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T.N. Sharma

Bio: T.N. Sharma is an academic researcher from Motilal Nehru National Institute of Technology Allahabad. The author has contributed to research in topics: Adaptive control & Nonlinear system. The author has an hindex of 1, co-authored 2 publications receiving 12 citations.

Papers
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Proceedings ArticleDOI
03 Jun 2011
TL;DR: This paper proposes the adaptive back stepping controller for a class of nonlinear discrete-time systems in strict-feedback form with unknown dead-zone using neural networks to guarantee uniform ultimate boundedness (UUB) for all signals in closed loop system.
Abstract: This paper proposes the adaptive back stepping controller for a class of nonlinear discrete-time systems in strict-feedback form with unknown dead-zone using neural networks. The control design is attained by introducing the dead-zone nonlinearity and using it in the controller design with back stepping technique. A dead-zone inverse is developed to compensate the dead-zone effect in nonlinear systems. In this scheme, Chebyshev Neural Network (CNN) is used to approximate the unknown nonlinear functions and also used to compensate the dead-zone nonlinearity. New weight updates laws are derived to guarantee uniform ultimate boundedness (UUB) for all signals in closed loop system.

12 citations

Proceedings ArticleDOI
07 Oct 2011
TL;DR: A back stepping controller for the class of discrete-time nonlinear system in the presence of input nonlinearities like saturation and dead-zone and weight update laws, based on Lyapunov theory are derived to make this scheme adaptive and the convergence properties are shown.
Abstract: This paper proposes a back stepping controller for the class of discrete-time nonlinear system in the presence of input nonlinearities like saturation and dead-zone. A robust adaptive neural network (NN) control is investigated for a general class of uncertain single-input-single-output (SISO) discrete-time nonlinear systems with unknown system dynamics and input nonlinearities i.e. combination of saturation and dead-zone. For input nonlinearities, discrete-time SISO nonlinear system in combination with back stepping and Lyapunov synthesis is proposed for adaptive neural network design with guaranteed stability. The actuator nonlinearities are assumed to be unknown and compensated by a pre compensator using Chebyshev neural network (CNN) and unknown nonlinear functions are also approximated by CNN. Weight update laws, based on Lyapunov theory are derived to make this scheme adaptive and the convergence properties are shown. Simulation results validate the effectiveness of proposed scheme.

Cited by
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Journal ArticleDOI
TL;DR: An adaptive fuzzy optimal control design is addressed for a class of unknown nonlinear discrete-time systems that contain unknown functions and nonsymmetric dead-zone and can be proved based on the difference Lyapunov function method.
Abstract: In this paper, an adaptive fuzzy optimal control design is addressed for a class of unknown nonlinear discrete-time systems. The controlled systems are in a strict-feedback frame and contain unknown functions and nonsymmetric dead-zone. For this class of systems, the control objective is to design a controller, which not only guarantees the stability of the systems, but achieves the optimal control performance as well. This immediately brings about the difficulties in the controller design. To this end, the fuzzy logic systems are employed to approximate the unknown functions in the systems. Based on the utility functions and the critic designs, and by applying the backsteppping design technique, a reinforcement learning algorithm is used to develop an optimal control signal. The adaptation auxiliary signal for unknown dead-zone parameters is established to compensate for the effect of nonsymmetric dead-zone on the control performance, and the updating laws are obtained based on the gradient descent rule. The stability of the control systems can be proved based on the difference Lyapunov function method. The feasibility of the proposed control approach is further demonstrated via two simulation examples.

