Approximation-based adaptive tracking control of nonlinear pure-feedback systems with time-varying output constraints

Kim, Bong Su; Yoo, Sung Jin

doi:10.1007/s12555-014-0084-6

Cited by 43 publications

(15 citation statements)

References 22 publications

(24 reference statements)

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“…The inequality constraint only depicts a general variation of

f_{i} ((),, {\overset{x}{true}}_{i}, x_{i + 1})

with x i + 1 , which has no special requirement for each specific point on the nonlinear curve. Figure B is an illustration of the common assumption utilized in other works . The conventional controllability condition of nonaffine functions is

0 < g_{i, normalm} \leq \partial f_{i} ((),, {\overset{x}{true}}_{i}, x_{i + 1}) false/ \partial x_{i + 1} \leq g_{i, normalM}

, which requires the nonaffine function to be differentiable and its partial derivative to keep positive all the time.…”

Section: Problem Statement and Preliminariesmentioning

confidence: 99%

“…The past decades have witnessed a great amount of studies on control for nonaffine systems where the control inputs take their actions through a nonlinear and implicit way . There are many systems falling into this category featured with nonaffine structure, such as mechanical systems, biochemical process, and aircraft flight control system .…”

Section: Introductionmentioning

confidence: 99%

“…Most notably, mean value theorem is typically used to build a transformational model for nonaffine system under the condition that ∂f ( x , u )/ ∂u is bounded, and then, control approaches such as adaptive fuzzy control, adaptive neural network control, and prescribed performance control can be constructed on the basis of the transformational model. Moreover, Taylor series expansion is also utilized to construct an equivalent system under the hypothesis that ∂f ( x , u )/ ∂u is bounded, and then, adaptive fuzzy controllers can be designed based on the pseudoaffine system …”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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“…The inequality constraint only depicts a general variation of

f_{i} ((),, {\overset{x}{true}}_{i}, x_{i + 1})

0 < g_{i, normalm} \leq \partial f_{i} ((),, {\overset{x}{true}}_{i}, x_{i + 1}) false/ \partial x_{i + 1} \leq g_{i, normalM}

, which requires the nonaffine function to be differentiable and its partial derivative to keep positive all the time.…”

Section: Problem Statement and Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Wang

et al. 2019

Intl J Robust & Nonlinear

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“…Recently, following the idea of tailoring the Lyapunov function to the requirements of the problem, the use of the barrier Lyapunov function (BLF) for the backstepping control of output/state‐constrained systems has been proposed. Up to present, the BLF‐based design has been widely used in various types of nonlinear systems, ranging from strict/semi‐strict feedback uncertain systems to pure‐feedback systems, to output feedback systems, and to many more complex systems such as time‐delay systems, stochastic systems, and switched systems . Besides theoretical contributions, the practical applications of BLF have also been discussed in different areas such as control of marine vessel, electrostatic torsional micromirror, electro‐hydraulic system, robotic manipulator .…”

Section: Introductionmentioning

confidence: 99%

“…Besides theoretical contributions, the practical applications of BLF have also been discussed in different areas such as control of marine vessel, electrostatic torsional micromirror, electro‐hydraulic system, robotic manipulator . Related works have focused on output constraints problem, whereas other works have dealt with state‐constrained systems. As demonstrated by Tee and Ge, the control design for state‐constrained systems is more difficult than that for output‐constrained systems because the virtual controllers in the backstepping procedure need to satisfy constraints themselves.…”

Section: Introductionmentioning

confidence: 99%

Robust adaptive control for a class of semi‐strict feedback systems with state and input constraints

Zhang

Duan

2018

Intl J Robust & Nonlinear

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Summary This paper proposes a dynamic surface control (DSC)–based robust adaptive control scheme for a class of semi‐strict feedback systems with full‐state and input constraints. In the control scheme, a constraint transformation method is employed to prevent the transgression of the full‐state constraints. Specifically, the state constraints are firstly represented as the surface error constraints, then, an error transformation is introduced to convert the constrained surface errors into new equivalent variables without constraints. By ensuring the boundedness of the transformed variables, the violation of the state constraints can be prevented. Moreover, in order to obtain magnitude limited virtual control signal for the recursive design, the saturations are incorporated into the control law. The auxiliary design systems are constructed to analyze the effects of the introduced saturations and the input constraints. Rigorous theoretical analysis demonstrates that the proposed control law can guarantee all the closed‐loop signals are uniformly ultimately bounded, the tracking error converges to a small neighborhood of origin, and the full‐state constraints are not violated. Compared with the existing results, the key advantages of the proposed control scheme include: (i) the utilization of the constraint transformation can handle both time‐varying symmetric and asymmetric state constraints and static ones in a unified framework; (ii) the incorporation of the saturations permits the removal of a feasibility analysis step and avoids solving the constrained optimization problem; and (iii) the “explosion of complexity” in traditional backstepping design is avoided by using the DSC technique. Simulations are finally given to confirm the effectiveness of the proposed approach.

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Adaptive optimized backstepping tracking control for full‐state constrained nonlinear strict‐feedback systems without using barrier Lyapunov function method

Zhu,

Xu,

Zong

et al. 2024

Optim Control Appl Methods

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In this article, the problem of adaptive optimal tracking control is studied for nonlinear strict‐feedback systems. While not directly measurable, the states of these systems are subject to both time‐varying and asymmetric constraints. Bypassing the conventional barrier Lyapunov function method, the constrained system is transformed into its unconstrained counterpart, thereby obviating the need for feasibility conditions. A specially designed reinforcement learning (RL) algorithm, featuring an observer‐critic‐actor architecture, is deployed in an adaptive optimal control scheme to ensure the stabilization of the converted unconstrained system. Within this architecture, the observer estimates the unmeasurable system states, the critic evaluates the control performance, and the actor executes the control actions. Furthermore, enhancements to the RL algorithm lead to relaxed conditions of persistent excitation, and the design methodology for the observer overcomes the restrictions imposed by the Hurwitz equation. The Lyapunov stability theorem is applied for two primary purposes: to ascertain the boundedness of all signals within the closed‐loop system, and to ensure the accuracy of the output signal in tracking the desired reference trajectory. Finally, numerical and practical simulations are provided to corroborate the effectiveness of the proposed control strategy.

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Approximation-based adaptive tracking control of nonlinear pure-feedback systems with time-varying output constraints

Cited by 43 publications

References 22 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

Robust adaptive control for a class of semi‐strict feedback systems with state and input constraints

Adaptive optimized backstepping tracking control for full‐state constrained nonlinear strict‐feedback systems without using barrier Lyapunov function method

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