Prescribed performance controller with affine equivalent model for a class of unknown nonlinear discrete-time systems

Treesatayapun, Chidentree

doi:10.1080/00207721.2020.1829161

Cited by 8 publications

(5 citation statements)

References 32 publications

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“…1 2 and 𝜁 t ,0 is the unknown nonlinear term in system (23). In case 2, L y = 0 and L u = 1, there must be a time-varying parameter vector 𝜙 t , called the PPD vector, so that the system (1) is transformed into the following equivalent CFDL model:…”

Section: Data-driven Model Via Ffdlmentioning

confidence: 99%

“…After Bechlioulis [19,20] developed the concept of prescribed performance control (PPC), most of the existing related work has been studied in continuous-time cases [21,22]. For discrete-time systems, PPC-based MFAC has also attached some attention [23][24][25]. In these works, the upper and lower bounds affine to the prescribed function are set as 1 or the same value, otherwise the offset error will occur in the steadystate.…”

Section: Introductionmentioning

confidence: 99%

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Model‐free adaptive integral sliding mode constrained control with modified prescribed performance

Huang

Dong

Zhang

et al. 2023

IET Control Theory & Appl

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In this work, a novel model‐free adaptive integral sliding model constrained control strategy with modified prescribed performance is proposed for nonlinear nonaffine systems via full‐form dynamic linearization (FFDL). Firstly, a generalized nonlinear nonaffine system with external disturbance is transformed into an affine system via the FFDL method, which contains a linearly parametric term affine to the control input and preceding output data, and an unknown nonlinear time‐varying term. Then, an adaptive estimation method and a discrete‐time extended state observer (DESO) are used to estimate the pseudo gradient (PG) vector and lumped uncertainties, respectively. Furthermore, an integral sliding mode control scheme containing a modified prescribed performance function and an anti‐windup compensator is designed to keep the output tracking error in the prescribed bound without causing any asymmetric offset error in the steady‐state and to suppress the influence of input saturation. Simulation results demonstrate the superiority of the proposed control scheme.

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Section: Data-driven Model Via Ffdlmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Model‐free adaptive integral sliding mode constrained control with modified prescribed performance

Huang

Dong

Zhang

et al. 2023

IET Control Theory & Appl

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show abstract

“…Until now, the PPC problems in continuous-time systems have been prosperously investigated [21]. Meanwhile, some researchers also studied the PPC problem with MFAC in discrete-time systems [22][23][24]. Among these works, the upper and lower bounds affine to the prescribed function are set as 1 or the same value, otherwise, an offset error would exist in the steady-state.…”

Section: Introductionmentioning

confidence: 99%

Discrete‐time extended state observer‐based model‐free adaptive constrained sliding mode control with modified prescribed performance via CFDL and PFDL

Huang,

Dong,

Zhang

et al. 2023

Asian Journal of Control

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To tackle the trajectory tracking problem and achieve high control accuracy in many actual nonlinear systems with unknown dynamics and input saturation, a novel discrete‐time extended state observer‐based model‐free adaptive constrained sliding mode control with modified prescribed performance is investigated via compact‐form dynamic linearization (CFDL) and partial‐form dynamic linearization (PFDL). Firstly, the original non‐affine system is turned into an affine one comprising an unknown nonlinear term and a linearly parametric term affine to the input via both PFDL and CFDL. Then, a discrete‐time extended state observer (DESO) is used to estimate the lumped disturbance containing the unknown nonlinear time‐varying term and the term relevant to the estimation error of pseudo partial derivative (PPD) parameter. Furthermore, a modified prescribed performance function is introduced in the model‐free adaptive sliding mode control scheme to keep the output tracking error in the prescribed bound without causing any asymmetric offset error in the steady‐state. Meanwhile, to suppress the influence of input saturation on the control system, an anti‐windup compensator is used. Finally, rigorous theoretical analyses show the robust convergence of the tracking error via the proposed CFDL and PFDL‐based methods under external disturbances. Simulations verify the superiority of the modified prescribed performance function, DESO, and anti‐windup compensator in the proposed method. Also, the effects of the PFDL‐based method and the CFDL‐based one are compared during the simulation.

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“…Nguyen et al 26 proposed a new approach by associating the discrete-time quasi-sliding mode control with the PPC method to get high tracking performance. Treesatayapun 27,28 developed the affine data-driven model by a multi-input fuzzy rule emulated network and used PPC to assure the tracking error converge to a small boundary. Liu et al 29,30 first considered the PPC in the MFAC with the sliding mode control method.…”

mentioning

confidence: 99%

“…Based on our best knowledge, no research has yet investigated the DESO-based model-free adaptive sliding mode control for the discrete-time nonlinear processes with external disturbance under predefined performance. Compared to the prescribed performance-based MFAC in discrete-time systems, [26][27][28][29][30][31] a DESO is firstly used to estimate the lumped unknown time-varying term in this paper. Compared to the DESO-based MFAC, 13,21 this paper not only embraces the term relevant to the estimation error of the PPD parameter in the extended state but also ensures that the output tracking error is convergent to a residual set with both prescribed transient-state and steady-state performance.…”

mentioning

confidence: 99%

Discrete‐time extended state observer‐based model‐free adaptive sliding mode control with prescribed performance

Huang

Dong

Zhang

et al. 2022

Intl J Robust & Nonlinear

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To tackle the trajectory tracking problem and achieve high control accuracy in many actual nonlinear systems with unknown disturbance, a novel discrete-time extended state observer-(DESO) based model-free adaptive sliding mode control strategy with prescribed tracking performance is studied, which only relies on the input/output data of the system rather than explicit model information. Firstly, a compact-form dynamic linearization method is used to reconstruct the discrete-time nonlinear process, where the time-varying parameter linearly connected with the control input is obtained by an adaptive method and the unknown nonlinear term is estimated by a DESO. Then, by considering the prescribed performance and using an unconstrained vector transformed from the constrained tracking error, one model-free sliding mode controller is designed. In addition, a rigorous stability analysis is presented to show the boundedness of the sliding mode function and the prescribed transient-state and steady-state performance of the output tracking error. Finally, the simulations with comparing results verify the effectiveness and superiority of the developed control scheme. K E Y W O R D Sdiscrete-time extended state observer, discrete-time system, model-free adaptive control, prescribed performance, sliding mode control INTRODUCTIONWith the continuous development of engineering technologies, the complexity of the practical system is intensively increasing, which leads to accurate system modeling becoming one of the most difficult tasks. 1 Thus, the control strategies based on mathematical models are not suitable for such complicated systems. To overcome this problem, data-driven control is proposed where only the input and output data are used. Data-driven methods have been applied in many practical scenes, for instance, quadrotor vehicles, 2 automated vehicles, 3 continuum robots, 4 and other industrial process systems. 5,6 Among these data-driven methods, model-free adaptive control (MFAC) approach has aroused a lot of attention because only the input and output data are used without employing explicit or implicit knowledge of the mathematic

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Prescribed performance controller with affine equivalent model for a class of unknown nonlinear discrete-time systems

Cited by 8 publications

References 32 publications

Model‐free adaptive integral sliding mode constrained control with modified prescribed performance

Model‐free adaptive integral sliding mode constrained control with modified prescribed performance

Discrete‐time extended state observer‐based model‐free adaptive constrained sliding mode control with modified prescribed performance via CFDL and PFDL

Discrete‐time extended state observer‐based model‐free adaptive sliding mode control with prescribed performance

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