Adaptive neural dynamic surface control of strict-feedback nonlinear systems with full state constraints and unmodeled dynamics ☆
TL;DR: Adaptive neural network (NN) dynamic surface control (DSC) is discussed for a class of strict-feedback nonlinear systems with full state constraints and unmodeled dynamics and a one to one nonlinear mapping is introduced.
About: This article is published in Automatica.The article was published on 2017-07-01. It has received 305 citations till now. The article focuses on the topics: Adaptive control & Lyapunov function.
Citations
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TL;DR: It is proven that all the signals in the closed-loop system are semiglobally uniformly ultimately bounded with full state constraints.
Abstract: The problem of adaptive fuzzy control is investigated for a class of nontriangular structural stochastic switched nonlinear systems with full state constraints in this paper. A remarkable feature of the nontriangular structural nonlinear system is the so-called algebraic loop problem in the existing backstepping-based analysis and design. Properties of fuzzy basis functions are utilized to circumvent this algebraic loop problem. Based on the Barrier Lyapunov function, an adaptive fuzzy stochastic switched control scheme is designed. It is proven that all the signals in the closed-loop system are semiglobally uniformly ultimately bounded with full state constraints. The effectiveness of the proposed control scheme is verified via simulation studies.
297 citations
TL;DR: In this article , an adaptive neural network (NN) output feedback optimized control design for a class of strict-feedback nonlinear systems that contain unknown internal dynamics and the states that are immeasurable and constrained within some predefined compact sets is proposed.
Abstract: This article proposes an adaptive neural network (NN) output feedback optimized control design for a class of strict-feedback nonlinear systems that contain unknown internal dynamics and the states that are immeasurable and constrained within some predefined compact sets. NNs are used to approximate the unknown internal dynamics, and an adaptive NN state observer is developed to estimate the immeasurable states. By constructing a barrier type of optimal cost functions for subsystems and employing an observer and the actor-critic architecture, the virtual and actual optimal controllers are developed under the framework of backstepping technique. In addition to ensuring the boundedness of all closed-loop signals, the proposed strategy can also guarantee that system states are confined within some preselected compact sets all the time. This is achieved by means of barrier Lyapunov functions which have been successfully applied to various kinds of nonlinear systems such as strict-feedback and pure-feedback dynamics. Besides, our developed optimal controller requires less conditions on system dynamics than some existing approaches concerning optimal control. The effectiveness of the proposed optimal control approach is eventually validated by numerical as well as practical examples.
217 citations
TL;DR: An observer-based adaptive fuzzy event-triggered control strategy is proposed for the full-state-constrained nonlinear system with actuator faults based on backstepping technique, which can guarantee that all the signals in the closed-loop system are bounded and the tracking error converges to a small neighborhood of the origin in a finite time.
Abstract: In this paper, an adaptive fuzzy output feedback control problem is investigated for a class of stochastic nonlinear systems in which the fuzzy logic systems are adopted to approximate the unknown nonlinear functions. A reduced-order observer and a general fault model are designed to observe the unavailable state variables and describe the actuator faults, respectively. An event-triggered control law is developed to reduce the communication burden from the controller to the actuator. Meanwhile, the barrier Lyapunov functions are constructed to guarantee that all the states of the stochastic nonlinear system are not to violate their constraints. Furthermore, an observer-based adaptive fuzzy event-triggered control strategy is proposed for the full-state-constrained nonlinear system with actuator faults based on backstepping technique, which can guarantee that all the signals in the closed-loop system are bounded and the tracking error converges to a small neighborhood of the origin in a finite time. Finally, simulation results are given to illustrate the effectiveness of the proposed control scheme.
213 citations
Cites background from "Adaptive neural dynamic surface con..."
...In order to eliminate the problem of “explosion of complexity” existed in [30], an adaptive neural network dynamic surface control scheme is presented in [31] for a class of strict-feedback nonlinear systems subject to unmodeled dynamics and full state constraints....
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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 neural dynamic surface con..."
...By taking advantage of the same design idea of [53] and [54], the pure-feedback systems with full state constraints are stabilized in [55] and [56]....
