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Journal ArticleDOI

Adaptive Controller Design-Based ABLF for a Class of Nonlinear Time-Varying State Constraint Systems

TL;DR: The time-varying asymmetric barrier Lyapunov functions (TABLFs) are employed in each step of the backsstepping design and a novel control TABLF scheme is established to ensure the asymptotic output tracking performance.
Abstract: In this paper, we address an adaptive control problem for a class of nonlinear strict-feedback systems with uncertain parameter. The full states of the systems are constrained in the bounded sets and the boundaries of sets are compelled in the asymmetric time-varying regions, i.e., the full state time-varying constraints are considered here. This is for the first time to control such a class of systems. To prevent that the constraints are overstepped, the time-varying asymmetric barrier Lyapunov functions (TABLFs) are employed in each step of the backsstepping design and we also establish a novel control TABLF scheme to ensure the asymptotic output tracking performance. The performances of the adaptive TABLF-based control are verified by a simulation example.
Citations
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Journal ArticleDOI
TL;DR: It is proved that under the presented control strategy, the system output tracks the reference signal in the sense of finite-time stability, the first time to handle the fault tolerant problem for switched system while the finite- time stability is also necessary.
Abstract: This paper concentrates upon the problem of finite-time fault-tolerant control for a class of switched nonlinear systems in lower-triangular form under arbitrary switching signals. Both loss of effectiveness and bias fault in actuator are taken into account. The method developed extends the traditional finite-time convergence from nonswitched lower-triangular nonlinear systems to switched version by designing appropriate controller and adaptive laws. In contrast to the previous results, it is the first time to handle the fault tolerant problem for switched system while the finite-time stability is also necessary. Meanwhile, there exist unknown internal dynamics in the switched system, which are identified by the radial basis function neural networks. It is proved that under the presented control strategy, the system output tracks the reference signal in the sense of finite-time stability. Finally, an illustrative simulation on a resistor-capacitor-inductor circuit is proposed to further demonstrate the effectiveness of the theoretical result.

329 citations


Cites background from "Adaptive Controller Design-Based AB..."

  • ...The multiple model systems are the switched systems [1]–[4], and the single model systems mean the nonswitched systems [5]–[16]....

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Journal ArticleDOI
TL;DR: An appropriate barrier Lyapunov function and an opportune backstepping design are used to avoid the constraint violation, and the Pade approximation and an intermediate variable are employed to eliminate the effect of the input delay.
Abstract: This paper addresses the problem of adaptive tracking control for a class of strict-feedback nonlinear state constrained systems with input delay. To alleviate the major challenges caused by the appearances of full state constraints and input delay, an appropriate barrier Lyapunov function and an opportune backstepping design are used to avoid the constraint violation, and the Pade approximation and an intermediate variable are employed to eliminate the effect of the input delay. Neural networks are employed to estimate unknown functions in the design procedure. It is proven that the closed-loop signals are semiglobal uniformly ultimately bounded, and the tracking error converges to a compact set of the origin, as well as the states remain within a bounded interval. The simulation studies are given to illustrate the effectiveness of the proposed control strategy in this paper.

241 citations


Cites background or methods from "Adaptive Controller Design-Based AB..."

  • ...Adaptive tracking controllers were designed to deal with the challenges of time-varying output constraint in [43] and time-varying state constraints in [44]....

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  • ...In addition, the authors in [22]–[25] and [33]–[44] proposed adaptive control method for nonlinear constrained systems without input delay....

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Journal ArticleDOI
TL;DR: It is proved that the system output is driven to track the reference signal to a bounded compact set, all the signals in the closed-loop system are guaranteed to be bounded, and all the states do not transgress their constrained sets.
Abstract: In the paper, the adaptive observer and controller designs based fuzzy approximation are studied for a class of uncertain nonlinear systems in strict feedback. The main properties of the considered systems are that all the state variables are not available for measurement and at the same time, they are required to limit in each constraint set. Due to the properties of systems, it will be a difficult task for designing the controller and the stability analysis. Based on the structure of the considered systems, a fuzzy state observer is framed to estimate the unmeasured states. To ensure that all the states do not violate their constraint bounds, the Barrier type of functions will be employed in the controller and the adaptation laws. In the stability analysis, the effect caused by the constraints for all the states can be overcome by using the Barrier Lyapunov functions. Based on the proposed control approach, it is proved that the system output is driven to track the reference signal to a bounded compact set, all the signals in the closed-loop system are guaranteed to be bounded, and all the states do not transgress their constrained sets. The effectiveness of the proposed control approach can be verified by setting a simulation example.

210 citations


Cites background from "Adaptive Controller Design-Based AB..."

  • ...The study of the stability on nonlinear parametric systems with the time-varying constraint is closely followed [45], [46]....

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  • ...In the previous works with the state constraints [46], [48], [52]–[54], the constraints are set in the measured states....

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Journal ArticleDOI
TL;DR: An adaptive fuzzy controller is constructed to address the finite-time tracking control problem for a class of strict-feedback nonlinear systems, where the full state constraints are strictly required in the systems.
Abstract: In this paper, an adaptive fuzzy controller is constructed to address the finite-time tracking control problem for a class of strict-feedback nonlinear systems, where the full state constraints are strictly required in the systems. Backstepping design with a tan-type barrier Lyapunov function is proposed. Meanwhile, fuzzy logic systems are used to approximate the unknown nonlinear functions. The addressed control scheme guarantees that the output is followed the reference signals within a bounded error, and all the signals in the closed-loop system are bounded. The simulation results demonstrate the validity of the proposed method.

