Adaptive prescribed performance control for nonlinear pure-feedback systems: a scalarly virtual parameter adaptation approach

Chen, Wu; Gao, Shigen; Dong, Hairong

doi:10.1007/s11071-020-06051-1

Cited by 5 publications

(6 citation statements)

References 36 publications

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“…) is either strictly positive or strictly negative for all [x t] ∈  ∑ N j=1 n j × R ≥0 to satisfy essential controllability condition of (1). Meanwhile, uncertain gain function g j (x 1 , … , x N , t) is bounded by unknown positive constant g * j , that is, (48). The target trajectories for all subsystems y r j , ∀j = 1, … , N, are  1 functions with unknown yet bounded first-order derivatives, that is, y r j ∈  1 and ̇yr j ∈  ∞ .…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

Extended prescribed performance control with input quantization for nonlinear systems

Gao

Zheng

et al. 2022

Intl J Robust & Nonlinear

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For a class of MIMO nonlinear systems, comprised of interconnected subsystems in Brunovsky canonical form, with uncertain yet locally Lipschitz nonlinearities among subsystems and quantized inputs, the target is to form a closed-loop system that exhibits extended prescribed performance on states tracking (accuracy determined by maximum overshoot, minimum convergence rate, maximum steady-state error, and control gains), yet still a low-complexity control structure, without requiring any identification, approximation, and filtering techniques, regardless of uncertainties. In this article, a static, decentralized, continuous, yet computationally inexpensive controller is designed, without requiring parameters of quantizers. Inheriting the merit of pioneering prescribed performance control (PPC) methodology, it is required that the reference signal is  1 function only, while, an essential difference and new feature is that, the pioneering PPC guarantees that state tracking errors are constrained by boundary functions (also known as prescribed performance functions, PPFs) only, while, the proposed extend PPC scheme achieves that state tracking errors are constrained by boundary functions and control gains simultaneously, in other words, without "tighter" PPFs, state tracking errors can still be adjusted to arbitrarily small by choosing proper control gains. Finally, comparative simulation results are given to verify the theoretical findings.

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Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

Extended prescribed performance control with input quantization for nonlinear systems

Gao

Zheng

et al. 2022

Intl J Robust & Nonlinear

Self Cite

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show abstract

“…A low-complexity PPC scheme based on the scalarly virtual parameter adaptation mechanism was proposed for SISO nonlinear systems. 10 The authors in Reference 11 applied PPC to MIMO nonlinear systems and presented an adaptive neural network (NN) control method, where a single NN was used to estimate the uncertain dynamics. On the basis of universal approximation capability of fuzzy logic systems, [12][13][14] the study 15 combined PPC with the generalized fuzzy hyperbolic model to obtain an adaptive control method to stabilize MIMO systems.…”

Section: Introductionmentioning

confidence: 99%

“…Without prior knowledge of tracking error, the PPC schemes based on the non-negative switching function were designed for pure-feedback systems 16 and for nonstrict-feedback systems, 17 respectively. The PPC strategies [9][10][11][15][16][17] only care about the convergence rate and steady-state accuracy of the tracking error, but do not guarantee that the output of system can track the desired trajectory in a finite time. To deal with this issue, the finite-time control strategies [18][19][20] seem to offer a solution.…”

Section: Introductionmentioning

confidence: 99%

“…1. Compared with the command-filtered-based finite-time controller, 20 prescribed performance controller, [9][10][11]15 the developed controller can guarantee that the tracking error vector converges to preassigned compact set around zero within preset time, and during the preset time, the converging rate is explicitly designed in advance. 2.…”

Section: Introductionmentioning

confidence: 99%

“…The prescribed performance control (PPC) technique proposed by Bechlioulis and Rovithakis, 9 for the first time, is an effective way to design a control law for nonlinear systems with prescribed performance attributes. A low‐complexity PPC scheme based on the scalarly virtual parameter adaptation mechanism was proposed for SISO nonlinear systems 10 . The authors in Reference 11 applied PPC to MIMO nonlinear systems and presented an adaptive neural network (NN) control method, where a single NN was used to estimate the uncertain dynamics.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Command‐filtered‐based neuroadaptive control for multi‐input multi‐output saturated nonstrict‐feedback nonlinear systems with prescribed tracking performance

Yang

Liu

Guo

2022

Adaptive Control & Signal

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Summary In this article, the prescribed performance control strategy is extended to multi‐input multi‐output nonstrict‐feedback nonlinear systems with asymmetric input saturation, and not only each element in tracking error vector converges to a prescribed small region within preassigned finite time, but also the converging mode during the preset time is prespecifiable and controllable explicitly. By blending the barrier function with novel speed function, a prescribed performance controller using command‐filtered‐based vector‐backstepping design framework is proposed to steer the tracking error vector for the first time, where the boundedness of filter errors is guaranteed by sufficiently small time constant and an error compensator is constructed to handle the effects of filter errors. To attenuate the adverse effects resulted from nondifferentiable input saturation, hyperbolic tangent function is utilized to estimate asymmetric saturation function such that the control input is designed as a new state variable with initial value of zero in augmented system. Nussbaum function is employed to overcome singularity problem caused by the differentiation of hyperbolic tangent function. At each step of backstepping design, the universal approximation property of neural network and the command filter system are utilized to approximate uncertain dynamics and to solve algebraic loop obstacle due to nonstrict‐feedback structure, respectively. Moreover, only one parameter needs to be updated online to cope with the lumped uncertain dynamics by virtual parameter technology, rendering a control strategy with low complexity computation. The validity of the presented controller is verified by theoretical analysis and two‐link robotic system.

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Adaptive coordinated control of networked non-affine nonlinear systems with a non-autonomous nonlinear leader

Dong

2023

Nonlinear Dyn

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Adaptive prescribed performance control for nonlinear pure-feedback systems: a scalarly virtual parameter adaptation approach

Cited by 5 publications

References 36 publications

Extended prescribed performance control with input quantization for nonlinear systems

Extended prescribed performance control with input quantization for nonlinear systems

Command‐filtered‐based neuroadaptive control for multi‐input multi‐output saturated nonstrict‐feedback nonlinear systems with prescribed tracking performance

Adaptive coordinated control of networked non-affine nonlinear systems with a non-autonomous nonlinear leader

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