Nonlinear PI robust adaptive control for uncertain multiple‐input multiple‐output nonlinear systems: Application to the visual servoing problem

Abstract

SummaryIn this work, a nonlinear proportional and integral controller is presented for multiple‐input multiple‐output (MIMO) unknown nonlinear systems in normal form with unknown disturbances. The proposed control laws utilize nonlinear PI gains with trigonometric terms along with neural network (NN) approximators in order to account for both unknown nonlinearities and control directions. A proper selection of the frequencies of the periodic functions used in the multiple control inputs ensures that, as the PI function increases, the periodic functions trace all possible control direction sign configurations. A new theoretical result is proved suitable for demonstrating the boundedness of the PI variables in a framework that also includes parameter estimation error terms. We then proceed to design a robust adaptive NN nonlinear PI MIMO controller that ensures both convergence of the tracking error to an arbitrarily small neighborhood of the origin and boundedness of all closed‐loop variables in the presence of unknown nonlinearities and external disturbances. An application to the uncalibrated visual servoing problem verifies the validity of our method.