Optimal Constraint Following for Fuzzy Mechanical Systems Based on a Time-Varying β-Measure and Cooperative Game Theory

Abstract

This article addresses a cooperative game-oriented optimal constraint-following problem for fuzzy mechanical systems. The state of the concerned system is affected by possibly (fast) time-varying uncertainty. The fuzzy set theory is adopted to describe such uncertainty. The task is to drive the system to obey a set of prescribed constraints optimally. Since the control objective may be changing along with the system uncertainty, a time-varying β-measure is defined to gauge the constraint-following error; based on which, an adaptive robust control scheme with two tunable parameters is then proposed to render it to be uniform boundedness and uniform ultimate boundedness. For the seeking of the optimal design parameters, two cost functions, each of which is dominated by one tunable parameter, are developed with the fuzzy information, and thereout a two-player cooperative game is formulated. Finally, the optimal design problem is successfully solved: with the existence, uniqueness, and analytical expression of the Pareto optimality.

Online Pareto optimal control of mean-field stochastic multi-player systems using policy iteration

“…. , ρ N ) ρ l 0 and N l=1 ρ l = 1 such that u * satisfies condition (3). Since all players choose to cooperate to minimize the cost function, the joint action is represented as…”

“…In the field of multiple optimizations with the LQ structure, the Pareto solution, which means that not all players' costs can be improved upon simultaneously, plays a crucial role owing to its excellent ability to achieve a maximum allocation for the limited resources. It has been applied in various fields such as electric power systems [1], economics [2], and gun turret-barrel systems [3]. The published results on Pareto optimal control are theoretically elegant and practically reliable, e.g., the finite and infinite horizon cooperative Pareto efficient equilibria for regular indefinite differential games [4], Paretobased guaranteed cost control problems [5], and Pareto optimal solutions and their application to the network security model [6].…”