Local basis functions in adaptive control of elastic systems

A new robust direct adaptive control method is presented using the cerebellar model arithmetic computer (CMAC). The method is also applicable when using neural networks, fuzzy sets, or spline models that contain local basis functions. Local basis functions are especially prone to weight drift (overlearning, parameter drift) when controlling systems with underdamped oscillations. The traditional robust weight update methods used to deal with this - leakage, e-modification, deadzone, and parameter projection - all require a significant sacrifice of performance. The proposed method uses a set of (finite) alternate weights trained on the control output. In addition, a set of weights is identified as the best choice found so far in the training, referred to as choice weights. The alternate weights and choice weights are used to keep weights from drifting without sacrificing performance. This new robust modification is shown to result in semi-global uniform ultimate boundedness of all signals, does not require knowledge of the bounds on uncertainties or nonlinearities, does not need pretraining, trains as quickly as other methods, and can achieve the same peak level of performance as the other methods. Simulation results demonstrate the method through trajectory tracking of a highly elastic, two-link flexible-joint robot.