366 citations

Journal ArticleDOI
TL;DR: By using the Lyapunov method, it is proved that the closed-loop system is stable in the sense that the semiglobally uniformly ultimately bounded of all the signals and the tracking errors converge to a bounded compact set.
Abstract: An adaptive neural network tracking control is studied for a class of multiple-input multiple-output (MIMO) nonlinear systems. The studied systems are in discrete-time form and the discretized dead-zone inputs are considered. In addition, the studied MIMO systems are composed of $N$ subsystems, and each subsystem contains unknown functions and external disturbance. Due to the complicated framework of the discrete-time systems, the existence of the dead zone and the noncausal problem in discrete-time, it brings about difficulties for controlling such a class of systems. To overcome the noncausal problem, by defining the coordinate transformations, the studied systems are transformed into a special form, which is suitable for the backstepping design. The radial basis functions NNs are utilized to approximate the unknown functions of the systems. The adaptation laws and the controllers are designed based on the transformed systems. By using the Lyapunov method, it is proved that the closed-loop system is stable in the sense that the semiglobally uniformly ultimately bounded of all the signals and the tracking errors converge to a bounded compact set. The simulation examples and the comparisons with previous approaches are provided to illustrate the effectiveness of the proposed control algorithm.

154 citations

Journal ArticleDOI
TL;DR: An effective adaptive control approach is constructed to stabilize a class of nonlinear discrete-time systems, which contain unknown functions, unknown dead-zone input, and unknown control direction, and the neural networks are used to approximate the unknown function.
Abstract: In this paper, an effective adaptive control approach is constructed to stabilize a class of nonlinear discrete-time systems, which contain unknown functions, unknown dead-zone input, and unknown control direction. Different from linear dead zone, the dead zone, in this paper, is a kind of nonlinear dead zone. To overcome the noncausal problem, which leads to the control scheme infeasible, the systems can be transformed into a $m$ -step-ahead predictor. Due to nonlinear dead-zone appearance, the transformed predictor still contains the nonaffine function. In addition, it is assumed that the gain function of dead-zone input and the control direction are unknown. These conditions bring about the difficulties and the complicacy in the controller design. Thus, the implicit function theorem is applied to deal with nonaffine dead-zone appearance, the problem caused by the unknown control direction can be resolved through applying the discrete Nussbaum gain, and the neural networks are used to approximate the unknown function. Based on the Lyapunov theory, all the signals of the resulting closed-loop system are proved to be semiglobal uniformly ultimately bounded. Moreover, the tracking error is proved to be regulated to a small neighborhood around zero. The feasibility of the proposed approach is demonstrated by a simulation example.

99 citations

Journal ArticleDOI
TL;DR: The stability and control issues of a class of uncertain nonlinear discrete-time systems in the strict feedback form are investigated and Lyapunov analysis method is utilized to prove the stability of the closed-loop system.
Abstract: In this paper, the stability and control issues of a class of uncertain nonlinear discrete-time systems in the strict feedback form are investigated. The dead-zone input in the systems, whose property is non-symmetric and discretized, is investigated. The unknown functions in the systems are approximated by using the radial basis function neural networks (RBFNNs). Backstepping design procedure is employed in the controller and the adaptation laws design. Lyapunov analysis method is utilized to prove the stability of the closed-loop system. A simulation example is given to illustrate the effectiveness of the proposed approach.

39 citations

Journal ArticleDOI
TL;DR: An adaptive predictive control algorithm is applied to control a class of SISO continuous stirred tank reactor (CSTR) system in discrete time and it is proven that all the signals of the resulting closed-loop system are guaranteed to be semi-global uniformly ultimately bounded, and the tracking error can be reduced to a small compact set.
Abstract: In this paper, an adaptive predictive control algorithm is applied to control a class of SISO continuous stirred tank reactor (CSTR) system in discrete time. The main contribution of the paper is that the considered systems belong to pure-feedback form where the unknown dead-zone is considered in the in-fan, and dead-zone is nonsymmetric, and it is first to control this class of systems. Radial basis function neural networks are used to approximate the unknown functions, and the mean value theorem is exploited in the design. Based on the Lyapunov analysis method, it is proven that all the signals of the resulting closed-loop system are guaranteed to be semi-global uniformly ultimately bounded, and the tracking error can be reduced to a small compact set. A simulation example for CSTR systems is studied to verify the effectiveness of the proposed approach.

17 citations