A parameter estimation perspective of continuous time model reference adaptive control

Goodwin, Graham C.; Mayne, D. Q.

doi:10.1016/0005-1098(87)90118-x

Cited by 368 publications

(131 citation statements)

References 10 publications

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“…satθ M (·) is the saturation function, which is used to limit the updating speed of the parameters.θ M is the maximum parameter updating speed determined in advance. Prθ is the standard projection mapping (Goodwin and Mayne, 1987;Yao and Tomizuka, 1997):…”

Section: Online Parameter Estimationmentioning

confidence: 99%

Posture control of a 3-RPS pneumatic parallel platform with parameter initialization and an adaptive robust method

Tao

Shang

Meng

et al. 2017

J. Zhejiang Univ. - Sci. C

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A control algorithm for a 3-RPS parallel platform driven by pneumatic cylinders is discussed. All cylinders are controlled by proportional directional valves while the kinematic and dynamic properties of the system are modeled. The method of adaptive robust control is applied to the controller using a back-stepping approach and online parameter estimation. To compensate for the uncertainty and the influence caused by estimations, a fast dynamic compensator is integrated in the controller design. To prevent any influence caused by the load applied to the moving platform changing in a practical working situation, the identification of parameters is taken as the initialization of unknown parameters in the controller, which can improve the adaptability of the algorithm. Using these methods, the response rate of the parameter estimation and control performance were improved significantly. The adverse effects of load and restriction forces were eliminated by the initialization and online estimation. Experiments under different situations illustrated the effectiveness of the adaptive robust controller with parameter initialization, approaching average tracking errors of less than 1%.

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Section: Online Parameter Estimationmentioning

confidence: 99%

Posture control of a 3-RPS pneumatic parallel platform with parameter initialization and an adaptive robust method

Tao

Shang

Meng

et al. 2017

J. Zhejiang Univ. - Sci. C

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“…N-degree-of-freedom revolute-joint robotic manipulators dynamic model is considered as follows [21][22][23][24][25][26][27]: ! is the control input torque vector of robotic manipulators.…”

Section: Dynamics Model Of Robotic Manipulatorsmentioning

confidence: 99%

Robust Control for Robotic Manipulators Base on Adaptive Neural Network

Zhang¹,

Ye²,

Jiang³

et al. 2014

TOMEJ

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Abstract:As robotic manipulators are increasingly applied in industrial production, higher precision control methods are being studied by researchers. But robotic manipulators are a coupled system with a lot of uncertainties; higher precision is difficult to obtain by traditional control methods. A novel adaptive robust control method based on neural network is proposed by the paper. Neural network controller has been designed for adaptive learning and compensate for the unknown system and approach errors as disturbance is eliminated by robust controller. The weight adaptive laws on-line based on Lyapunov theory are designed. Robust controller is proposed based on H ∞ theory. These can assure the stability of the whole system, and L 2 gain also is less than the index value. Simulation studies show that the proposed control strategy is able to achieve higher control precision and has important engineering applications value.

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“…So, the more subgrids, the more possible centers. Since the higher order subgrids probably have some nodes that are the same as the lower order subgrids, the set of the new possible centers provided by the th order subgrid is defined as and for (11) where is an empty set. It shows that the possible center set corresponding to the th subgrid does not include those that are given by the lower order subgrids, i.e., (12) For example, in the two-dimensional (2-D) case, let the edge length of rectangulars on the th subgrid be half of the th subgrid.…”

Section: A Variable Gridmentioning

confidence: 99%

“…Here, in order to avoid parameter drift in the presence of modeling error, the application of the projection algorithm [11], [15], [45] gives the following adaptive laws for the parameter estimates and , as in (46) and (47), shown at the bottom of the page. It is clear that, if the initial weights are chosen such that and , the weight vectors and are confined to the sets and , respectively.…”

Section: A Adaptation Lawsmentioning

confidence: 99%

Variable neural networks for adaptive control of nonlinear systems

Liu

Kadirkamanathan

Billings

1999

IEEE Trans. Syst., Man, Cybern. C

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Abstract-This paper is concerned with the adaptive control of continuous-time nonlinear dynamical systems using neural networks. A novel neural network architecture, referred to as a variable neural network, is proposed and shown to be useful in approximating the unknown nonlinearities of dynamical systems. In the variable neural networks, the number of basis functions can be either increased or decreased with time according to specified design strategies so that the network will not overfit or underfit the data set. Based on the Gaussian radial basis function (GRBF) variable neural network, an adaptive control scheme is presented. The location of the centers and the determination of the widths of the GRBF's in the variable neural network are analyzed to make a compromise between orthogonality and smoothness. The weight adaptive laws developed using the Lyapunov synthesis approach guarantee the stability of the overall control scheme, even in the presence of modeling error. The tracking errors converge to the required accuracy through the adaptive control algorithm derived by combining the variable neural network and Lyapunov synthesis techniques. The operation of an adaptive control scheme using the variable neural network is demonstrated using two simulated examples.Index Terms-Adaptive control, neural networks, nonlinear systems, radial basis functions.

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A parameter estimation perspective of continuous time model reference adaptive control

Cited by 368 publications

References 10 publications

Posture control of a 3-RPS pneumatic parallel platform with parameter initialization and an adaptive robust method

Posture control of a 3-RPS pneumatic parallel platform with parameter initialization and an adaptive robust method

Robust Control for Robotic Manipulators Base on Adaptive Neural Network

Variable neural networks for adaptive control of nonlinear systems

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