Observer-Based Adaptive Fuzzy Backstepping Dynamic Surface Control for a Class of MIMO Nonlinear Systems
01 Aug 2011-Vol. 41, Iss: 4, pp 1124-1135
TL;DR: An adaptive fuzzy backstepping dynamic surface control approach is developed for a class of multiple-input-multiple-output nonlinear systems with immeasurable states and is proved that all the signals of the closed-loop adaptive-control system are semiglobally uniformly ultimately bounded, and the tracking errors converge to a small neighborhood of the origin.
Abstract: In this paper, an adaptive fuzzy backstepping dynamic surface control (DSC) approach is developed for a class of multiple-input-multiple-output nonlinear systems with immeasurable states. Using fuzzy-logic systems to approximate the unknown nonlinear functions, a fuzzy state observer is designed to estimate the immeasurable states. By combining adaptive-backstepping technique and DSC technique, an adaptive fuzzy output-feedback backstepping-control approach is developed. The proposed control method not only overcomes the problem of “explosion of complexity” inherent in the backstepping-design methods but also overcomes the problem of unavailable state measurements. It is proved that all the signals of the closed-loop adaptive-control system are semiglobally uniformly ultimately bounded, and the tracking errors converge to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approach.
Citations
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TL;DR: It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are bounded and the partial state tracking errors are confined all times within the prescribed bounds.
Abstract: In this paper, a partial tracking error constrained fuzzy output-feedback dynamic surface control (DSC) scheme is proposed for a class of uncertain multi-input and multi-output (MIMO) nonlinear systems. The considered MIMO nonlinear systems contain unknown functions and without the requirement of their states being available for the controller design. With the help of fuzzy logic systems identifying the MIMO unknown nonlinear systems, a fuzzy adaptive observer is established to estimate the unmeasured states. By transforming the tracking errors into new virtual error variables and based on the DSC backstepping recursive design technique, a new adaptive fuzzy output-feedback control method is developed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are bounded and the partial state tracking errors are confined all times within the prescribed bounds. The simulation results and comparisons with the previous control approaches confirm the effectiveness and utility of the proposed scheme.
475 citations
Cites background or methods from "Observer-Based Adaptive Fuzzy Backs..."
...,mj , is called error surface; θj,ij is a state variable, which is obtained through a firstorder filter on intermediate control function αj,ij −1 ; and χj,ij is called the output error of the first-order filter [17]–[19]....
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...To show the effectiveness of the prescribed performance introduced in this study, we apply the control method in [19] to the systems (96) and (97)....
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...Note that if the control method in this paper does not adopt the prescribed performance, then it becomes the control method in [19]....
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...2327987 adaptive NN and fuzzy backstepping dynamic surface control (DSC) schemes were proposed for uncertain nonlinear systems in [17]–[19]....
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...In addition, the simulation comparisons with the previous control method [19] are made to illustrate the effectiveness of the prescribed performance....
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TL;DR: A novel finite-time command filtered backstepping approach is proposed by using the new virtual control signals and the modified error compensation signals, which not only has the advantages of the conventional command-filtered backstepped control, but also guarantees the finite- time convergent property.
472 citations
TL;DR: An observer-based adaptive consensus tracking control strategy is developed for a class of high-order nonlinear multiagent systems, of which each follower agent is modeled in a semi-strict-feedback form.
Abstract: Combined with backstepping techniques, an observer-based adaptive consensus tracking control strategy is developed for a class of high-order nonlinear multiagent systems, of which each follower agent is modeled in a semi-strict-feedback form By constructing the neural network-based state observer for each follower, the proposed consensus control method solves the unmeasurable state problem of high-order nonlinear multiagent systems The control algorithm can guarantee that all signals of the multiagent system are semi-globally uniformly ultimately bounded and all outputs can synchronously track a reference signal to a desired accuracy A simulation example is carried out to further demonstrate the effectiveness of the proposed consensus control method
455 citations
Cites background from "Observer-Based Adaptive Fuzzy Backs..."
...In tracking control of nonliear systems, observer-based adaptive control has been well developed (see [25]–[34]), where [25]–[30] are for single-input and single-output nonlinear systems, [31]–[34] for multiple-input and multiple-output nonlinear systems....
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TL;DR: The main features of the proposed adaptive control approach are that it can guarantee the stability of the closed-loop system, and the tracking errors converge to a small neighborhood of zero, and it can solve the problems of unknown control direction, unknown dead-zone, and unmeasured states simultaneously.
Abstract: In this paper, an adaptive fuzzy backstepping output-feedback tracking control approach is proposed for a class of multi-input and multi-output (MIMO) stochastic nonlinear systems. The MIMO stochastic nonlinear systems under study are assumed to possess unstructured uncertainties, unknown dead-zones, and unknown control directions. By using a linear state transformation, the unknown control coefficients and the unknown slopes characteristic of the dead-zones are lumped together, and the original system is transformed to a new system on which the control design becomes feasible. Fuzzy logic systems are used to approximate the unstructured uncertainties, and a fuzzy state observer is designed to estimate the unmeasured states. By introducing a special Nussbaum gain function into the backstepping control design, a stable adaptive fuzzy output-feedback tracking control scheme is developed. The main features of the proposed adaptive control approach are that it can guarantee the stability of the closed-loop system, and the tracking errors converge to a small neighborhood of zero. Moreover, it can solve the problems of unknown control direction, unknown dead-zone, and unmeasured states simultaneously. Two simulation examples are provided to show the effectiveness of the proposed approach.
410 citations
TL;DR: A new fuzzy controller with the composite parameters adaptive laws are developed and it is proved that all the signals of the closed-loop system are bounded and the system output can follow the given bounded reference signal.
Abstract: In this paper, a composite adaptive fuzzy output-feedback control approach is proposed for a class of single-input and single-output strict-feedback nonlinear systems with unmeasured states and input saturation. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a fuzzy state observer is designed to estimate the unmeasured states. By utilizing the designed fuzzy state observer, a serial–parallel estimation model is established. Based on adaptive backstepping dynamic surface control technique and utilizing the prediction error between the system states observer model and the serial–parallel estimation model, a new fuzzy controller with the composite parameters adaptive laws are developed. It is proved that all the signals of the closed-loop system are bounded and the system output can follow the given bounded reference signal. A numerical example and simulation comparisons with previous control methods are provided to show the effectiveness of the proposed approach.
403 citations
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
2,208 citations
"Observer-Based Adaptive Fuzzy Backs..." refers background in this paper
...However, the separation principle does not hold for nonlinear systems [3]; thus, the observer-based adaptive-output-feedback-control design is more complex and difficult than the counterpart based on state feedback....
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...In an effort to extend the backstepping-control idea to larger classes of nonlinear systems, the authors in [3] studied the adaptivecontrol problem of parametric pure-feedback systems and obtained local stability results, and [4] proposed several adaptive approaches to nonlinear systems with a triangular structure....
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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
"Observer-Based Adaptive Fuzzy Backs..." refers background in this paper
...In fact, the explosion of complexity is caused by repeated differentiations of certain nonlinear functions, such as virtual controls, as pointed out by [22]–[25]....
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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
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
"Observer-Based Adaptive Fuzzy Backs..." refers methods in this paper
...As a breakthrough in nonlinear control, adaptive-backstepping control was introduced to achieve global stability and asymptotic tracking for a class of nonlinear systems in parametric strict-feedback form by [1]....
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