Abstract:
This technical note is concerned with the Pareto optimality of the mean-field stochastic linear-quadratic (LQ) multi-criteria optimal control problems over a finite time ...Show MoreMetadata
Abstract:
This technical note is concerned with the Pareto optimality of the mean-field stochastic linear-quadratic (LQ) multi-criteria optimal control problems over a finite time horizon. Firstly, we present a fact that when each one of the payoff functions is convex, then the weighted sum of payoff functions is also convex, but the inverse does not hold. Secondly, for a fixed initial value, the payoff functions are derived to be convex as a result of the conditions imposed on the weighting matrices combining with the solutions to the mean-field stochastic linear difference equation, which makes the minimization of the weighted sum of payoff functions a necessary and sufficient criterion to obtain Pareto efficient controls. Furthermore, all the Pareto efficient controls are obtained in light of the solutions to the weighted cross-coupled backward difference Riccati equations (DREs) and the weighting method. Finally, all the Pareto solutions are presented by the optimal feedback matrices of efficient controls and the solutions to the weighted cross-coupled backward difference Lyapunov equations (DLEs).
Date of Conference: 09-11 October 2020
Date Added to IEEE Xplore: 30 November 2020
ISBN Information: