Solving Potential Games With Dynamical Constraint

Active Disturbance Rejection Control of Euler-Lagrange Systems Exploiting Internal Damping

Active disturbance rejection control (ADRC) is an efficient control technique to accommodate both internal uncertainties and external disturbances. In the typical ADRC framework, however, the design philosophy is to "force" the system dynamics into a double-integral form by an extended state observer (ESO) and then the controller is designed. Especially, the systems' physical structure has been neglected in such a design paradigm. In this article, a new ADRC framework is proposed by incorporating at a fundamental level the physical structure of the Euler-Lagrange (EL) systems. In particular, the differential feedback gain can be selected considerably small or even 0, due to the effective exploitation of the system's internal damping. The design principle stems from an analysis of the energy balance of EL systems, yielding a physically interpretable design. Moreover, the exploitation of the system's internal damping is thoroughly discussed, which is of practical significance for applications of the proposed design. Besides, a sliding-mode ESO is designed to improve the estimation performance over traditional linear ESO. Finally, the proposed control framework is illustrated through tracking control of an omnidirectional mobile robot. Extensive experimental tests are conducted to verify the proposed design as well as the discussions.

Distributed Robust Seeking of Nash Equilibrium for Networked Games: An Extended State Observer-Based Approach

This article aims to accommodate networked games in which the players' dynamics are subjected to unmodeled and disturbance terms. The unmodeled and disturbance terms are regarded as extended states for which observers are designed to estimate them. Compensating the players' dynamics with the observed values, the control laws are designed to achieve the robust seeking of the Nash equilibrium for networked games. First, we consider the case in which the players' dynamics are subject to time-varying disturbances only. In this case, the seeking strategy is developed by employing a smooth observer based on the proportional-integral (PI) control. By utilizing the designed strategy, we show that the players' actions would converge to a small neighborhood of the Nash equilibrium. Moreover, the ultimate bound can be adjusted to be arbitrarily small by tuning the control gains. Then, we further consider the case in which both an unmodeled term and a disturbance term coexist in the players' dynamics. In this case, we adapt the idea from the robust integral of the sign of the error (RISE) method in the strategy design to achieve the asymptotic seeking of the Nash equilibrium. Both strategies are analytically investigated via the Lyapunov stability analysis. The applications of the proposed methods for a network of velocity-actuated vehicles are discussed. Finally, the effectiveness of the proposed methods is verified via conducting numerical simulations.

Distributed Algorithms for Searching Generalized Nash Equilibrium of Noncooperative Games

In this paper, the distributed Nash equilibrium (NE) searching problem is investigated, where the feasible action sets are constrained by nonlinear inequalities and linear equations. Different from most of the existing investigations on distributed NE searching problems, we consider the case where both cost functions and feasible action sets depend on actions of all players, and each player can only have access to the information of its neighbors. To address this problem, a continuous-time distributed gradient-based projected algorithm is proposed, where a leader-following consensus algorithm is employed for each player to estimate actions of others. Under mild assumptions on cost functions and graphs, it is shown that players' actions asymptotically converge to a generalized NE. Simulation examples are presented to demonstrate the effectiveness of the theoretical results.

Pricing Mechanism With Noncooperative Game and Revenue Sharing Contract in Electricity Market

In this paper, a pricing mechanism is proposed for the electricity supply chain, which is consisting of one generation company (GC), multiple consumers, and competing utility companies (UCs). The UC participates in electricity supply chain management by a revenue sharing contract (RSC). In the electricity supply chain, the electricity real-time balance has an important role in the stable operation of the power system. Therefore, we introduce the demand response into the electricity supply chain to match supply with demand under forecast errors. Hence, we formulate a noncooperative game to characterize the interactions among the multiple competing UCs, which set the retail prices to maximize their profits. Besides, the UCs select their preferred contractual terms offered by the GC to maximize its profits and coordinate the electricity supply chain simultaneously. The existence and uniqueness of the Nash equilibrium (NE) are examined, and an iterative algorithm is developed to obtain the NE. Furthermore, we analyze the RSC that can coordinate the electricity supply chain and align the NE with the cooperative optimum under the RSC. Finally, numerical results demonstrate the superiority of the proposed model and the influence of market demand disruptions on the profits of the UCs, GC, and supply chain.