Tao Li

Xiaofeng Zong, Tao Li, Ji-Feng Zhang

This work is concerned with stochastic consensus conditions of multi-agent systems with both time-delays and measurement noises. For the case of additive noises, we develop some necessary conditions and sufficient conditions for stochastic weak consensus by estimating the differential resolvent function for delay equations. By the martingale convergence theorem, we obtain necessary conditions and sufficient conditions for stochastic strong consensus. For the case of multiplicative noises, we consider two kinds of time-delays, appeared in the measurement term and the noise term, respectively. We first show that stochastic weak consensus with the exponential convergence rate implies stochastic strong consensus. Then by constructing degenerate Lyapunov functional, we find the sufficient consensus conditions and show that stochastic consensus can be achieved by carefully choosing the control gain according to the noise intensities and the time-delay in the measurement term.

Yang Meng, Tao Li, Ji-Feng Zhang

In this note, the coordination of linear discrete-time multi-agent systems over digital networks is investigated with unmeasurable states in agents' dynamics. The quantized-observer based communication protocols and Certainty Equivalence principle based control protocols are proposed to characterize the inter-agent communication and the cooperative control in an integrative framework. By investigating the structural and asymptotic properties of the equations of stabilization and estimation errors nonlinearly coupled by the finite-level quantization scheme, some necessary conditions and sufficient conditions are given for the existence of such communication and control protocols to ensure the inter-agent state observation and cooperative stabilization. It is shown that these conditions come down to the simultaneous stabilizability and the detectability of the dynamics of agents and the structure of the communication network.

Wushun Chen, Tao Li

We consider the economic dispatch (ED) for an Energy Internet composed of energy routers (ERs), interconnected microgrids and main grid. The microgrid consists of several bus nodes associated with distributed generators (DGs) and intelligent control units (ICUs). We propose a distributed ED algorithm for the grid-connected microgrid, where each ICU iterates the estimated electricity price of the distribution system and the estimation for the average power mismatch of the whole microgrid by leader-following and average consensus algorithms, respectively. The ER iterates the incremental power exchanged with the distribution system. By constructing an auxiliary consensus system, we prove that if the communication topology of the Energy Internet contains a spanning tree with the ER as the root and there is a path from each ICU to the ER, then the estimated electricity price of the distribution system converges to its real value, the power supply and demand achieves balance and the ED achieves optimal asymptotically. Furthermore, we propose an autonomous distributed ED algorithm covering both grid-connected and isolated modes of the microgrid by feeding back the estimated average power mismatch for updating the incremental costs with penalty factor. It is proved that if the communication topology of the microgrid is connected and there exists an ICU bi-directionally neighboring the ER, then the microgrid can switches between the two modes reliably. The simulation results demonstrate the effectiveness of the proposed algorithms.

Jiexiang Wang, Tao Li, Xiwei Zhang

We analyze convergence of decentralized cooperative online estimation algorithms by a network of multiple nodes via information exchanging in an uncertain environment. Each node has a linear observation of an unknown parameter with randomly time-varying observation matrices. The underlying communication network is modeled by a sequence of random digraphs and is subjected to nonuniform random time-varying delays in channels. Each node runs an online estimation algorithm consisting of a consensus term taking a weighted sum of its own estimate and neighbours' delayed estimates, and an innovation term processing its own new measurement at each time step. By stochastic time-varying system, martingale convergence theories and the binomial expansion of random matrix products, we transform the convergence analysis of the algorithm into that of the mathematical expectation of random matrix products. Firstly, for the delay-free case, we show that the algorithm gains can be designed properly such that all nodes' estimates converge to the true parameter in mean square and almost surely if the observation matrices and communication graphs satisfy the stochastic spatiotemporal persistence of excitation condition. Secondly, for the case with time delays, we introduce delay matrices to model the random time-varying communication delays between nodes. It is shown that under the stochastic spatio-temporal persistence of excitation condition, for any given boundeddelays, proper algorithm gains can be designed to guarantee mean square convergence for the case with conditionally balanced digraphs.