Adaptive prescribed performance control of nonlinear output‐feedback systems with unknown control direction

Abstract

Summary This paper focuses on the output‐feedback tracking control problem for a class of nonlinear systems with both unknown nonlinearities and unknown control directions. An adaptive prescribed performance controller combined with a Nussbaum gain and a dividing line is proposed to solve the problem. Compared with the existing results, (i) both the convergence rate and the ultimate bound of the tracking error can be prescribed; (ii) no approximating structures such as neuro/fuzzy systems are used, regardless of unknown nonlinear functions; and (iii) the computational burden is alleviated in the sense that the iterative calculation of command derivatives is avoided and the number of online learning parameters is largely reduced. Simulation results are given to further illustrate the established theoretical findings.

Global output feedback control for nonlinear cascade systems with unknown output functions and unknown control directions

“…Remark Assumptions and are common conditions used in the work of Jiang et al and Wu et al, while Assumption is used by Wu et al Assumption indicates that the considered system is different from the related results Jiang et al, Wu et al, and Zhang and Yang in that the output function allows to be nondifferentiable and does not require any prior knowledge about the upper and lower bounds of the generalized derivative.…”

“…A unified framework was presented for the global regulation of nonlinear cascade systems with iISS inverse dynamics and unknown control directions in the work of Jiang et al; the results of Jiang et al were extended to more general nonlinear uncertain systems with unmeasurable state components, where the observer gain was designed by a Riccati differential equation. In addition, the global adaptive output regulation for nonlinear systems with iISS inverse dynamic was investigated in the work of Xu et al Recently, the global robust regulation problem was considered by Wu et al for cascade nonlinear systems subject to the external disturbance, and an adaptive prescribed performance tracking control problem for nonlinear output feedback systems with unknown nonlinearities was studied in the work of Zhang and Yang …”

“…The output feedback control results in these works all need to know the state information of the first subsystem, that is, the output equation is y = x 1 . As claimed by Zhai and Qian, in practical control systems, the relationship between the sensors output (eg, voltage output from the sensor) and x 1 of the system (eg, real physical value such as displacement, angle, temperature, etc.)…”

“…The main contributions of this paper are summarized as follows: Compared with the existing output feedback control results, the restrictive conditions on the output function are relaxed. Particularly, the unknown output function involved in this paper only requires to have a generalized derivative (ie, the output function does not need to be differentiable as in other works), and the prior knowledge on the upper and lower bounds of the generalized derivative need not to be known. Although the feedback control schemes for nonlinear cascade systems with known output functions have been developed, they rely on the state information x 1 which is not available in the concerned control problem; thus, they cannot be directly applied to the system concerned in this paper. More importantly, when the unknown output function and the unknown control direction exist simultaneously, the analysis scheme provided in the work of Jiang et al and Wu et al will no longer be feasible since the integrability of the derivative of the Lyapunov function depends on the generalized derivative of the unknown output function.…”

Low‐complexity adaptive tracking control of MIMO nonlinear systems with unknown control directions

“…To counteract the effects caused by disturbances, a set of sliding mode observers were employed in the work of Chen et al, yielding the structure of the controller complicated. As the solutions of the aforesaid problems have been reported in other works, it is notable that the a priori known control direction was necessary in the works of Theodorakopoulos and Rovithakis and Zhang and Yang and that the methods proposed in the works of Zhang and Yang were suitable only for SISO systems. Until now, the problem of low‐complexity robust control of MIMO nonlinear systems under unknown control directions still remains open.…”