China
Africa
Explore chapters and articles related to this topic
Deterministic Learning from Closed-Loop Control
Published in Cong Wang, David J. Hill, Deterministic Learning Theory, 2018
Consider the following nonlinear system in the strict-feedback form [119] () {x˙1=f1(x1)+x2x˙2=f2(x1,x2)+u
Backstepping Control
Published in Bogdan M. Wilamowski, J. David Irwin, Control and Mechatronics, 2018
The adaptive backstepping design with tuning functions is now generalized to a class of nonlinear system as in the following parametric strict-feedback form () x˙1=x2+ϕ1T(x1)θ+ψ1(x1)x˙2=x3+ϕ2T(x1,x2)θ+ψ2(x1,x2)⋮x˙n−1=xn+ϕn−1T(x1,…,xn−1)θ+ψn(x1,…,xn−1)x˙n=bu+ϕnT(x)θ+ψn(x),
Measurement feedback control of nonlinear systems: a small-gain approach
Published in Journal of Control and Decision, 2020
The existing study of robust nonlinear control with measurement feedback is by no means complete. The control designs proposed in this paper are restricted to systems in specific forms, e.g. strict-feedback form and output-feedback form. While popular in research to demonstrate designs with supporting theory, they are closer to mathematical abstraction of a model of some physical systems than direct modelling of physical systems, say, Euler–Lagrange equations. However, in given practical case studies, such results are a useful guide if not directly applicable. Nevertheless, despite the popularity of these forms, extensions of the designs to more general nonlinear systems would contribute a lot to nonlinear control theory. Again, these structural issues have an earlier form in discussions of how to extend control designs based on backstepping and forwarding to more general structures (Sepulchre, Jankovic, & Kokotović, 1997).
Adaptive neural network control for nonlinear non-strict feedback time-delay systems
Published in Systems Science & Control Engineering, 2021
However, the existing results on adaptive control for nonlinear input delay systems are mainly presented for strict-feedback systems. Theoretically, these control strategies cannot be directly applied to the systems with non-strict feedback form, which include the strict-feedback form as a special case. Even though there are some backstepping-based adaptive neural or fuzzy control schemes of non-strict feedback systems to be reported, in these existing control designs the proposed virtual control signals involve the information on the state variables of the subsequent subsystems. That generates the algebraic loop phenomenon and does not meet the backstepping design rule.
Adaptive fuzzy control for uncertain nonlinear systems
Published in Journal of Control and Decision, 2019
Apparently, it can be seen that there exist problems of ‘explosion of complexity’. In fact, the problems of ‘explosion of complexity’ are cased by repeated differentiations of virtual controllers. In order to overcome the problem of ‘explosion of complexity’ existing in the traditional adaptive backstepping recursive design process, Swaroop, Hedrick, Yip, and Gerdes (2000) first presented the dynamic surface control (DSC) technique for the nonlinear system. Subsequently, Wang, Liu, and Shi (2011) and Xu, Shi, Yang, and Sun (2014) presented the adaptive neural DSC schemes for SISO strict-feedback and pure-feedback nonlinear systems with measured states. It can be seen obviously that the presented control methods can deal with the problems of ‘explosion of complexity’, and it can make the controller become simpler simultaneously. Besides, Tong, Li, Li, and Liu (2011), Tong, Li, Feng, and Li (2011) and Long and Zhao (2016) presented adaptive fuzzy output-feedback control schemes for SISO and MIMO nonlinear systems with unmeasured states and interconnected large-scale systems with unmeasured states (Tong, Li, & Wang, 2013; Tong, Li, & Zhang, 2011). It is worth pointing out that all the aforementioned works are feasible under the presupposition that the controlled systems are in a pure-feedback or strict-feedback form. To overcome the difficulty in the traditional fuzzy adaptive backstepping control design, Yao and Tomizuka (1997, 2001) relaxed the system structure and presented the concept of semi-strict-feedback systems. The system can be expressed as where is the state vector, and u and y are the control input and output, respectively. is the known shape function, and is the vector of the unknown constant parameter. is the unknown nonlinear function.