This paper presents sufficient conditions for the existence of a common quadratic Lyapunov functions for two classes of switched linear systems which possess negative row strictly diagonally dominant and diagonalizable stable state matrices, respectively. Numerical examples will be given to verify the correctness of the proposed theorems.

This paper investigates the charging control strategy design problem of a large-scale plug-in electric vehicle (PEV) group, where each PEV aims to find an optimal charging strategy to minimize its own cost function. It should be noted that the collective behavior of the group is coupled in the individual cost function, which complicates the design of decentralized charging strategies. To obtain the decentralized charging strategy, a mean-field game (MFG) formulation is proposed where a penalty on collective consensus is embedded and a class of mean-field coupled time-varying stochastic systems is targeted for solving the MFG which involves the charging model of PEVs as a special case. Then, an augmented system with dimension extension and the policy iteration algorithm are proposed to solve the mean-field game problem for the class of mean-field coupled time-varying stochastic systems. Moreover, analysis of the convergence of proposed approach has been studied. Last, simulation is conducted to illustrate the effectiveness of the proposed MFG-based charging control strategy and shows that the charging control strategy can achieve desired mean-field state and impact to the power grid can be buffered.

This paper studies the infinite time horizon optimal control problem for continuous-time nonlinear systems. A completely model-free approximate optimal control design method is proposed, which only makes use of the real-time measured data from trajectories instead of a dynamical model of the system. This approach is based on the actor-critic structure, where the weights of the critic neural network and the actor neural network are updated sequentially by the method of weighted residuals. It should be noted that an external input is introduced to replace the input-to-state dynamics to improve the control policy. Moreover, strict proof of convergence to the optimal solution along with the stability of the closed-loop system is given. Finally, a numerical example is given to show the efficiency of the method.