Adaptive Fuzzy Control for Nonstrict-Feedback Systems With Input Saturation and Output Constraint
01 Jan 2017-Vol. 47, Iss: 1, pp 1-12
TL;DR: An adaptive fuzzy control approach for a category of uncertain nonstrict-feedback systems with input saturation and output constraint is presented, and the simulation results reveal the effectiveness of the proposed approach.
Abstract: This paper presents an adaptive fuzzy control approach for a category of uncertain nonstrict-feedback systems with input saturation and output constraint. A variable separation approach is introduced to overcome the difficulty arising from the nonstrict-feedback structure. The problem of input saturation is solved by introducing an auxiliary design system, and output constraint is handled by utilizing a barrier Lyapunov function. Combing fuzzy logic system with the adaptive backstepping technique, the semi-global boundedness of all variables in the closed-loop systems is guaranteed, and the tracking error is driven to the origin with a small neighborhood. The stability of the closed-loop systems is proved, and the simulation results reveal the effectiveness of the proposed approach.
Citations
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TL;DR: A finite-time fuzzy adaptive control scheme is presented to overcome the “explosion of complexity” problem for a class of multi-input and multi-output (MIMO) nonlinear nonstrict feedback systems.
Abstract: This paper investigates the finite-time adaptive fuzzy control problem for a class of multi-input and multi-output (MIMO) nonlinear nonstrict feedback systems. During the control design process, fuzzy logic systems (FLSs) are utilized to approximate the unknown nonlinear functions, and fuzzy state observer is constructed to estimate the unmeasured states. By combining adaptive backstepping with the dynamic surface control (DSC) technique, a finite-time fuzzy adaptive control scheme is presented to overcome the “explosion of complexity” problem. The stability of the close-loop systems can be proved based on the finite-time Lyapunov stability theory. The presented control scheme demonstrates that the closed-loop systems are semiglobal practical finite-time stability, and tracking errors converge to a small neighborhood of the origin in a finite time. Finally, two simulation examples are provided to show the effectiveness of the presented control method.
347 citations
Cites background from "Adaptive Fuzzy Control for Nonstric..."
...[26] developed the fuzzy adaptive control for a class of single-input and single-output (SISO) nonstrict feedback nonlinear systems with output constraint....
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...In order to deal with this problem, recently, some significant adaptive fuzzy or NNs control approaches have been presented for uncertain nonlinear systems in nonstrict feedback form, for example, [23]–[26]....
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TL;DR: This paper considers the trajectory tracking of a marine surface vessel in the presence of output constraints and uncertainties, and an asymmetric barrier Lyapunov function is employed to cope with the output constraints.
Abstract: In this paper, we consider the trajectory tracking of a marine surface vessel in the presence of output constraints and uncertainties. An asymmetric barrier Lyapunov function is employed to cope with the output constraints. To handle the system uncertainties, we apply adaptive neural networks to approximate the unknown model parameters of a vessel. Both full state feedback control and output feedback control are proposed in this paper. The state feedback control law is designed by using the Moore–Penrose pseudoinverse in case that all states are known, and the output feedback control is designed using a high-gain observer. Under the proposed method the controller is able to achieve the constrained output. Meanwhile, the signals of the closed loop system are semiglobally uniformly bounded. Finally, numerical simulations are carried out to verify the feasibility of the proposed controller.
322 citations
TL;DR: In order to overcome the difficulty of controller design for nonstrict-feedback system in backstepping design process, a variables separation method is introduced and an adaptive fuzzy controller is designed to guarantee all the signals of the resulting closed-loop system to be bounded.
Abstract: This paper investigates the problem of adaptive fuzzy state-feedback control for a category of single-input and single-output nonlinear systems in nonstrict-feedback form. Unmodeled dynamics and input constraint are considered in the system. Fuzzy logic systems are employed to identify unknown nonlinear characteristics existing in systems. An appropriate Lyapunov function is chosen to ensure unmodeled dynamics to be input-to-state practically stable. A smooth function is introduced to tackle input saturation. In order to overcome the difficulty of controller design for nonstrict-feedback system in backstepping design process, a variables separation method is introduced. Moreover, based on small-gain technique, an adaptive fuzzy controller is designed to guarantee all the signals of the resulting closed-loop system to be bounded. Finally, two illustrative examples are given to validate the effectiveness of the new design techniques.
283 citations
Cites background from "Adaptive Fuzzy Control for Nonstric..."
...[55] proposed an adaptive fuzzy tracking control scheme for nonstrict-feedback systems in presence of input and output constraints....
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...Up to now, tremendous progress has been made in nonstrict-feedback systems [55]–[58]....
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TL;DR: This article investigates the adaptive fault-tolerant tracking control problem for a class of discrete-time multiagent systems via a reinforcement learning algorithm and proves that all signals of the closed-loop system are semiglobally uniformly ultimately bounded.
