Social optima in linear quadratic mean field control with unmodeled dynamics and multiplicative noise

This paper investigates cooperative linear quadratic differential games for uncertain dynamic systems with conservative players, who attempt to optimize the worst‐case outcomes with limited a priori knowledge about the uncertainties. Without properly designed control strategies, the uncertainties could cause significant impacts on the performance indexes of players and spoil the cooperation among players. In this paper, compensation‐based robust control techniques are applied to handle the uncertainties, including parameter perturbations and external disturbances, by transforming the impacts of the uncertainties into a more tractable form. Subsequently, using Vickrey–Clarke–Groves principles, an auction‐based control allocation mechanism is designed to incentivize the players to cooperatively implement the compensation. With the methods proposed, the worst‐case performance indexes of players can be improved, and the cooperation among players is maintained in the uncertain system. Numerical examples demonstrate the effectiveness of the proposed methods.

Section: X(t)mentioning

confidence: 99%

Section: V(t) = −𝑓 Iv(t) − 𝑓 B δ(T) V(0) = 𝟎mentioning

confidence: 99%

Section: V(t) = −𝑓 Iv(t) − 𝑓 B δ(T) V(0) = 𝟎mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Cooperative linear quadratic differential games for uncertain systems with conservative players

Zhang

Shi

Zhong

2023

“…Later, several solutions to the robust control problem were proposed, with

{H}_{\infty }

control solutions playing an important role in this problem [10]. Thereafter, several approaches to solving robust control [11–13] and robust estimation [14–16] problems are proposed for the next few years. Two categories can also be established on the basis of linear matrix inequality (LMI) and algebraic Riccati equations (ARE).…”

Section: Introductionmentioning

confidence: 99%

Robust linear quadratic regulator applied to an inverted pendulum

Escalante

Jutinico

Terra

et al. 2022

The natural instability of an inverted pendulum and its dynamics richness, in terms of nonlinearity, provide a nice apparatus to reproduce behaviors of analogous systems. In this way, it is useful to perform benchmark tests for new control approaches developed. In this paper, we address the main inverted pendulum problems: pendulum stabilization, tracking, and catching swing‐up control. We show how robust recursive, control and filtering, techniques improve the system performance. They are developed to solve stochastic problems based on deterministic approaches, in order to decrease the worst influence of uncertainties. Experimental results of the proposed robust approach provide robust stability and performance despite parametric uncertainties, disturbances, and noise effects.

Decentralized ϵ‐Nash strategy for linear quadratic mean field games using a successive approximation approach

Shen

2023

This paper presents a successive approximation method for decentralized strategy design in the large‐scale linear quadratic (LQ) Gaussian game. The strategy consists of transforming the original mean field game (MFG) problem into solving decoupled ordinary differential equations (ODEs) whose numerical solutions are obtained by a new two‐loop iteration algorithm. It should be noted that we employ the augmented model technique and the LQ framework to derive these low‐dimensional solvable ODEs, which is the cornerstone of constructing the decentralized ‐Nash strategy. In addition, the quadratic ODEs contained therein are approximately solved for by a sequence of iterative linear ordinary differential equations (LODEs) with guaranteed convergence. A numerical example is given to show the effectiveness of the proposed algorithm.