Real-Time Progressive Learning: Mutually Reinforcing Learning and Control with Neural-Network-Based Selective Memory

Memory, as the basis of learning, determines the storage, update and forgetting of the knowledge and further determines the efficiency of learning. Featured with a mechanism of memory, a radial basis function neural network (RBFNN) based learning control scheme named real-time progressive learning (RTPL) is proposed to learn the unknown dynamics of the system with guaranteed stability and closed-loop performance. Instead of the stochastic gradient descent (SGD) update law in adaptive neural control (ANC), RTPL adopts the selective memory recursive least squares (SMRLS) algorithm to update the weights of the RBFNN. Through SMRLS, the approximation capabilities of the RBFNN are uniformly distributed over the feature space and thus the passive knowledge forgetting phenomenon of SGD method is suppressed. Subsequently, RTPL achieves the following merits over the classical ANC: 1) guaranteed learning capability under low-level persistent excitation (PE), 2) improved learning performance (learning speed, accuracy and generalization capability), and 3) low gain requirement ensuring robustness of RTPL in practical applications. Moreover, the RTPL based learning and control will gradually reinforce each other during the task execution, making it appropriate for long-term learning control tasks. As an example, RTPL is used to address the tracking control problem of a class of nonlinear systems with RBFNN being an adaptive feedforward controller. Corresponding theoretical analysis and simulation studies demonstrate the effectiveness of RTPL.