In this paper, we study the distributed generalized Nash equilibrium seeking problem of non-cooperative games in dynamic environment. Each player in the game aims to minimize its own time-varying cost function subject to a local action set. The action sets of all players are coupled through a shared convex inequality constraint. Each player can only have access to its own cost function, its own set constraint and a local block of the inequality constraint, and can only communicate with its neighbours via a connected graph. Moreover, players do not have prior knowledge of their future cost functions. To address this problem, an online distributed algorithm is proposed based on consensus algorithms and a primal-dual strategy. The performance of the algorithm is measured by a dynamic regret. Under mild assumptions on graphs and cost functions, we prove that the regret, as well as the violation of inequality constraint, is bounded by product of a term depending on the deviation of generalized Nash equilibrium sequence and a sublinear function of learning time. A simulation is presented to demonstrate the effectiveness of our theoretical results.

This article analyzes the global stability of synchronous reference frame phase-locked loops (SRF-PLLs) from a large signal viewpoint. First, a large-signal model of SRF-PLL is accurately established, without applying any linearization method. Then, according to the phase portrait and Lyapunov argument, the global performance of SRF-PLL is discussed in the nonlinear frame. Compared with the small-signal analysis methods, the proposed analysis, not relying on the small-signal model and linearization method, provides a global discussion of the SRF-PLL performance. The contributions of this article are as follows. First, it is found that SRF-PLL has infinite equilibrium points, including stable points and saddle points. Second, it provides a way to divide the global region of SRF-PLL into many small regions. In each small region, the SRF-PLL only has one stable equilibrium point. And for any initial states $(\tilde{\theta }(t_0),\tilde{\omega }(t_0))$ in a small region, all states $(\tilde{\theta }(t),\tilde{\omega }(t)),t>t_0$ will remain in this small region, and SRF-PLL will converge to the unique stable equilibrium point of this small region. Third, by dividing the global region of SRF-PLL into many small regions, it is found that when the frequency of grids varies largely, the SRF-PLL will converge to a new equilibrium point that is far away from the original equilibrium point. It is the reason why the frequency convergence of SRF-PLL has many oscillations and SRF-PLL has a rather slow dynamic, when the frequency changes largely. The experimental results are provided to verify the proposed global stability analysis of SRF-PLL.

Distributed dynamic compensators play a key role in the output consensus problem of heterogeneous nonlinear multiagent systems. The existing distributed dynamic compensators require the compensators’ information to be exchanged through communication networks and to satisfy additional stability conditions in the controller design. This article proposes a distributed dynamic compensator to address the adaptive output consensus problem of heterogeneous nonlinear multiagent systems with unknown parameters. The distributed dynamic compensator only requires the output information to be exchanged through communication networks. In addition, the distributed dynamic compensator converts the original consensus problem into standard asymptotic tracking problems of nonlinear systems, without requiring extra stability conditions in the literature. Then, well-established and standard control approaches can be used to design tracking controllers and solve the standard asymptotic tracking problems. This article adopts the standard adaptive backstepping approach as an example to design adaptive tracking controllers. It is further proved that all signals in the closed-loop system are globally uniformly bounded, and the proposed scheme enables the outputs of all agents to track the leader’s signal asymptotically. A simulation is presented to illustrate the effectiveness of the design methodology.

This paper aims at addressing the problem of global adaptive stabilisation by output feedback for a class of nonlinear systems, in which both the input and output are logarithmically quantised. The nonlinear functions of the systems are not necessary to be completely known and contain time-varying parameters that belong to an unknown bounded set. Based on dynamic high-gain technique, a linear-like quantised controller computed from quantised output is constructed and a guideline is derived to select the parameters of the quantisers. It is proved that, with the proposed scheme, all the states of the system can be globally steered to the origin while keeping the other signals of the closed-loop system bounded.