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S Jagannathan - One of the best experts on this subject based on the ideXlab platform.
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near optimal event triggered control of Nonlinear Discrete time systems using neurodynamic programming
IEEE Transactions on Neural Networks, 2016Co-Authors: Avimanyu Sahoo, S JagannathanAbstract:This paper presents an event-triggered near optimal control of uncertain Nonlinear Discrete-time systems. Event-driven neurodynamic programming (NDP) is utilized to design the control policy. A neural network (NN)-based identifier, with event-based state and input vectors, is utilized to learn the system dynamics. An actor–critic framework is used to learn the cost function and the optimal control input. The NN weights of the identifier, the critic, and the actor NNs are tuned aperiodically once every triggered instant. An adaptive event-trigger condition to decide the trigger instants is derived. Thus, a suitable number of events are generated to ensure a desired accuracy of approximation. A near optimal performance is achieved without using value and/or policy iterations. A detailed analysis of nontrivial inter-event times with an explicit formula to show the reduction in computation is also derived. The Lyapunov technique is used in conjunction with the event-trigger condition to guarantee the ultimate boundedness of the closed-loop system. The simulation results are included to verify the performance of the controller. The net result is the development of event-driven NDP.
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adaptive neural network based event triggered control of single input single output Nonlinear Discrete time systems
IEEE Transactions on Neural Networks, 2016Co-Authors: Avimanyu Sahoo, Hao Xu, S JagannathanAbstract:This paper presents a novel adaptive neural network (NN) control of single-input and single-output uncertain Nonlinear Discrete-time systems under event sampled NN inputs. In this control scheme, the feedback signals are transmitted, and the NN weights are tuned in an aperiodic manner at the event sampled instants. After reviewing the NN approximation property with event sampled inputs, an adaptive state estimator (SE), consisting of linearly parameterized NNs, is utilized to approximate the unknown system dynamics in an event sampled context. The SE is viewed as a model and its approximated dynamics and the state vector, during any two events, are utilized for the event-triggered controller design. An adaptive event-trigger condition is derived by using both the estimated NN weights and a dead-zone operator to determine the event sampling instants. This condition both facilitates the NN approximation and reduces the transmission of feedback signals. The ultimate boundedness of both the NN weight estimation error and the system state vector is demonstrated through the Lyapunov approach. As expected, during an initial online learning phase, events are observed more frequently. Over time with the convergence of the NN weights, the inter-event times increase, thereby lowering the number of triggered events. These claims are illustrated through the simulation results.
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neural network based adaptive event triggered control of affine Nonlinear Discrete time systems with unknown internal dynamics
American Control Conference, 2013Co-Authors: Avimanyu Sahoo, S JagannathanAbstract:In this paper, the design of a neural network (NN) based adaptive model-based event-triggered control of an uncertain single input single output (SISO) Nonlinear Discrete time system in affine form is presented. The controller uses an adaptive estimator consisting of a single-layer NN not only to approximate the internal dynamics of an affine Nonlinear Discrete-time system but also to provide an estimate of the state vector during inter event interval. The NN weights of the adaptive NN estimator are tuned in a aperiodic manner at the event trigger instants unlike periodic updates in standard adaptive neural network (NN) control. A dead zone operator is used to reset the event trigger error to zero as long as the system states continue to remain in a bounded region due to NN reconstruction errors. Lyapunov method is used to derive the event trigger condition, prove uniform ultimate boundedness (UUB) of the NN weight estimation error and system states.
