Finding a near-optimal neural-adaptive control solution without increasing the training time

This paper proposes a new robust modification for weight update laws in direct adaptive control using the Cerebellar Model Articulation Controller (CMAC) that will quickly find a near-optimal control. The method uses two sets of supervisory weights, identified using cost functionals as the best found so far in the training, to guide the online weight updates in a supervised leakage term. The first set compensates for nonlinearities along the desired trajectory, acting like a feedforward component. Once the error has been driven close to the origin, additional supervisory weights seek an optimal control that penalizes extra control effort and error about the origin, providing a near-optimal feedback component. The algorithm to identify these best-weights-so-far takes advantage of the local nature of the CMAC basis function domains i.e. local cost functionals correspond to a particular weight. A Lyapunov analysis guarantees uniformly ultimately bounded signals. Simulations with a flexible-joint arm, where the control needs to compensate for gravity and a sinusoidal external disturbance, show that the proposed method significantly outperforms both a CMAC with trained with leakage and a model-based LQR control, without increased control effort or training time.