Command‐filtered‐based neuroadaptive control for multi‐input multi‐output saturated nonstrict‐feedback nonlinear systems with prescribed tracking performance

• Published in: International journal of adaptive control and signal processing Vol. 37; no. 3; pp. 617 - 643
• Main Authors: Yang, Di, Liu, Weijun, Guo, Chen
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.03.2023
• Subjects: adaptive control; asymmetric input saturation; Asymmetry; command filtered backstepping; Compensators; Controllability; Controllers; Convergence; Feedback; Hyperbolic functions; Mathematical analysis; MIMO nonstrict‐feedback nonlinear systems; neural network; Neural networks; Nonlinear systems; Parameters; prescribed performance; Singularity (mathematics); Time constant; Tracking errors
• ISSN: 0890-6327; 1099-1115
• DOI: 10.1002/acs.3539

Summary In this article, the prescribed performance control strategy is extended to multi‐input multi‐output nonstrict‐feedback nonlinear systems with asymmetric input saturation, and not only each element in tracking error vector converges to a prescribed small region within preassigned finite time, but also the converging mode during the preset time is prespecifiable and controllable explicitly. By blending the barrier function with novel speed function, a prescribed performance controller using command‐filtered‐based vector‐backstepping design framework is proposed to steer the tracking error vector for the first time, where the boundedness of filter errors is guaranteed by sufficiently small time constant and an error compensator is constructed to handle the effects of filter errors. To attenuate the adverse effects resulted from nondifferentiable input saturation, hyperbolic tangent function is utilized to estimate asymmetric saturation function such that the control input is designed as a new state variable with initial value of zero in augmented system. Nussbaum function is employed to overcome singularity problem caused by the differentiation of hyperbolic tangent function. At each step of backstepping design, the universal approximation property of neural network and the command filter system are utilized to approximate uncertain dynamics and to solve algebraic loop obstacle due to nonstrict‐feedback structure, respectively. Moreover, only one parameter needs to be updated online to cope with the lumped uncertain dynamics by virtual parameter technology, rendering a control strategy with low complexity computation. The validity of the presented controller is verified by theoretical analysis and two‐link robotic system.