Adaptive tracking control for a class of nonlinear non-strict-feedback systems

Li, Qiuni; Yang, Rennong; Liu, Zongcheng

doi:10.1007/s11071-016-3327-7

Cited by 25 publications

(22 citation statements)

References 30 publications

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“…Remark 1: Despite some efforts such as [27] and [35] have been made to relax the boundedness assumption of control gain functions, the considered works have limited application because they consider ideal control gain functions not perturbed by any disturbance term.…”

Section: A Problem Formulationmentioning

confidence: 99%

“…Theorem 1: Consider the strict-feedback nonlinear system described by (1) with Assumptions 1-2. Consider the intermediate virtual control laws (18), (34), the actual control law (54), and the adaptive laws (19), (20), (35), (36), (55), and (56). For any ξ > 0, and bounded initial conditions satisfyinĝ ψ i (0) ≥ 0,Ξ i (0) ≥ 0 and V (0) ≤ ξ with ξ being any given positive constant, there exist design parameters c i , σ i , υ i , and τ i such that: i) The compact set Ω n × Ω 0 × Ω θ is an invariant set, namely, V (t) ≤ ξ for ∀t > 0, and hence all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB); ii) The output tracking error z 1 satisfies lim t→∞ |z 1 | ≤ √ 2Σ, where Σ > 0 is a constant that can be made arbitrarily small by properly selecting the design parameters.…”

Section: Consider the Quadratic Lyapunov Function Candidatementioning

confidence: 99%

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Nonlinear Systems With Uncertain Periodically Disturbed Control Gain Functions: Adaptive Fuzzy Control With Invariance Properties

Schutter

et al. 2020

IEEE Trans. Fuzzy Syst.

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This paper proposes a novel adaptive fuzzy dynamic surface control (DSC) method for an extended class of periodically disturbed strict-feedback nonlinear systems. The peculiarity of this extended class is that the control gain functions are not bounded a priori but simply taken to be continuous and with a known sign. In contrast with existing strategies, controllability must be guaranteed by constructing appropriate compact sets ensuring that all trajectories in the closed-loop system never leave these sets. We manage to do this by means of invariant set theory in combination with Lyapunov theory. In other words, boundedness is achieved a posteriori as a result of stability analysis. The approximator composed of fuzzy logic systems (FLSs) and Fourier series expansion (FSE) is constructed to deal with the unknown periodic disturbance terms.

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Section: A Problem Formulationmentioning

confidence: 99%

Section: Consider the Quadratic Lyapunov Function Candidatementioning

confidence: 99%

Nonlinear Systems With Uncertain Periodically Disturbed Control Gain Functions: Adaptive Fuzzy Control With Invariance Properties

Schutter

et al. 2020

IEEE Trans. Fuzzy Syst.

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“…This effectively relaxes the a priori boundedness assumption. Despite some other techniques available to relax this assumption [22,23], the case has limited application in practice if the prescribed performance constraint and input saturation constraint are not taken into account. This complicates the control design of nonlinear systems due to the couplings between the output and input constraints.…”

Section: Assumption 1 the Reference Signal Is A Sufficiently Smooth mentioning

confidence: 99%

“…The DSC technique has allowed scholars to construct approximation-based adaptive control schemes for many nonlinear strict-feedback and nonstrict-feedback systems [16][17][18][19][20][21]; however, these control schemes are all based on the assumption that the control gain functions must be bounded. To relax this restrictive hypothesis, two adaptive NNs control schemes were developed for strict-feedback and nonstrictfeedback systems by assuming that control gain functions are continuous and are bounded on a compact set [22,23]. However, these schemes do not consider the simultaneous occurrence of prescribed performance and input saturation constraints due to inherent difficulties in the design.…”

Section: Introductionmentioning

confidence: 99%

Approximation‐Based Robust Adaptive Backstepping Prescribed Performance Control for a Huger Class of Nonlinear Systems

Wang

Zhang

2019

Mathematical Problems in Engineering

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This paper proposes an innovative adaptive neural prescribed performance control (PPC) scheme for large classes of nonlinear, nonstrict-feedback systems under input saturation constraint. A restrictive hypothesis under which the upper and lower bounds of control gain functions exist a priori is first relieved by constructing appropriate compact sets within which all state trajectories are held. A novel asymmetry error transformed variable is then introduced to cope with the nondifferentiable obstacle and complex deductions corresponding to traditional PPC schemes. To efficiently manage the input saturation constraint, a new auxiliary dynamic system with a bounded compensation tangent function term is established as the strictly bounded assumption of the dynamic system is canceled. It is rigorously proven that all signals in the closed-loop systems are semiglobally uniformly ultimately bounded under both Lyapunov and invariant set theories. The tracking errors converge to a small tunable residual set with prescribed performance under the effect of the input saturation constraint. The effectiveness of the proposed control scheme is thoroughly verified by two simulation examples.

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“…In the last several decades, adaptive control techniques have been found to be powerful for controlling the trianglestructural nonlinear systems in terms of either pure-feedback or strict-feedback [1]- [17]. Specifically, pure-feedback systems do not have the explicit control input, which makes the control design very difficult and draws much interest in the control community for a long time [8]- [17]. In [10], to solve the prescribed performance tracking control problem, a low-complexity control scheme is designed for a class of unknown pure-feedback systems.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Tracking Control for a Class of Pure-Feedback Nonlinear Systems

Wei

Liu

2019

IEEE Access

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This paper studies the adaptive asymptotic tracking problem for a class of unknown nonlinear systems in pure-feedback form. Different from the traditional literatures which only tackle the bounded tracking problem for pure-feedback systems, this paper investigates the asymptotic tracking problem by developing a novel controller design method. Moreover, the differentiable assumption on nonaffine functions is canceled, and only a mild semi-bounded assumption is required as the controllability condition. By utilizing Lyapunov theorem, it is proved that all the variables of the resulting closed-loop system are semiglobally uniformly ultimately bounded, and the output tracking error can converge to zero asymptotically by choosing design parameters appropriately. Finally, a simulation result is presented to verify the effectiveness of the proposed control scheme. INDEX TERMS Asymptotic stability, neural networks, nonlinear control systems, pure-feedback systems.

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Adaptive tracking control for a class of nonlinear non-strict-feedback systems

Cited by 25 publications

References 30 publications

Nonlinear Systems With Uncertain Periodically Disturbed Control Gain Functions: Adaptive Fuzzy Control With Invariance Properties

Nonlinear Systems With Uncertain Periodically Disturbed Control Gain Functions: Adaptive Fuzzy Control With Invariance Properties

Approximation‐Based Robust Adaptive Backstepping Prescribed Performance Control for a Huger Class of Nonlinear Systems

Asymptotic Tracking Control for a Class of Pure-Feedback Nonlinear Systems

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