Uma nova metodologia de jogos dinâmicos lineares quadráticos

Abstract

The game theory is a branch of mathematics concerned with the study of situations that arise when multiple decision agents seek to attain their own objectives, possibly con icting each other. In a dynamic linear quadratic (LQ) formulation, the Nash equilibrium solutions of the players can be obtained in terms of the coupled algebraic Riccati equations, which, depending on the method used for calculation, can yield unsatisfactory results under the stability and the numerical precision points of view. In this sense, this work proposes a new algorithm for an alternative solution for the coupled algebraic Riccati equations associated with the dynamic (LQ) games, with open-loop structure information, through concepts of the duality theory and static convex optimization. In addition, a new methodology for the synthesis of a family of optimal controllers it's obtained. The game theory also reveals great potential application for multi-objective control problems, where the H∞ control is included, which can be formulated as a zero-sum dynamic game. Considering this formulation, the new proposed methodologies in this work are extended to H∞ control problems with disturbance rejection, yielding results with better stability and performance properties than the ones obtained via modi ed algebraic Riccati equation. Finally, through numerical examples and computational simulations, the new methodologies are confronted with the traditional methodologies, showing the most relevant aspects from each approach.