Robust networked H ∞ synchronization of nonidentical chaotic Lur'e systems

We develop an optimal tracking control method for chaotic system with unknown dynamics and disturbances. The method allows the optimal cost function and the corresponding tracking control to update synchronously. According to the tracking error and the reference dynamics, the augmented system is constructed. Then the optimal tracking control problem is defined. The policy iteration (PI) is introduced to solve the min-max optimization problem. The off-policy adaptive dynamic programming (ADP) algorithm is then proposed to find the solution of the tracking Hamilton-Jacobi-Isaacs (HJI) equation online only using measured data and without any knowledge about the system dynamics. Critic neural network (CNN), action neural network (ANN), and disturbance neural network (DNN) are used to approximate the cost function, control, and disturbance. The weights of these networks compose the augmented weight matrix, and the uniformly ultimately bounded (UUB) of which is proven. The convergence of the tracking error system is also proven. Two examples are given to show the effectiveness of the proposed synchronous solution method for the chaotic system tracking problem.

Section: Introductionmentioning

confidence: 99%

Chaotic system optimal tracking using data-based synchronous method with unknown dynamics and disturbances

Song¹,

Wei²

2017

“…Recently, many valuable control methods have been developed to control chaotic systems, such as the sliding mode control method, [21] adaptive control method, [22] backstepping method, [23,24] the passivity feedback control method, [25,26] constrained generalized predictive control, [27] predictive control, [28][29][30] and other methods. [31,32] This paper investigates the control of chaos problem in PMSG via predictive control approach. This method is based on combining the delay feedback control method of continuous chaotic systems with the predictive control method of discrete time chaotic systems.…”

Section: Introductionmentioning

confidence: 99%

Predictive control of a chaotic permanent magnet synchronous generator in a wind turbine system

Messadi¹,

Mellit²,

Kemih³

et al. 2015

This paper investigates how to address the chaos problem in a permanent magnet synchronous generator (PMSG) in a wind turbine system. Predictive control approach is proposed to suppress chaotic behavior and make operating stable; the advantage of this method is that it can only be applied to one state of the wind turbine system. The use of the genetic algorithms to estimate the optimal parameter values of the wind turbine leads to maximization of the power generation. Moreover, some simulation results are included to visualize the effectiveness and robustness of the proposed method.

“…Since the synchronization between two identical chaotic systems with different initial conditions has been proposed by Pecora and Carroll in 1990, [1] chaos synchronization has received increasing attention due to its potential applications in many areas, such as secure communication, information processing, biological systems, and chemical reaction. Many methods have been proposed for chaos synchronization, including the feedback method, [2] back-stepping technique, [3] H ∞ approach, [4] sliding control, [5] and so on.…”

Section: Introductionmentioning

confidence: 99%

Observer of a class of chaotic systems: An application to Hindmarsh–Rose neuronal model

Luo¹,

Zhang²

2015

This paper first investigates the observer of a class of chaotic systems, and then discusses the synchronization between two identical Hindmarsh–Rose (HR) neuronal chaotic systems. Both the drive and response systems are assumed to have only one state variable available. By constructing proper observers, some novel criteria for synchronization are proposed via a scalar input. Numerical simulations are given to demonstrate the efficiency of the proposed approach.