimal Control and Optimal Control Subject to Integral Constraints
Year: 2010
Journal of Computational Mathematics, Vol. 28 (2010), Iss. 4 : pp. 517–551
Abstract
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 [25]. We illustrate our method using examples from flight path planning and robotic navigation in the presence of friendly and adversarial observers.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1003-m0015
Journal of Computational Mathematics, Vol. 28 (2010), Iss. 4 : pp. 517–551
Published online: 2010-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 35
Keywords: Optimal control Multiobjective optimization Pareto front Vector dynamic programming Hamilton-Jacobi equation Discontinuous viscosity solution Semi-Lagrangian discretization.