Reinforcement Learning Design-Based Adaptive Tracking Control With Less Learning Parameters for Nonlinear Discrete-Time MIMO Systems

Abstract

Based on the neural network (NN) approximator, an online reinforcement learning algorithm is proposed for a class of affine multiple input and multiple output (MIMO) nonlinear discrete-time systems with unknown functions and disturbances. In the design procedure, two networks are provided where one is an action network to generate an optimal control signal and the other is a critic network to approximate the cost function. An optimal control signal and adaptation laws can be generated based on two NNs. In the previous approaches, the weights of critic and action networks are updated based on the gradient descent rule and the estimations of optimal weight vectors are directly adjusted in the design. Consequently, compared with the existing results, the main contributions of this paper are: 1) only two parameters are needed to be adjusted, and thus the number of the adaptation laws is smaller than the previous results and 2) the updating parameters do not depend on the number of the subsystems for MIMO systems and the tuning rules are replaced by adjusting the norms on optimal weight vectors in both action and critic networks. It is proven that the tracking errors, the adaptation laws, and the control inputs are uniformly bounded using Lyapunov analysis method. The simulation examples are employed to illustrate the effectiveness of the proposed algorithm.

Recurrent-Neural-Network-Based Multivariable Adaptive Control for a Class of Nonlinear Dynamic Systems With Time-Varying Delay

“…4) The amplitude of the switching gain to obtain the specific convergent set of switching surface is verified. 5) Simulations, including the reinforcement learning control [9], the robust control for known NARMA with uncertainty, and the proposed RNNBMAC for the unknown NARMA with known time-varying delay, are presented to confirm the effectiveness and robustness of our developed RNNBMAC.…”

“…In the past, most people used a multilayer neural network (MNN) or a radial basis function neural network (RBFNN), combined with tapped delays for the input, and a backpropagation or gradient training algorithm to deal with the dynamic problem [7]- [9]. On the other hand, recurrent neural networks (RNNs) have important capabilities not shown in MNN or RBFNN, such as dynamic mapping without the need for tapped delays for the input.…”

Spatial Trajectory Tracking Control of a Fully Actuated Helicopter in Known Static Environment

“…21 is introduced to improve the robustness in the presence of the RBFNN approximation error ε 1 [63][64][65][66]. Furthermore, σ 1Ŵ1 can easily be replaced by e-modification adaptation term like σ 1 |r new |Ŵ 1 .…”

Neural network-based adaptive control for a class of chemical reactor systems with non-symmetric dead-zone

“…The study of discrete system has scored important achievements, and some adaptive control algorithms were introduce in [27][28][29][30][31][32], with the help of neural network the unknown functions of these discrete-time systems could be approximated, then, the appropriate controllers are introduced, and the stability of the closed-loop discrete-time systems are guaranteed. But, because of these algorithms need to satisfy the strict feedback form or matching condition [33][34][35][36]52], so they could not satisfy the stabilized of the systems of pure feedback form [37][38].…”