Numerical Algorithms For State-Linear Optimal Impulsive Control Problems Based On Feedback Necessary Optimality Conditions

We propose and compare three numeric algorithms for optimal control of state-linear impulsive systems. The algorithms rely on the standard transformation of impulsive control problems through the discontinuous time rescaling, and the so-called “feedback”, direct and dual, maximum principles. The fee...

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Published in:Cybernetics and physics no. Issue Volume 9, 2020, Number 3; pp. 152 - 158
Main Authors: Sorokin, Stepan, Staritsyn, Maxim
Format: Journal Article
Language:English
Published: 30.11.2020
ISSN:2223-7038, 2226-4116
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Abstract We propose and compare three numeric algorithms for optimal control of state-linear impulsive systems. The algorithms rely on the standard transformation of impulsive control problems through the discontinuous time rescaling, and the so-called “feedback”, direct and dual, maximum principles. The feedback maximum principles are variational necessary optimality conditions operating with feedback controls, which are designed through the usual constructions of the Pontryagin’s Maximum Principle (PMP); though these optimality conditions are formulated completely in the formalism of PMP, they essentially strengthen it. All the algorithms are non-local in the sense that they are aimed at improving non-optimal extrema of PMP (local minima), and, therefore, show the potential of global optimization.
AbstractList We propose and compare three numeric algorithms for optimal control of state-linear impulsive systems. The algorithms rely on the standard transformation of impulsive control problems through the discontinuous time rescaling, and the so-called “feedback”, direct and dual, maximum principles. The feedback maximum principles are variational necessary optimality conditions operating with feedback controls, which are designed through the usual constructions of the Pontryagin’s Maximum Principle (PMP); though these optimality conditions are formulated completely in the formalism of PMP, they essentially strengthen it. All the algorithms are non-local in the sense that they are aimed at improving non-optimal extrema of PMP (local minima), and, therefore, show the potential of global optimization.
Author Sorokin, Stepan
Staritsyn, Maxim
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  organization: Optimal Control, Matrosov Institute for System Dynamics and Control Theory SB RAS, Russia
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Snippet We propose and compare three numeric algorithms for optimal control of state-linear impulsive systems. The algorithms rely on the standard transformation of...
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