Adaptive Learning Control of Uncertain Systems via Weight and Intrinsic Plasticity-Based Neural Networks

Although the "universal" approximation and learning capabilities of artificial neural networks (ANNs) are widely used for the control design of continuous nonlinear systems, two important issues regarding the mathematical model of ANNs and their function approximation are often overlooked. The first is that the neuronal intrinsic plasticity (IP) mechanism of the basis function is not rigorously considered in the control context. The second is the common assumption that the input of the neural network (NN) must lie within a compact set, despite a lack of theoretical justification. If both factors are incorporated into the function approximation, the control design becomes more challenging, as there is currently no a priori knowledge on how to determine the optimal IP parameters and how to ensure the effectiveness of the NN-based function approximation. In this article, we propose a novel IP-NN-associated control method for nonlinear systems. First, inspired by the physiological characteristics of biological nervous systems, we develop an alternative mathematical model for NNs that includes both weight plasticity and IP plasticity. However, due to the introduction of the neuron's IP mechanism, the original basis function is no longer directly available for the control design. By invoking the mean value theorem, we convert the nonaffine function with the IP parameters into an approximately affine form. Together with the virtual parameter estimation technique, only the core information about the basis function is used, and the detailed IP parameter is not needed. Second, based on the Lyapunov stability theorem, we propose an alternative barrier certificate to theoretically guarantee the existence of a compact set and to prevent the NN input from exceeding this set. Experimental verification on a 3-DoF robotic manipulator also confirms the benefits of the proposed IP-NN-based control.