# Australian Research Council (ARC)

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This is a collection of ARC-funded research publications authored by Flinders academics.

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### Browsing Australian Research Council (ARC) by Subject "Control systems"

Now showing 1 - 4 of 4

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Item Averaging and linear programming in some singularly perturbed problems of optimal control(Springer Verlag, 2014-06-11) Gaitsgory, Vladimir; Rossomakhine, SergeyThe paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite time horizon. We mostly focus on problems with time discounting criteria but a possibility of the extension of results to periodic optimization problems is discussed as well. Our consideration is based on earlier results on averaging of SP control systems and on linear programming formulations of optimal control problems. The idea that we exploit is to first asymptotically approximate a given problem of optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with two numerical examples.Item On average control generating families for singularly perturbed optimal control problems with long run average optimality criteria(Springer Verlag, 2014-10-12) Gaitsgory, Vladimir; Manic, Ludmila; Rossomakhine, SergeyThe paper aims at the development of tools for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems with long run average optimality criteria. The idea that we exploit is to first asymptotically approximate a given problem of optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional (ID) linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with a numerical example.Item On sets of occupational measures generated by a deterministic control system on an infinite time horizon(Elsevier, 2013-09) Gaitsgory, Vladimir; Quincampoix, MarcWe give a representation for the closed convex hull of the set of discounted occupational measures generated by control-state trajectories of a deterministic control system. We also investigate the limit behavior of the latter when the discount factor tends to zero and compare it with the limit behavior of the long run time average occupational measures set. The novelty of our results is in that we allow the control set dependence on the state variables that make the results to be applicable to differential inclusions.Item Stabilization with discounted optimal control(Elsevier, 2015-08) Gaitsgory, Vladimir; Grune, Lars; Thatcher, NeilWe provide a condition under which infinite horizon discounted optimal control problems can be used in order to obtain stabilizing controls for nonlinear systems. The paper gives a mathematical analysis of the problem as well as an illustration by a numerical example.