Adaptive Prescribed Performance Output Regulation of Nonlinear Systems with Nonlinear Exosystems

Jia, Fujin; Cui, Lei; Lu, Junwei; Chu, Yu‐Ming

doi:10.1007/s12555-019-0443-4

Cited by 15 publications

(6 citation statements)

References 29 publications

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“…Therefore, ε 2 has the same sign as ε 3 and u has a sign opposite of ε 2 . By analogy, one can conclude that ε i , i = 1, 2, 3 and u i , i = 1, 2, 3(u = u 3 ) have the same sign with each other, respectively, but ε i , i = 1, 2, 3 have opposite sign against u i , i = 1, 2, 3(u = u 3 ), which helps the use of the condition |u| > |u 1 + u 2 | in (28).…”

Section: B Proposed Theorem and Proofmentioning

confidence: 90%

Approximation-free control based on the bioinspired reference model for suspension systems with uncertainty and unknown nonlinearity

Hu¹,

Wen²,

Yin³

et al. 2022

Preprint

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Uncertainty and unknown nonlinearity are often inevitable in the suspension systems, which were often solved using fuzzy logic system (FLS) or neural networks (NNs). However, these methods are restricted by the structural complexity of the controller and the huge computing cost. Meanwhile, the estimation error of such approximators is affected by adopted adaptive laws and learning gains. Thus, in view of the above problem, this paper proposes the approximation-free control based on the bioinspired reference model for a class of uncertain suspension systems with unknown nonlinearity. The proposed method integrates the superior vibration suppression of the bioinspired reference model and the structural advantage of the prescribed performance function (PPF) in approximation-free control. Then, the vibration suppression performance is improved, the calculation burden is relieved, and the transient performance is improved, which is analyzed theoretically in this paper. Finally, the simulation results validate the approach, and the comparisons show the advantages of the proposed control method in terms of good vibration suppression, fast convergence, and less calculation burden.

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Section: B Proposed Theorem and Proofmentioning

confidence: 90%

Approximation-free control based on the bioinspired reference model for suspension systems with uncertainty and unknown nonlinearity

Hu¹,

Wen²,

Yin³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Remark Different from control methods in References 13,14,30, and 31, the unknown function F i contains all the partial derivatives of the virtual controller a i , so as to approximate F i with a fuzzy logic system, so that the designed virtual controller a i does not contain the partial derivative of a i − 1 . Therefore, this method avoids the “amount of calculation” problem of the backstepping method.…”

Section: Adaptive Fuzzy Control Designmentioning

confidence: 99%

“…Assumption 3 (14). The function 𝜅(v) is a polynomial about v, and its coefficient is determined by 𝛼.…”

Section: Internal Modelmentioning

confidence: 99%

“…In Reference 13, the output regulation for a class of uncertain nonlinear systems with time‐delay and immeasurable states was concerned. Reference 14 studied the prescribed performance output regulation problem for a class of nonlinear uncertain strict‐feedback systems which are driven by nonlinear exosystems. The common characteristic of the above control methods is that the virtual control coefficient of the system is assumed to be 1.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive finite‐time control for output regulation of nonlinear systems with completely unknown control directions

Jia

LuJunwei

LiYongmin

2021

Adaptive Control & Signal

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This article studies the finite‐time output regulation problem for nonlinear strict‐feedback systems with completely unknown control directions and unknown functions. First, according to the necessary conditions for the solvability of the output regulation problem, the output regulation problem of nonlinear strict‐feedback systems and the external system is transformed into a stabilization problem of nonlinear systems. Second, an internal model with external signals is designed. Third, based on finite time, fuzzy control, output feedback control, and Nussbaum gain functions, the control law is designed so that all signals of the closed‐loop system are the semi‐global practically finite‐time stable (SGPFS), and the tracking error converges to a small neighborhood of the origin in a finite‐time. Finally, the proposed algorithm is applied to the finite‐time tracking problem of Chua's oscillator system.

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“…In [7] is introduced an optimal average cost learning framework for output regulation controller design when linear systems have unknown dynamics. In [8] is used a fuzzy adaptive output feedback control scheme to approximate unknown functions for a class of nonlinear uncertain strict-feedback systems under the action of nonlinear exosystems. Moreover, in the case of PDE's introducing an adaptive internal model that estimates unknown frequencies, output regulation, and disturbance rejection are achieved, even if the disturbance is generated by an unknown finitedimensional exosystem [9], [10], or the exosystem coefficients are time-varying [11].…”

Section: Introductionmentioning

confidence: 99%

On the Output Regulation for an Underactuated Inverse Pendulum When the Exosystem Is a High-Gain Observer

et al. 2023

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This paper is devoted to solving the output regulation problem on the basis of the new Francis equations for arbitrary reference/disturbance signals, whose model are obtained by High-Gain observers, providing in this way, the regulation of unmodeled but measurable reference signals. The design is given by fixing a steady state globally attractive by means of LMIs which allows controlling the decay rate by considering input bounds; while the regulation problem is solved by computing the steady-state input based on a modified set of the regulation equations, when the exosystem is constructed upon High-Gain observers, extending in this way, the classical output regulation theory for unmodeled reference/disturbance signal. The Furuta pendulum is used to illustrate the viability of the proposed approach.INDEX TERMS Output regulation, high-gain observer, linear matrix inequality.

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Adaptive Prescribed Performance Output Regulation of Nonlinear Systems with Nonlinear Exosystems

Cited by 15 publications

References 29 publications

Approximation-free control based on the bioinspired reference model for suspension systems with uncertainty and unknown nonlinearity

Approximation-free control based on the bioinspired reference model for suspension systems with uncertainty and unknown nonlinearity

Adaptive finite‐time control for output regulation of nonlinear systems with completely unknown control directions

On the Output Regulation for an Underactuated Inverse Pendulum When the Exosystem Is a High-Gain Observer

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