202 citations

Journal ArticleDOI
TL;DR: A high-order tan-type barrier Lyapunov function (BLF) is constructed to handle the full-state constraints of the control systems and by the BLF and combining a backstepping design technique, an adding a power integrator, and a fuzzy control, the proposed approach can control high- order uncertain nonlinear system with full- state constraints.
Abstract: This paper focuses on the practical output tracking control for a category of high-order uncertain nonlinear systems with full-state constraints. A high-order tan-type barrier Lyapunov function (BLF) is constructed to handle the full-state constraints of the control systems. By the BLF and combining a backstepping design technique, an adding a power integrator, and a fuzzy control, the proposed approach can control high-order uncertain nonlinear system with full-state constraints. A novel controller is designed to ensure that the tracking errors approach to an arbitrarily small neighborhood of zero, and the constraints on system states are not violated. The numerical example demonstrates effectiveness of the proposed control method.

200 citations


Cites background or methods from "Adaptive Controller Design-Based AB..."

  • ...In [24], by using a time-varying asymmetric BLF, the adaptive tracking control is considered for a kind of full-state constrained strict-feedback...

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  • ...Based on two kinds of BLF, a series of research results have been presented in [24]–[27]....

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References
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Journal ArticleDOI
TL;DR: This paper presents control designs for single-input single-output (SISO) nonlinear systems in strict feedback form with an output constraint, and explores the use of an Asymmetric Barrier Lyapunov Function as a generalized approach that relaxes the requirements on the initial conditions.

1,999 citations


"Adaptive Controller Design-Based AB..." refers background or methods in this paper

  • ...[23] provided a control approach for SISO nonlinear strict feedback systems with an output constraint and a barrier Lyapunov function (BLF) is employed to prevent constraint violation....

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  • ...The controller design of nonlinear systems with output constraints in time-varying was studied in [27] to avoid the restriction of constant output constraint in [23]–[26]....

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  • ...The constraint of these approaches in [23]–[27] only focused on the output....

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Journal ArticleDOI
TL;DR: A systematic procedure for the design of adaptive regulation and tracking schemes for a class of feedback linearizable nonlinear systems is developed, which substantially enlarges the class of non linear systems with unknown parameters for which global stabilization can be achieved.
Abstract: A systematic procedure for the design of adaptive regulation and tracking schemes for a class of feedback linearizable nonlinear systems is developed. The coordinate-free geometric conditions, which characterize this class of systems, do not constrain the growth of the nonlinearities. Instead, they require that the nonlinear system be transformable into the so-called parametric-pure feedback form. When this form is strict, the proposed scheme guarantees global regulation and tracking properties, and substantially enlarges the class of nonlinear systems with unknown parameters for which global stabilization can be achieved. The main results use simple analytical tools, familiar to most control engineers. >

1,722 citations

Proceedings ArticleDOI
26 Jun 1991
TL;DR: In this paper, a systematic procedure is developed for the design of adaptive regulation and tracking schemes for a class of feedback linearizable nonlinear systems, which are transformable into the so-called pure-feedback form.
Abstract: A systematic procedure is developed for the design of new adaptive regulation and trackdng schemes for a class of feedback linearizable nonlinear systems. The coordinate-free geometric conditions, which characterize this class of systems, neither restrict the location of the unknown parameters, nor constrain the growth of the nonlinearities. Instead, they require that the nonlinear system be transformable into the so-called pure-feedback form. When this form is "strict", the proposed scheme guarantees global regulation and tracking properties, and substantially enlarges the class of nonlinear systems with unknown parameters for which global stabilization can be achieved. The main results of this paper use simple analytical tools, familiar to most control engineers.

1,517 citations


"Adaptive Controller Design-Based AB..." refers methods in this paper

  • ...The distinguished works on adaptive technique were proposed for pure-feedback systems [1], linear parametrization [2], [3], and nonlinear parameterization [4], [34]....

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Journal ArticleDOI
TL;DR: The auxiliary design system is introduced to analyze the effect of input constraints, and its states are used to adaptive tracking control design, and the closed-loop semi-global uniformly ultimate bounded stability is achieved via Lyapunov synthesis.

861 citations


"Adaptive Controller Design-Based AB..." refers background in this paper

  • ...Adaptive control achievements of nonlinear systems with input constraints such as backlash [17], hysteresis [18], saturation [19], [20], and deadzone [21], [22] were designed....

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Journal ArticleDOI
TL;DR: A barrier Lyapunov function (BLF) is introduced to address two open and challenging problems in the neuro-control area: for any initial compact set, how to determine a priori the compact superset on which NN approximation is valid; and how to ensure that the arguments of the unknown functions remain within the specified compact supersets.
Abstract: In this brief, adaptive neural control is presented for a class of output feedback nonlinear systems in the presence of unknown functions. The unknown functions are handled via on-line neural network (NN) control using only output measurements. A barrier Lyapunov function (BLF) is introduced to address two open and challenging problems in the neuro-control area: 1) for any initial compact set, how to determine a priori the compact superset, on which NN approximation is valid; and 2) how to ensure that the arguments of the unknown functions remain within the specified compact superset. By ensuring boundedness of the BLF, we actively constrain the argument of the unknown functions to remain within a compact superset such that the NN approximation conditions hold. The semiglobal boundedness of all closed-loop signals is ensured, and the tracking error converges to a neighborhood of zero. Simulation results demonstrate the effectiveness of the proposed approach.

818 citations


"Adaptive Controller Design-Based AB..." refers background in this paper

  • ...In [24], a BLF is extended in the adaptive neural control area for uncertain nonlinear systems in the presence of output constraint....

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  • ...Lemma 1 [24]: For all |ξ | < 1 and a positive integer p, the inequality log 1/(1 − ξ2p) < ξ2p/(1 − ξ2p) is true....

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