Improved prescribed performance constraint control for a strict feedback non‐linear dynamic system

Han, Seong-Ik; Lee, Jang Myung

doi:10.1049/iet-cta.2013.0181

Cited by 84 publications

(40 citation statements)

References 21 publications

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“…Prescribed performance means that the tracking error e ( t ) converges to an adjustable residual set with expected convergence time and the maximum overshoot less than a designed value . The above conception can be expressed as follows:

- ρ ((), t) < e ((), t) < ρ ((), t), \forall t \geq 0 .

The performance function ρ ( t ) is typically selected as

ρ ((), t) = ((), ρ_{0} - ρ_{\infty}) e^{- italiclt} + ρ_{\infty},

where ρ 0 , ρ ∞ , and l are positive design parameters, ρ 0 = ρ (0), ρ ∞ = ρ (∞), and ρ 0 is selected such that | e (0)| < ρ (0) and ρ 0 > ρ ∞ .…”

Section: Prescribed Performancementioning

confidence: 99%

“…Remark Considering that the aforementioned PPC technique designed by Bechlioulis et al may have a singularity problem, an improved PPC was developed in Han and Lee, which is supposed to bypass the singularity problem and simplify the controller. In the aforementioned work, the transformed error is defined as z ( t ) = ζ ( t )/(1 − ζ ( t )), where ζ ( t ) = e ( t )/ ρ ( t ) and

ρ ((), t) = q \overset{φ}{true} ((), t) + ((), 1 - q) \underline{φ} ((), t)

\overset{φ}{true} ((), t)

and

\underline{φ} ((), t)

are asymmetry performance functions.…”

Section: Prescribed Performancementioning

confidence: 99%

“…Many constraint control schemes have been utilized to cope with output constraint control problems such as Barrier Lyapunov function, funnel control (FC), and prescribed performance control (PPC) . Moreover, PPC, as an alternative method of FC, is proposed for nonlinear systems of higher relative degree .…”

Section: Introductionmentioning

confidence: 99%

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Improved prescribed performance control for nonaffine pure‐feedback systems with input saturation

Wang

et al. 2019

Intl J Robust & Nonlinear

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Summary This work considers an input and output constraint control problem for pure‐feedback systems with nonaffine functions possibly being in‐differentiable. A locally semibounded and continuous condition for nonaffine functions is presented to guarantee the controllability, and the nonaffine system is transformed to an equivalent pseudoaffine one based on the mild condition. Combined with backstepping technique, a novel prescribed performance controller with new performance functions is constructed to circumvent high frequency chattering in control input. An auxiliary system with bounded compensation term is utilized in this paper, successfully avoiding the overrun of control input. The methodology achieves the desired transient and steady‐state performance and presents excellent robustness against the system uncertainty. Finally, two numerical simulations are performed to demonstrate the effectiveness of the proposed approach.

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- ρ ((), t) < e ((), t) < ρ ((), t), \forall t \geq 0 .

The performance function ρ ( t ) is typically selected as

ρ ((), t) = ((), ρ_{0} - ρ_{\infty}) e^{- italiclt} + ρ_{\infty},

where ρ 0 , ρ ∞ , and l are positive design parameters, ρ 0 = ρ (0), ρ ∞ = ρ (∞), and ρ 0 is selected such that | e (0)| < ρ (0) and ρ 0 > ρ ∞ .…”

Section: Prescribed Performancementioning

confidence: 99%

ρ ((), t) = q \overset{φ}{true} ((), t) + ((), 1 - q) \underline{φ} ((), t)

\overset{φ}{true} ((), t)

and

\underline{φ} ((), t)

are asymmetry performance functions.…”

Section: Prescribed Performancementioning

confidence: 99%

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Improved prescribed performance control for nonaffine pure‐feedback systems with input saturation

Wang

et al. 2019

Intl J Robust & Nonlinear

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show abstract

“…Therefore, the prescribed performance control problem has been widely studied for various nonlinear systems in related literatures, such as [2][3][4][5][6][7] for the interconnected large-scale nonlinear systems, [27][28][29][30][31][32] for the SISO nonlinear systems, and [33] for MIMO nonlinear systems. Therefore, the prescribed performance control problem has been widely studied for various nonlinear systems in related literatures, such as [2][3][4][5][6][7] for the interconnected large-scale nonlinear systems, [27][28][29][30][31][32] for the SISO nonlinear systems, and [33] for MIMO nonlinear systems.…”

