In this paper, a new online scheme is presented to design the optimal coordination control for the consensus problem of multiagent differential games by fuzzy adaptive dynamic programming, which brings together game theory, generalized fuzzy hyperbolic model (GFHM), and adaptive dynamic programming. In general, the optimal coordination control for multiagent differential games is the solution of the coupled Hamilton-Jacobi (HJ) equations. Here, for the first time, GFHMs are used to approximate the solutions (value functions) of the coupled HJ equations, based on policy iteration algorithm. Namely, for each agent, GFHM is used to capture the mapping between the local consensus error and local value function. Since our scheme uses the single-network architecture for each agent (which eliminates the action network model compared with dual-network architecture), it is a more reasonable architecture for multiagent systems. Furthermore, the approximation solution is utilized to obtain the optimal coordination control. Finally, we give the stability analysis for our scheme, and prove the weight estimation error and the local consensus error are uniformly ultimately bounded. Further, the control node trajectory is proven to be cooperative uniformly ultimately bounded.

Leader-Based Optimal Coordination Control for the Consensus Problem of Multiagent Differential Games via Fuzzy Adaptive Dynamic Programming

This paper focuses on the problem of neural-network-based decentralized adaptive output-feedback control for a class of nonlinear strict-feedback large-scale stochastic systems. The dynamic surface control technique is used to avoid the explosion of computational complexity in the backstepping design process. A novel direct adaptive neural network approximation method is proposed to approximate the unknown and desired control input signals instead of the unknown nonlinear functions. It is shown that the designed controller can guarantee all the signals in the closed-loop system to be semiglobally uniformly ultimately bounded in a mean square. Simulation results are provided to demonstrate the effectiveness of the developed control design approach.

Neural-Network-Based Decentralized Adaptive Output-Feedback Control for Large-Scale Stochastic Nonlinear Systems

This paper presents a method to control chaotic behavior of a typical Smart Grid based on generalized fuzzy hyperbolic model (GFHM). As more and more distributed generations (DG) are incorporated into the Smart Grid, the chaotic behavior occurs increasingly. To verify the behavior, a dynamic model which describes a power system with DG is presented firstly. Then, the simulation result shows that the power system can lead to chaos under certain initial conditions. Based on the universal approximation of GFHM, we confirm that the chaotic behavior could be suppressed by a new controller, which is designed by means of solving a linear matrix inequality (LMI). This approach could make a good application to suppress the chaos in Smart Grid. Finally, a numerical example is given to demonstrate the effectiveness of the proposed chaotic suppression strategy.

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Chaotic Dynamics in Smart Grid and Suppression Scheme via Generalized Fuzzy Hyperbolic Model

This paper develops a guaranteed cost networked control (GCNC) method for Takagi-Sugeno (T-S) fuzzy systems with time delays. The state feedback controller is designed via the networked control system (NCS) theory. The stability of the overall fuzzy system using GCNC is also established. Network-induced delay in network transmission and packet dropout are analyzed. Some deductions are also extended to uncertain systems. Simulation results show the validity of the present control scheme

Guaranteed Cost Networked Control for T–S Fuzzy Systems With Time Delays

An adaptive fuzzy controller design is studied for uncertain nonlinear systems in this paper. The considered systems are of the discrete-time form in a triangular structure and include the backlash and the external disturbance. By using the prediction function of future states, the systems are transformed into an n-step ahead predictor. The fuzzy logic systems (FLSs) are used to approximate the unknown functions, unknown backlash, and backlash inversion, respectively. A discrete-time tuning algorithm is developed to estimate the optimal fuzzy parameters. Compared with the previous works for the discrete-time systems with backlash, the main contributions of the paper are that 1) the rigorous restriction for the functional estimation error is removed, and 2) the external disturbance is bounded, but the bound is not required to be known. A novel controller and the adaptation laws are constructed by using the discrete Taylor series expansion and the difference Lyapunov analysis, and thus, those limitations in the previous works are overcome. It is proven that all the signals in the closed-loop system are bounded and that the system output can be to follow the reference signal to a bounded compact set. A simulation example is provided to illustrate the effectiveness of the proposed approach.

Adaptive Fuzzy Control for a Class of Nonlinear Discrete-Time Systems With Backlash

In this paper, we propose a new fuzzy hyperbolic model for a class of complex systems, which is difficult to model. The fuzzy hyperbolic model is a nonlinear model in nature and can be easily derived from a set of fuzzy rules. It can also be seen as a feedforward neural network model and so we can identify the model parameters by BP-algorithm. We prove that the stable controller can be designed based on linear system theory. Two methods of designing the controller for the fuzzy hyperbolic model are proposed. The results of simulation support the effectiveness of the model and the control scheme.

Quan Yongbing

Papers

Modeling, identification, and control of a class of nonlinear systems