In this paper, we propose a new economic dispatch model with random wind power, demand response and carbon tax. The specific feature of the demand response model is that the consumer's electricity demand is divided into two parts: necessary part and non-essential part. The part of the consumer's participation in the demand response is the non-essential part of the electricity consumption. The optimal dispatch objective is to obtain the minimum total cost (fuel cost, random wind power cost and emission cost) and the maximum consumer's non-essential demand response benefit while satisfying some given constraints. In order to solve the optimal dispatch objective, a multi-subpopulation bat optimization algorithm (MSPBA) is proposed by using different search strategies. Finally, a case of an economic dispatch model is given to verify the feasibility and effectiveness of the established mathematical model and proposed algorithm. The economic dispatch model includes three thermal generators, two wind turbines and two consumers. The simulation results show that the proposed model can reduce the consumer's electricity demand, reduce fuel cost and reduce the impact on the environment while considering random wind energy, non-essential demand response and carbon tax. In addition, the superiority of the proposed algorithm is verified by comparing with the optimization results of CPLEX+YALMIP toolbox for MATLAB, BA, DBA and ILSSIWBA.
In this paper, the problem of adaptive output feedback stabilization is investigated for a class of nonlinear systems with sensor uncertainty in measured output and a growth rate of polynomial-of-output multiplying an unknown constant in the nonlinear terms. By developing a dual-domination approach, an adaptive observer and an output feedback controller are designed to stabilize the nonlinear system by directly utilizing the measured output with uncertainty. Besides, two types of extension are made such that the proposed methods of adaptive output feedback stabilization can be applied for nonlinear systems with a large range of sensor uncertainty. Finally, numerical simulations are provided to illustrate the correctness of the theoretical results.
The problem of observer design for a class of nonlinear discrete-time systems with time-delay is considered. A new approach of nonlinear observer design is proposed for the class of systems. Based on differential mean value theory, the error dynamic is transformed into linear parameter variable system. By using Lyapunov stability theory and Schur complement lemma, the sufficient conditions expressed in terms of matrix inequalities are obtained to guarantee the observer error converges asymptotically to zero. Furthermore, the problem of observer design with affine gain is investigated. The computing method for observer gain matrix is given and it is also demonstrated that the observer error converges asymptotically to zero. Finally, an illustrative example is given to validate the effectiveness of the proposed method.
In this paper, a novel consensus algorithm is presented to handle with the leader-following consensus problem for lower-triangular nonlinear MASs (multi-agent systems) with unknown controller and measurement sensitivities under a given undirected topology. As distinguished from the existing results, the proposed consensus algorithm can tolerate to a relative wide range of controller and measurement sensitivities. We present some important matrix inequalities, especially a class of matrix inequalities with multiplicative noises. Based on these results and a dual-domination gain method, the output consensus error with unknown measurement noises can be used to construct the compensator for each follower directly. Then, a new distributed output feedback control is designed to enable the MASs to reach consensus in the presence of large controller perturbations. In view of a Lyapunov function, sufficient conditions are presented to guarantee that the states of the leader and followers can achieve consensus asymptotically. In the end, the proposed consensus algorithm is tested and verified by an illustrative example.
In this paper, a robust sampled-data observer is proposed for Lipschitz nonlinear systems. Under the minimum-phase condition, it is shown that there always exists a sampling period such that the estimation errors converge to zero for whatever large Lipschitz constant. The optimal sampling period can also be achieved by solving an optimal problem based on linear matrix inequalities (LMIs). The design methods are extended to Lipschitz nonlinear systems with large external disturbances as well. In such a case, the estimation errors converge to a small region of the origin. The size of the region can be small enough by selecting a proper parameter. Compared with the existing results, the design parameters can be easily obtained by solving LMIs.