Abstract: This article investigates the adaptive fault-tolerant tracking control problem for a class of discrete-time multiagent systems via a reinforcement learning algorithm. The action neural networks (NNs) are used to approximate unknown and desired control input signals, and the critic NNs are employed to estimate the cost function in the design procedure. Furthermore, the direct adaptive optimal controllers are designed by combining the backstepping technique with the reinforcement learning algorithm. Comparing the existing reinforcement learning algorithm, the computational burden can be effectively reduced by using the method of less learning parameters. The adaptive auxiliary signals are established to compensate for the influence of the dead zones and actuator faults on the control performance. Based on the Lyapunov stability theory, it is proved that all signals of the closed-loop system are semiglobally uniformly ultimately bounded. Finally, some simulation results are presented to illustrate the effectiveness of the proposed approach.
272 citations
Cites methods from "Adaptive Fuzzy Control for Nonstric..."
...Remark 1: In the existing results [35]–[38], the NNs were used to estimate the unknown nonlinear functions....
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TL;DR: A finite-time controller, which is capable of ensuring the semiglobal practical finite- time stability for the closed-loop systems, is developed using the adaptive neural networks control method, adding one power integrator technique and backstepping scheme.
Abstract: This article addresses the finite-time optimal control problem for a class of nonlinear systems whose powers are positive odd rational numbers. First of all, a finite-time controller, which is capable of ensuring the semiglobal practical finite-time stability for the closed-loop systems, is developed using the adaptive neural networks (NNs) control method, adding one power integrator technique and backstepping scheme. Second, the corresponding design parameters are optimized, and the finite-time optimal control property is obtained by means of minimizing the well-defined and designed cost function. Finally, a numerical simulation example is given to further validate the feasibility and effectiveness of the proposed optimal control strategy.
269 citations
References
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01 Feb 1994TL;DR: This paper presents a meta-analysis of the design and stability analysis of fuzzy identifiers of nonlinear dynamic systems fuzzy adaptive filters of adaptive fuzzy controllers using input-output linearization concepts.
Abstract: Description and analysis of fuzzy logic systems training of fuzzy logic systems using back-propagation training of fuzzy logic systems using orthogonal least squares training of fuzzy logic systems using a table-lookup scheme training of fuzzy logic systems using nearest neighbourhood clustering comparison of adaptive fuzzy systems with artificial neural networks stable indirect adaptive fuzzy control of nonlinear systems stable direct adaptive fuzzy control of nonlinear systems design of adaptive fuzzy controllers using input-output linearization concepts design and stability analysis of fuzzy identifiers of nonlinear dynamic systems fuzzy adaptive filters.
2,455 citations
"Adaptive Fuzzy Control for Nonstric..." refers background in this paper
...INTRODUCTION RECENTLY, the developments of controller design for nonlinear system were investigated intensively, and various control approaches have been proposed, such as adaptive backstepping control [1]–[13], fuzzy-model based control [14]–[23] and sliding mode control [24]–[28]....
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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 backstepping based control design for a class of nonlinear systems in strict-feedback form with arbitrary uncertainty is developed and is able to eliminate the problem of "explosion of complexity" inherent in the existing method.
Abstract: The dynamic surface control (DSC) technique was developed recently by Swaroop et al. This technique simplified the backstepping design for the control of nonlinear systems in strict-feedback form by overcoming the problem of "explosion of complexity." It was later extended to adaptive backstepping design for nonlinear systems with linearly parameterized uncertainty. In this paper, by incorporating this design technique into a neural network based adaptive control design framework, we have developed a backstepping based control design for a class of nonlinear systems in strict-feedback form with arbitrary uncertainty. Our development is able to eliminate the problem of "explosion of complexity" inherent in the existing method. In addition, a stability analysis is given which shows that our control law can guarantee the uniformly ultimate boundedness of the solution of the closed-loop system, and make the tracking error arbitrarily small.
1,079 citations
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 Fuzzy Control for Nonstric..." refers methods in this paper
...[47] presented a new adaptive fuzzy tracking control method for uncertain MIMO nonlinear systems with input constraints....
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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 Fuzzy Control for Nonstric..." refers background in this paper
...Definition 1 [56]: A BLF V(x) (V(x) > 0) is a scalar continuous function, defined with respect to the system ẋ = f (x) on an open region D containing the origin....
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...Lemma 4 [56]: For any positive constant kd1, if z1 in the interval of |z1| < kd1, z1 will satisfy the following inequality:...
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...Lemma 3 [56]: For arbitrary positive constant kd1, define two open sets as Z1 := {z1 ∈ R : |z1| < kd1} ⊂ R and N := Rl × Z1 ⊂ Rl+1....
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...Assumption 2 [56]: The reference signal yr and y (k) r (t) are sufficiently smooth and bounded, y r (t) means kth derivatives of yr in time t....
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