Necessary optimality conditions for a singular surface in the form of synthesis

Melikyan, Arik

doi:10.1007/bf02191851

Cited by 13 publications

(9 citation statements)

References 1 publication

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“…From Definition 3.13 (Robbins 1967;Krener 1977;Powers 1980;Melikyan 1994) have developed some higher-order necessary conditions for optimality to distinguish the optimal controls from non-optimal controls which satisfy the first-order conditions (25).…”

Section: Standard Results and Second-order Necessary Conditionmentioning

confidence: 99%

Practical optimal state feedback control law for continuous-time switched affine systems with cyclic steady state

Patiño

Riedinger

Iung

2009

International Journal of Control

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In this article, a method for computing an optimal state feedback control law for continuous-time switched affine systems exhibiting cyclic behaviour in steady state is presented. The hybrid solutions are deduced from the Fillipov solutions. It is shown that the optimal trajectory synthesis implies to determine singular arcs. Algebraic conditions are given to obtain these particular arcs of the trajectory. A numerical procedure is then proposed to generate optimal trajectories on a given state space area avoiding the classical two-point boundary value problem occurring in optimal control synthesis. The interpolation of the solutions set, through a neural network, yields a state feedback control law. Several examples in the power converters field show the feasibility and the efficiency of the method.

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Section: Standard Results and Second-order Necessary Conditionmentioning

confidence: 99%

Practical optimal state feedback control law for continuous-time switched affine systems with cyclic steady state

Patiño

Riedinger

Iung

2009

International Journal of Control

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“…The optimal strategy of the prey in this model, which we found by using the Hamilton-Jacobi-Bellman (HJB) approach combined with the method of singular characteristics [18][19][20], follows the following rules (figures 1 and 2):…”

Section: Optimal Control Model With Energy Dynamicsmentioning

confidence: 99%

Joining or opting out of a Lotka–Volterra game between predators and prey: does the best strategy depend on modelling energy lost and gained?

et al. 2013

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One contribution of 11 to a Theme Issue 'Modelling biological evolution: recent progress, current challenges and future direction'. Apart from interacting, prey and predators may also avoid each other by moving into refuges where they lack food, yet survive by switching to an energy-saving physiological state. Lotka -Volterra models of predatorprey interactions ignore this option. Therefore, we have modelled this game of 'joining versus opting out' by extending Lotka-Volterra models to include portions of populations not in interaction and with different energy dynamics. Given this setting, the prey's decisions to join or to opt out influence those of the predator and vice versa, causing the set of possible strategies to be complex and large. However, using game theory, we analysed and published two models showing (i) which strategies are best for the prey population given the predator's strategy, and (ii) which are best for prey and predator populations simultaneously. The predicted best strategies appear to match empirical observations on plant-inhabiting predator and prey mites. Here, we consider a plausible third model that does not take energy dynamics into account, but appears to yield contrasting predictions. This supports our assumption to extend Lotka -Volterra models with 'interaction-dependent' energy dynamics, but more work is required to prove that it is essential and that what is best for the population is also best for the individual.

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“…More difficulty arises when the system has uncontrollable state manifold, necessary optimality conditions for a "This research is supported by COE research project, which is supported by the Japanese Ministry of Education, Sciences, Sports and Culture. singular control is presented in [6].…”

Section: Introductionmentioning

confidence: 99%

Computation of time optimal swing up control of single pendulum

Furuta

Xu²,

Габасов³

IECON'99. Conference Proceedings. 25th Annual Conference of the IEEE Industrial Electronics Society (Cat. No.99CH37029)

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Time optimal control under bounded input has been studied. This paper presents a computational strategy to obtain the time optimal control for nonlinear systems, and discrete time control under input bound is considered. The swing up control of a single pendulum from pendant stable equilibrium to upright unstable equilibrium is used to illustrate our approaches. For simplified model of the single pendulum, which is a second-order system, an approach based on Linear Programming method is introduced, while for the actual single pendulum, an approach based on Nonlinear Optimization is introduced. Simulation results show that our computational approaches are feasible.

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Necessary optimality conditions for a singular surface in the form of synthesis

Cited by 13 publications

References 1 publication

Practical optimal state feedback control law for continuous-time switched affine systems with cyclic steady state

Practical optimal state feedback control law for continuous-time switched affine systems with cyclic steady state

Joining or opting out of a Lotka–Volterra game between predators and prey: does the best strategy depend on modelling energy lost and gained?

Computation of time optimal swing up control of single pendulum

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