Neural Networks in Feedback Control Systems

Lewis, Frank L.; Ge, Shuzhi Sam

doi:10.1002/0471777455.ch19

Cited by 23 publications

(14 citation statements)

References 52 publications

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“…In recent years, a more aggressive objective has been to use the Adaptive Critic methodology to accomplish design of optimal controllers, with stability and robustness included! [32] Application of the Adaptive Critic methodology via NN s to the design of optimal controllers benefited from the confluence of three developments: 1) Reinforcement Learning, mentioned above, 2) Dynamic Programming, and 3) Backpropagation-based learning algorithms.…”

Section: Learning Via Neural Networkmentioning

confidence: 99%

“…A number of approaches were undertaken to deal with this issue, and various strategies for performing ADP-based procedures were developed that assured stability during the design process. Summaries of these approaches have been published, for example one in which I participated [30], but the most complete and mathematically sophisticated one(s) to my awareness are by the chair of this special session, Frank Lewis [32], whose group has contributed heavily to the field along this line. The reader is directed to such references.…”

Section: Ax I (T) Au I (T) Ax I (T) (T + 1)[axk (T + 1) + Axk (T + 1)mentioning

confidence: 99%

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A retrospective on Adaptive Dynamic Programming for control

Lendaris

2009

2009 International Joint Conference on Neural Networks

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Some three decades ago, certain computational intelligence methods of reinforcement learning were recognized as implementing an approximation of Bellman's Dynamic Programming method, which is known in the controls community as an important tool for designing optimal control policies for nonlinear plants and sequential decision making. Significant theoretical and practical developments have occurred within this arena, mostly in the past decade, with the methodology now usually referred to as Adaptive Dynamic Programming (ADP). The objective of this paper is to provide a retrospective of selected threads of such developments. In addition, a commentary is offered concerning present status of ADP, and threads for future research and development within the controls field are suggested.

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Section: Learning Via Neural Networkmentioning

confidence: 99%

Section: Ax I (T) Au I (T) Ax I (T) (T + 1)[axk (T + 1) + Axk (T + 1)mentioning

confidence: 99%

A retrospective on Adaptive Dynamic Programming for control

Lendaris

2009

2009 International Joint Conference on Neural Networks

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“…In recent years, theory and applications of nonlinear neural networks (NNs), which embed brainlike structures in the field of feedback control, have been well documented (F. L. Lewis et al 2006. The use of NNs in feedback control systems was first proposed by Werbos (1989).…”

Section: Introductionmentioning

confidence: 99%

An Online Nonlinear Optimal Controller Synthesis for Aircraft with Model Uncertainties

Ding

Balakrishnan

2010

AIAA Guidance, Navigation, and Control Conference

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In this paper, a new neural network approach/architecture, called the -Cost Function Based Single Network Adaptive Critic (J-SNAC)‖ is presented to solve difficult nonlinear control problems. This approach is applicable to a wide class of nonlinear systems where the optimal control equation can be explicitly expressed in terms of the state and cost variables. After the ‗training', the output of the neural network represents the optimal cost for a quadratic cost function. This neural network is synthesized by solving the equations associated with an optimal control problem for a control-affine nonlinear system. Optimal control is obtained by finding the derivatives of the output of the network with respect to its input and using it in the expression for optimal control. Development of this algorithm is presented in paper with an approximate dynamic programming (ADP) formulation.Synthesis of an optimal neurocontroller for the nominal system is described first. The optimal controller synthesis includes an ‗approximated system' which contains with an estimate of the uncertainties. The cost network is updated at every step to account for the uncertainties and help provide optimal control for the changed plant. An aircraft control problem has been solved with the J-SNAC approach in this paper. Flight control of an F-16 short-period mode is synthesized in which the dynamic nonlinearities are dependent not only on the states of the system, but also on the control inputs. NomenclatureB = a constant n×m matrix = unmodeled dynamics = neural network approximation of the actual plant = unmodeled dynamics for the i th state of the system = the difference between the states of the actual plant and the states of the virtual plant = cost = target cost at time step k = actual cost (output of the critic network) at time step k k = time index = a design parameter = weighting matrices for state = weighting matrices for control = time = state vector X 0 = an initial point X N = a final desired point = control vector = costate vector Ψ = utility function = states vector of the virtual plant n = number of NNs for the unmodeled dynamics = accuracy = the basis function of the critic network = the critic network weights = the basis function of the uncertainty network = the uncertainty network weights = reference inputDownloaded by CARLETON UNIVERSITY LIBRARY on July 30, 2015 | http://arc.aiaa.org | = desired steady state control = reference input = desired steady state control = positive-definite, continuously differentiable return function = angle of attack (deg) = pitch rate (deg) = incremental elevator deflection (deg) r = commanded reference input (deg)

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“…The use of artificial neural networks (NNs) is a common suggestion in this respect and NNbased controllers have nowadays entered the mainstream of control theory as a natural extension of adaptive control to systems that are nonlinear in the tunable parameters [1]. Most of the existing training methods for NNs rely on the gradient descent methodology and involve the computation of partial derivatives, or sensitivity functions.…”

Section: Introductionmentioning

confidence: 99%

Neuro‐adaptive sliding‐mode tracking control of robot manipulators

Topalov

Kaynak

Aydın

2007

Adaptive Control & Signal

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In this work, a new dynamical on-line learning algorithm for robust model-free neuro-adaptive control of a class of nonlinear systems with uncertain dynamics is proposed and experimentally tested in order to evaluate its performance and practical feasibility in industrial settings. The control application studied is the trajectory tracking control task for the first three joints of an open architecture articulated robot manipulator. The control scheme makes use of variable structure systems theory and the feedback-errorlearning concept. An inner sliding motion is established in terms of the neurocontroller parameters, aiming to lead the error in its control signal towards zero. The outer sliding motion bears on the system under control, the state tracking error vector of which is simultaneously driven towards the origin of the phase space. The existing relation between the two sliding motions is shown. Experimental results illustrate that the proposed neural-network-based controller possesses a remarkable learning capability to control complex dynamical systems, virtually without requiring a priori knowledge of the plant dynamics and laborious start-up procedures.

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Neural Networks in Feedback Control Systems

Cited by 23 publications

References 52 publications

A retrospective on Adaptive Dynamic Programming for control

A retrospective on Adaptive Dynamic Programming for control

An Online Nonlinear Optimal Controller Synthesis for Aircraft with Model Uncertainties

Neuro‐adaptive sliding‐mode tracking control of robot manipulators

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