Section: Remarkmentioning

confidence: 99%

Decentralized prescribed performance adaptive tracking control for Markovian jump uncertain nonlinear systems with input saturation

Chang

Fang

Liu

et al. 2016

Adaptive Control & Signal

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A decentralized prescribed performance adaptive tracking control problem is investigated for Markovian jump uncertain nonlinear interconnected large-scale systems. The considered interconnected large-scale systems contain unknown nonlinear uncertainties, unknown control gains, actuator saturation, and Markovian jump signals, and the Markovian jump subsystems are in the form of triangular structure. First, by defining a novel state transformation with the performance function, the prescribed performance control problem is transformed to stabilization problem. Then, introducing an intermediate control signal into the control design, employing neural network to approximate the unknown composite nonlinear function, and based on the framework of the backstepping control design and adaptive estimation method, a corresponding decentralized prescribed performance adaptive tracking controller is designed. It is proved that all the signals in the closed-loop system are bounded, and the prescribed tracking performances are guaranteed. A numerical example is provided to illustrate the effectiveness of the proposed control strategy. 256 R. CHANG ET AL. constraint and recurrent fuzzy neural networks were used to achieve a prescribed tracking performance for a strict-feedback nonlinear dynamic system, the decentralized adaptive recurrent fuzzy neural networks control scheme was proposed in [6]. Based on the backstepping recursive design technique and the prescribed performance technique, a new adaptive fuzzy output-feedback control method was developed for a class of nonlinear large-scale systems, such that the tracking errors converged to an adjustable neighborhood of the origin with the prescribed performance bounds [7].For the interconnected large-scale systems, actuator saturation can lead to a cascading effect, and then, it may result in overall system collapse. An example of a cascading effect caused by actuator saturation is the 3 August 1996 blackout in Malaysia [8]. In recent years, some results on the decentralized control problem under actuator saturation have been reported. For example, a novel decentralized adaptive neural control scheme was proposed for a class of interconnected large-scale uncertain nonlinear time-delay systems with input saturation [9]. The decentralized H 1 controller was designed for a multi-zone space heating system, which is an interconnected dynamical system subject to external disturbances and input saturation [10]. Two decentralized sliding mode control laws were proposed and analyzed for spacecraft attitude synchronization under actuator failures, and the results could be extended to the case with control input saturation in the second controller [11]. The decentralized adaptive neural control was studied for a class of interconnected nonlinear systems with input saturation in [12,13].However, the aforementioned decentralized control methods in [2][3][4][5][6][7][8][9][10][11][12][13] are for non-switched nonlinear interconnected large-scale systems; therefore, they cannot be used to dea...

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“…In this way, the tracking error will remain within an arbitrarily small predefined residual set as long as the stability of the closed‐loop system is guaranteed. In recent years, many PPC schemes have been reported for nonlinear systems . In the work of Han and Lee and Wang et al, backstepping PPC schemes were developed for strict‐feedback nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

Prescribed performance adaptive neural output feedback dynamic surface control for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics

Zhang

Sun

2019

Intl J Robust & Nonlinear

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Summary This paper studies the output feedback tracking control problem for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics using a prescribed performance adaptive neural dynamic surface control design approach. A nonlinear mapping technique is employed to address the state constraints. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions. The unmodeled dynamics is addressed by introducing an available dynamic signal. Subsequently, we construct the controller and parameter adaptive laws using a backstepping technique. Based on Lyapunov stability theory, it is shown that all signals in the closed‐loop system are semiglobally uniformly ultimately bounded and that the tracking error always remains within the prescribed performance bound. Simulation results are presented to demonstrate the effectiveness of the proposed control scheme.

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Improved prescribed performance constraint control for a strict feedback non‐linear dynamic system

Cited by 84 publications

References 21 publications

Improved prescribed performance control for nonaffine pure‐feedback systems with input saturation

Improved prescribed performance control for nonaffine pure‐feedback systems with input saturation

Decentralized prescribed performance adaptive tracking control for Markovian jump uncertain nonlinear systems with input saturation

Prescribed performance adaptive neural output feedback dynamic surface control for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics

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