Robust LS-SVM-based adaptive constrained control for a class of uncertain nonlinear systems with time-varying predefined performance

• Published in: Communications in nonlinear science & numerical simulation Vol. 56; pp. 561 - 587
• Main Authors: Luo, Jianjun, Wei, Caisheng, Dai, Honghua, Yuan, Jianping
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.03.2018; Elsevier Science Ltd
• Subjects: Adaptive control; Approximation; Computer simulation; Control systems design; Design parameters; Differentiators; Finite-time-convergent differentiator; Least square support vector machine; Nonlinear systems; Predefined performance; Robust control; Robustness (mathematics); Saturation; Tracking errors; Predefined performance; Least square support vector machine; Nonlinear systems; Finite-time-convergent differentiator
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2017.09.004

•A novel predefined performance function with time-varying design parameters is proposed which improves the transient and steady-state performance of the controlled systems.•A quite simple finite-time-convergent differentiator is developed to obtain accurate estimations of the unknown state variables and derivatives of the virtual controllers.•Only two least-square-support-vector-machine-based approximators involving two design parameters are utilized to approximate the unknown nonlinearities with high accuracy without any aid of specialized optimization techniques. This paper focuses on robust adaptive control for a class of uncertain nonlinear systems subject to input saturation and external disturbance with guaranteed predefined tracking performance. To reduce the limitations of classical predefined performance control method in the presence of unknown initial tracking errors, a novel predefined performance function with time-varying design parameters is first proposed. Then, aiming at reducing the complexity of nonlinear approximations, only two least-square-support-vector-machine-based (LS-SVM-based) approximators with two design parameters are required through norm form transformation of the original system. Further, a novel LS-SVM-based adaptive constrained control scheme is developed under the time-vary predefined performance using backstepping technique. Wherein, to avoid the tedious analysis and repeated differentiations of virtual control laws in the backstepping technique, a simple and robust finite-time-convergent differentiator is devised to only extract its first-order derivative at each step in the presence of external disturbance. In this sense, the inherent demerit of backstepping technique–“explosion of terms” brought by the recursive virtual controller design is conquered. Moreover, an auxiliary system is designed to compensate the control saturation. Finally, three groups of numerical simulations are employed to validate the effectiveness of the newly developed differentiator and the proposed adaptive constrained control scheme.