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online optimal control of affine Nonlinear Discrete time systems with unknown internal dynamics by using time based policy update
IEEE Transactions on Neural Networks, 2012Co-Authors: Travis Dierks, S JagannathanAbstract:In this paper, the Hamilton-Jacobi-Bellman equation is solved forward-in-time for the optimal control of a class of general affine Nonlinear Discrete-time systems without using value and policy iterations. The proposed approach, referred to as adaptive dynamic programming, uses two neural networks (NNs), to solve the infinite horizon optimal regulation control of affine Nonlinear Discrete-time systems in the presence of unknown internal dynamics and a known control coefficient matrix. One NN approximates the cost function and is referred to as the critic NN, while the second NN generates the control input and is referred to as the action NN. The cost function and policy are updated once at the sampling instant and thus the proposed approach can be referred to as time-based ADP. Novel update laws for tuning the unknown weights of the NNs online are derived. Lyapunov techniques are used to show that all signals are uniformly ultimately bounded and that the approximated control signal approaches the optimal control input with small bounded error over time. In the absence of disturbances, an optimal control is demonstrated. Simulation results are included to show the effectiveness of the approach. The end result is the systematic design of an optimal controller with guaranteed convergence that is suitable for hardware implementation.
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online optimal control of Nonlinear Discrete time systems using approximate dynamic programming
Journal of Control Theory and Applications, 2011Co-Authors: Travis Dierks, S JagannathanAbstract:In this paper, the optimal control of a class of general affine Nonlinear Discrete-time (DT) systems is undertaken by solving the Hamilton Jacobi-Bellman (HJB) equation online and forward in time. The proposed approach, referred normally as adaptive or approximate dynamic programming (ADP), uses online approximators (OLAs) to solve the infinite horizon optimal regulation and tracking control problems for affine Nonlinear DT systems in the presence of unknown internal dynamics. Both the regulation and tracking controllers are designed using OLAs to obtain the optimal feedback control signal and its associated cost function. Additionally, the tracking controller design entails a feedforward portion that is derived and approximated using an additional OLA for steady state conditions. Novel update laws for tuning the unknown parameters of the OLAs online are derived. Lyapunov techniques are used to show that all signals are uniformly ultimately bounded and that the approximated control signals approach the optimal control inputs with small bounded error. In the absence of OLA reconstruction errors, an optimal control is demonstrated. Simulation results verify that all OLA parameter estimates remain bounded, and the proposed OLA-based optimal control scheme tunes itself to reduce the cost HJB equation.
Avimanyu Sahoo - One of the best experts on this subject based on the ideXlab platform.
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near optimal event triggered control of Nonlinear Discrete time systems using neurodynamic programming
IEEE Transactions on Neural Networks, 2016Co-Authors: Avimanyu Sahoo, S JagannathanAbstract:This paper presents an event-triggered near optimal control of uncertain Nonlinear Discrete-time systems. Event-driven neurodynamic programming (NDP) is utilized to design the control policy. A neural network (NN)-based identifier, with event-based state and input vectors, is utilized to learn the system dynamics. An actor–critic framework is used to learn the cost function and the optimal control input. The NN weights of the identifier, the critic, and the actor NNs are tuned aperiodically once every triggered instant. An adaptive event-trigger condition to decide the trigger instants is derived. Thus, a suitable number of events are generated to ensure a desired accuracy of approximation. A near optimal performance is achieved without using value and/or policy iterations. A detailed analysis of nontrivial inter-event times with an explicit formula to show the reduction in computation is also derived. The Lyapunov technique is used in conjunction with the event-trigger condition to guarantee the ultimate boundedness of the closed-loop system. The simulation results are included to verify the performance of the controller. The net result is the development of event-driven NDP.
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adaptive neural network based event triggered control of single input single output Nonlinear Discrete time systems
IEEE Transactions on Neural Networks, 2016Co-Authors: Avimanyu Sahoo, Hao Xu, S JagannathanAbstract:This paper presents a novel adaptive neural network (NN) control of single-input and single-output uncertain Nonlinear Discrete-time systems under event sampled NN inputs. In this control scheme, the feedback signals are transmitted, and the NN weights are tuned in an aperiodic manner at the event sampled instants. After reviewing the NN approximation property with event sampled inputs, an adaptive state estimator (SE), consisting of linearly parameterized NNs, is utilized to approximate the unknown system dynamics in an event sampled context. The SE is viewed as a model and its approximated dynamics and the state vector, during any two events, are utilized for the event-triggered controller design. An adaptive event-trigger condition is derived by using both the estimated NN weights and a dead-zone operator to determine the event sampling instants. This condition both facilitates the NN approximation and reduces the transmission of feedback signals. The ultimate boundedness of both the NN weight estimation error and the system state vector is demonstrated through the Lyapunov approach. As expected, during an initial online learning phase, events are observed more frequently. Over time with the convergence of the NN weights, the inter-event times increase, thereby lowering the number of triggered events. These claims are illustrated through the simulation results.
