An efficient method for multiobjective optimal control and optimal control subject to integral constraints
For researchers in optimal control and robotics, this provides a more efficient alternative to existing weighted-sum methods for problems with multiple objectives or integral constraints.
The paper introduces a new numerical method for multiobjective optimal control and optimal control under integral constraints by extending the state space and solving an augmented Hamilton-Jacobi-Bellman PDE efficiently using a semi-Lagrangian marching method. The method is demonstrated on flight path planning and robotic navigation examples.
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.