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...[54] proposed two adaptive control schemes for nonlinear strict-feedback systems with full state constraints....
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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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TL;DR: In this article, an event-triggered robust fuzzy adaptive prescribed performance finite-time control strategy is presented for a class of strict-feedback nonlinear systems with external disturbances, and the dynamic surface control technique is applied to address the computational complexity problem.
Abstract: In this article, an event-triggered robust fuzzy adaptive prescribed performance finite-time control strategy is presented for a class of strict-feedback nonlinear systems with external disturbances. The relative-threshold-based event-triggered signal is introduced to reduce communication burden, and the dynamic surface control technique is applied to address the computational complexity problem. A disturbance observer is designed to estimate the compounded disturbances, which are composed of external disturbances and fuzzy approximation errors. The proposed control strategy can guarantee that the closed-loop system is semiglobally practically finite-time stable, and the tracking error converges to a small residual set by incorporating the prescribed performance bound in finite-time. Finally, simulation results are provided to verify the effectiveness of the proposed robust fuzzy control strategy.
198 citations
Cites background from "Adaptive neural dynamic surface con..."
...However, the control strategies proposed in [4], [6], [13], and [14] do not consider approximation errors and external disturbances....
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...PROBLEM FORMULATION Assumption 1 ([14]): The reference signal yr(t), and its time derivatives ẏr(t), ÿr(t) are bounded and known....
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...It is noted that some approximatorbased control strategies have been proposed for nonlinear plants [4], [6], [13], [14]....
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...[14] proposed a state feedback DSC scheme for strict-feedback nonlinear systems with unmodeled dynamics and full state constraints....
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References
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Book•
01 Jan 1995
TL;DR: In this paper, the focus is on adaptive nonlinear control results introduced with the new recursive design methodology -adaptive backstepping, and basic tools for nonadaptive BackStepping design with state and output feedbacks.
Abstract: From the Publisher:
Using a pedagogical style along with detailed proofs and illustrative examples, this book opens a view to the largely unexplored area of nonlinear systems with uncertainties. The focus is on adaptive nonlinear control results introduced with the new recursive design methodology--adaptive backstepping. Describes basic tools for nonadaptive backstepping design with state and output feedbacks.
6,923 citations
TL;DR: A direct adaptive tracking control architecture is proposed and evaluated for a class of continuous-time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible.
Abstract: A direct adaptive tracking control architecture is proposed and evaluated for a class of continuous-time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible. The architecture uses a network of Gaussian radial basis functions to adaptively compensate for the plant nonlinearities. Under mild assumptions about the degree of smoothness exhibit by the nonlinear functions, the algorithm is proven to be globally stable, with tracking errors converging to a neighborhood of zero. A constructive procedure is detailed, which directly translates the assumed smoothness properties of the nonlinearities involved into a specification of the network required to represent the plant to a chosen degree of accuracy. A stable weight adjustment mechanism is determined using Lyapunov theory. The network construction and performance of the resulting controller are illustrated through simulations with example systems. >
2,254 citations
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
TL;DR: A method is proposed for designing controllers with arbitrarily small tracking error for uncertain, mismatched nonlinear systems in the strict feedback form and it is shown that these low pass filters allow a design where the model is not differentiated, thus ending the complexity arising due to the "explosion of terms" that has made other methods difficult to implement in practice.
Abstract: A method is proposed for designing controllers with arbitrarily small tracking error for uncertain, mismatched nonlinear systems in the strict feedback form. This method is another "synthetic input technique," similar to backstepping and multiple surface control methods, but with an important addition, /spl tau/-1 low pass filters are included in the design where /spl tau/ is the relative degree of the output to be controlled. It is shown that these low pass filters allow a design where the model is not differentiated, thus ending the complexity arising due to the "explosion of terms" that has made other methods difficult to implement in practice. The backstepping approach, while suffering from the problem of "explosion of terms" guarantees boundedness of tracking errors globally; however, the proposed approach, while being simpler to implement, can only guarantee boundedness of tracking error semiglobally, when the nonlinearities in the system are non-Lipschitz.
1,901 citations
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