Linear programming approach to optimal impulse control problems with functional constraints

2019/10/02 by Alexey Piunovskiy, Yi Zhang, Piunovskiy, Alexey +1 · 1 citation
Engineering · Computer Science · #Advanced Control Systems Optimization #Optimization and Variational Analysis #Stability and Control of Uncertain Systems

paper · pdf · doi:10.48550/arxiv.1910.01098

Abstract

This paper considers an optimal impulse control problem of dynamical systems generated by a flow. The performance criteria are total costs over the infinite time horizon. Apart from the main performance to be minimized, there are multiple constraints on performance functionals of a similar type. Under a natural set of compactness-continuity conditions on the system primitives, we establish a linear programming approach, and prove the existence of a stationary optimal control strategy out of a more general class of randomized strategies. This is done by making use of the tools from Markov decision processes.

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