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adaptive neural network based event triggered control of single input single output Nonlinear Discrete time systems
IEEE Transactions on Neural Networks, 2016Co-Authors: Avimanyu Sahoo, S JagannathaAbstract:This paper presents a novel adaptive neural network (NN) control of single-input and single-output uncertain Nonlinear Discrete-time systems under event sampled NN inputs. In this control scheme, the feedback signals are transmitted, and the NN weights are tuned in an aperiodic manner at the event sampled instants. After reviewing the NN approximation property with event sampled inputs, an adaptive state estimator (SE), consisting of linearly parameterized NNs, is utilized to approximate the unknown system dynamics in an event sampled context. The SE is viewed as a model and its approximated dynamics and the state vector, during any two events, are utilized for the event-triggered controller design. An adaptive event-trigger condition is derived by using both the estimated NN weights and a dead-zone operator to determine the event sampling instants. This condition both facilitates the NN approximation and reduces the transmission of feedback signals. The ultimate boundedness of both the NN weight estimation error and the system state vector is demonstrated through the Lyapunov approach. As expected, during an initial online learning phase, events are observed more frequently. Over time with the convergence of the NN weights, the inter-event times increase, thereby lowering the number of triggered events. These claims are illustrated through the simulation results.
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neural network based adaptive event triggered control of affine Nonlinear Discrete time systems with unknown internal dynamics
American Control Conference, 2013Co-Authors: Avimanyu Sahoo, S JagannathanAbstract:In this paper, the design of a neural network (NN) based adaptive model-based event-triggered control of an uncertain single input single output (SISO) Nonlinear Discrete time system in affine form is presented. The controller uses an adaptive estimator consisting of a single-layer NN not only to approximate the internal dynamics of an affine Nonlinear Discrete-time system but also to provide an estimate of the state vector during inter event interval. The NN weights of the adaptive NN estimator are tuned in a aperiodic manner at the event trigger instants unlike periodic updates in standard adaptive neural network (NN) control. A dead zone operator is used to reset the event trigger error to zero as long as the system states continue to remain in a bounded region due to NN reconstruction errors. Lyapunov method is used to derive the event trigger condition, prove uniform ultimate boundedness (UUB) of the NN weight estimation error and system states.
Huaguang Zhang - One of the best experts on this subject based on the ideXlab platform.
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online adaptive policy learning algorithm for h state feedback control of unknown affine Nonlinear Discrete time systems
IEEE Transactions on Systems Man and Cybernetics, 2014Co-Authors: Huaguang Zhang, Chunbin Qin, Bin Jiang, Yanhong LuoAbstract:The problem of H ∞ state feedback control of affine Nonlinear Discrete-time systems with unknown dynamics is investigated in this paper. An online adaptive policy learning algorithm (APLA) based on adaptive dynamic programming (ADP) is proposed for learning in real-time the solution to the Hamilton-Jacobi-Isaacs (HJI) equation, which appears in the H ∞ control problem. In the proposed algorithm, three neural networks (NNs) are utilized to find suitable approximations of the optimal value function and the saddle point feedback control and disturbance policies. Novel weight updating laws are given to tune the critic, actor, and disturbance NNs simultaneously by using data generated in real-time along the system trajectories. Considering NN approximation errors, we provide the stability analysis of the proposed algorithm with Lyapunov approach. Moreover, the need of the system input dynamics for the proposed algorithm is relaxed by using a NN identification scheme. Finally, simulation examples show the effectiveness of the proposed algorithm.
