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

Abstract

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.

Integral reinforcement learning solutions for a synchronisation system with constrained policies

“…An IRL approach based on a policy iteration mechanism is adopted for continuous‐time control systems in [16]. An off‐policy IRL optimal control tracking algorithm is proposed for a Lorenz chaotic system in [20]. Another off‐policy RL control algorithm is adopted to solve a rotational/translational actuator non‐linear benchmark problem in [21].…”

Chaos Control in Chaotic Dynamical Systems Via Auto-tuning Hamilton Energy Feedback

“…In particular, the research related to tracking control of the chaotic system itself focuses on two different classes. One of these two classes is where the system output is directed to a specific chaotic output [9,13,14,15,16]. Another category of chaotic system tracking is that anti control of the chaos.…”

A novel stable value iteration-based approximate dynamic programming algorithm for discrete-time nonlinear systems

“…The iterative value functions and control laws are obtained iteratively, and the iterative control laws must stabilize the system. [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] An initial stabilizing control law is required, however, it is often difficult to obtain. While in most applications, fewer iterations are required, and computationally demanding is more than that of the VI iteration algorithm.…”