Adaptive Compensation and Adaptive Optimal Control of a Single Link Manipulator

Abstract

This paper presents an online solution to the finite-horizon optimal tracking control problem for continuous-time nonlinear systems with partially unknown dynamics, based on an Adaptive Dynamic Programming (ADP) approach. The method employs a dual-approximation identifier–critic neural network (NN) architecture, with both networks tuned simultaneously during online implementation. The unknown weights of the identifier and critic activation functions are estimated using a filter-based adaptive algorithm, which provides a simple online validation of the persistence of excitation (PE) condition required for convergence of the control parameters. The controller is evaluated in simulation on an ideal single-link robotic manipulator with partially unknown dynamics and is compared against two classical adaptive nonlinear control strategies: an adaptive Lyapunov-based nonlinear (ALN) controller and an adaptive backstepping (ABS) controller. Performance is assessed in terms of adaptive parameter convergence, tracking accuracy, control input smoothness, and tuning complexity. The ADP-based controller demonstrates the most intuitive tuning process, as its parameters are directly linked to observed system behaviour, and achieves superior tracking performance with the smoothest control input among the three controllers.