Continuous robust control design for nonlinear uncertain systems without a priori knowledge of control direction

Kaloust, J.; Qu, Zhihua

doi:10.1109/9.341792

Cited by 85 publications

(45 citation statements)

References 12 publications

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“…For convenience, let us introduce the following notations: (30) and it is obvious that . Substituting (27) into (29) and noting that , we obtain (31) where and it is trivial to show that .…”

Section: Adaptive Nn Control Designmentioning

confidence: 99%

“…As mentioned in Section II-C, there exists an ideal constant weights vector , such that (27) where is the NN approximation error and is a sufficient large compact set.…”

Section: Adaptive Nn Control Designmentioning

confidence: 99%

“…According to (26) and (27), the better the NN approximation is (the smaller the NN approximation error is), the smaller is. If , we have .…”

Section: Nn Learning Performancementioning

confidence: 99%

“…In [26], the projected parameter approach was used for adaptive control of the first-order nonlinear systems with unknown control directions. In [27], online identification of the unknown control directions was proposed for a class of the second-order nonlinear systems.…”

mentioning

confidence: 99%

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Output Feedback NN Control for Two Classes of Discrete-Time Systems With Unknown Control Directions in a Unified Approach

Yang

Chen

et al. 2008

IEEE Trans. Neural Netw.

207

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Abstract-In this paper, output feedback adaptive neural network (NN) controls are investigated for two classes of nonlinear discrete-time systems with unknown control directions: 1) nonlinear pure-feedback systems and 2) nonlinear autoregressive moving average with exogenous inputs (NARMAX) systems. To overcome the noncausal problem, which has been known to be a major obstacle in the discrete-time control design, both systems are transformed to a predictor for output feedback control design. Implicit function theorem is used to overcome the difficulty of the nonaffine appearance of the control input. The problem of lacking a priori knowledge on the control directions is solved by using discrete Nussbaum gain. The high-order neural network (HONN) is employed to approximate the unknown control. The closed-loop system achieves semiglobal uniformly-ultimately-bounded (SGUUB) stability and the output tracking error is made within a neighborhood around zero. Simulation results are presented to demonstrate the effectiveness of the proposed control.Index Terms-Discrete Nussbaum gain, discrete-time system, nonlinear autoregressive moving average with exogenous inputs (NARMAX) systems, neural networks (NNs), pure-feedback system, unknown control directions.

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Section: Adaptive Nn Control Designmentioning

confidence: 99%

“…As mentioned in Section II-C, there exists an ideal constant weights vector , such that (27) where is the NN approximation error and is a sufficient large compact set.…”

Section: Adaptive Nn Control Designmentioning

confidence: 99%

“…According to (26) and (27), the better the NN approximation is (the smaller the NN approximation error is), the smaller is. If , we have .…”

Section: Nn Learning Performancementioning

confidence: 99%

mentioning

confidence: 99%

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Output Feedback NN Control for Two Classes of Discrete-Time Systems With Unknown Control Directions in a Unified Approach

Yang

Chen

et al. 2008

IEEE Trans. Neural Netw.

207

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show abstract

“…Recently, there are many papers that deal with robust adaptive control problems for parametric feedback nonlinear systems with exogenous disturbances and/or nonparametric uncertain nonlinearities [11][12][13][14][16][17][18]. However, the known nonlinearities that appeared at the control input were still restricted to [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Robust Adaptive Control for Strict-Feedback Nonlinear Systems

Mizumoto

Gopaluni

Shah

et al. 2008

Asian Journal of Control

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In this paper, we propose a robust adaptive tracking control based on the backstepping strategy for strict-feedback nonlinear systems with nonparametric uncertain nonlinearities. It is shown that one can design a stable adaptive control system provided that the uncertain nonlinearities can be decomposed by unknown bounded nonlinear functions and known nonlinear functions. The proposed method can deal with uncertain nonlinearities that appear at the control input term too. It is also shown that suitable choice of design parameters guarantees the convergence of tracking error to any desired bound.

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Adaptive iterative learning control of discrete‐time varying systems with unknown control direction

Yan

Sun

2012

Adaptive Control & Signal

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Without using Nussbaum gain, a novel method is presented to solve the unknown control direction problem for discrete-time systems. The underlying idea is to fully exploit the convergence property of parameter estimates in well-known adaptive algorithms. By incorporating two modifications into the control and the parameter update laws, respectively, we present an adaptive iterative learning control scheme for discretetime varying systems without the prior knowledge of the sign of control gain. It is shown that the proposed adaptive iterative learning control can achieve perfect tracking over the finite time interval while all the closed-loop signals remain bounded. An illustrative example is presented to verify effectiveness of the proposed scheme.where p k is randomly iteration-variant in the interval OE0, 1.Define the performance index J k D max 16t 6200 jy k .t / y k .t /j. The iteration stops when J k < 0.01. The proposed adaptive ILC scheme is applied in the simulation. The tracking performance is achieved at the 57th iteration. Figure 2 shows the convergence history of the performance index J k . Figure 3 shows the system output y k .t / and the reference trajectory y k .t / at k D 57, which clearly shows that y k .t / converges to y k .t / for all t 2 f1, 2,, 200g. Figure 4 shows the control input u k .t / at k D 57. The singularity of the control law is successfully avoided via the proposed approach.

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Continuous robust control design for nonlinear uncertain systems without a priori knowledge of control direction

Cited by 85 publications

References 12 publications

Output Feedback NN Control for Two Classes of Discrete-Time Systems With Unknown Control Directions in a Unified Approach

Output Feedback NN Control for Two Classes of Discrete-Time Systems With Unknown Control Directions in a Unified Approach

Robust Adaptive Control for Strict-Feedback Nonlinear Systems

Adaptive iterative learning control of discrete‐time varying systems with unknown control direction

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