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adaptive dynamic programming based optimal control of unknown nonaffine Nonlinear Discrete time systems with proof of convergence
Neurocomputing, 2012Co-Authors: Xin Zhang, Huaguang ZhangAbstract:In this paper, a novel neuro-optimal control scheme is proposed for unknown nonaffine Nonlinear Discrete-time systems by using adaptive dynamic programming (ADP) method. A neuro identifier is established by employing recurrent neural networks (RNNs) model to reconstruct the unknown system dynamics. The convergence of the identification error is proved by using the Lyapunov theory. Then based on the established RNN model, the ADP method is utilized to design the approximate optimal controller. Two neural networks (NNs) are used to implement the iterative algorithm. The convergence of the action NN error and weight estimation errors is demonstrated while considering the NN approximation errors. Finally, two numerical examples are used to demonstrate the effectiveness of the proposed control scheme.
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Optimal Tracking Control for a Class of Nonlinear Discrete-Time Systems With Time Delays Based on Heuristic Dynamic Programming
IEEE Transactions on Neural Networks, 2011Co-Authors: Huaguang Zhang, Ruizhuo Song, Tieyan ZhangAbstract:In this paper, a novel heuristic dynamic programming (HDP) iteration algorithm is proposed to solve the optimal tracking control problem for a class of Nonlinear Discrete-time systems with time delays. The novel algorithm contains state updating, control policy iteration, and performance index iteration. To get the optimal states, the states are also updated. Furthermore, the “backward iteration” is applied to state updating. Two neural networks are used to approximate the performance index function and compute the optimal control policy for facilitating the implementation of HDP iteration algorithm. At last, we present two examples to demonstrate the effectiveness of the proposed HDP iteration algorithm.
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a new fuzzy increment inverse control for unknown Nonlinear Discrete dynamical system
International Conference on Control Applications, 2007Co-Authors: Zhenwei Liu, Huaguang ZhangAbstract:A new fuzzy increment inverse control based on input/output fuzzy hyperbolic model is proposed for general unknown Nonlinear Discrete-time dynamical system in this paper. The increment inverse controller is derived from the input/output fuzzy hyperbolic model, and it is based on property of hyperbolic tangent function and reduces the complexity of system. The stability of control system is derived. The simulations demonstrate the performance of proposed fuzzy increment inverse control.
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fuzzy h_ infty filter design for a class of Nonlinear Discrete time systems with multiple time delays
IEEE Transactions on Fuzzy Systems, 2007Co-Authors: Huaguang Zhang, Shuxian Lun, Derong LiuAbstract:This paper studies the fuzzy Hinfin filter design problem for signal estimation of Nonlinear Discrete-time systems with multiple time delays and unknown bounded disturbances. First, the Takagi-Sugeno (T-S) fuzzy model is used to represent the state-space model of Nonlinear Discrete-time systems with time delays. Next, we design a stable fuzzy Hinfin filter based on the T-S fuzzy model, which guarantees asymptotic stability and a prescribed Hinfin index for the filtering error system, irrespective of the time delays and uncertain disturbances. A sufficient condition for the existence of such a filter is established by using the linear matrix inequality (LMI) approach. The proposed LMI problem can be efficiently solved with global convergence guarantee using convex optimization techniques such as the interior point algorithm. Simulation examples are provided to illustrate the design procedure of the present method.
Shaocheng Tong - One of the best experts on this subject based on the ideXlab platform.
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fuzzy adaptive control with state observer for a class of Nonlinear Discrete time systems with input constraint
IEEE Transactions on Fuzzy Systems, 2016Co-Authors: Yanjun Liu, Shaocheng Tong, Ying GaoAbstract:In this paper, an adaptive fuzzy controller is constructed for a class of Nonlinear Discrete-time systems with unknown functions and bounded disturbances. The main characteristics of the systems are that they take into account the effect of Discrete-time dead zone and the system states are not required to be measurable. The stability problem of this class of systems is for the first time to be addressed in this paper. Due to the unavailability of the states and the presence of the Discrete-time dead zone, the controller design becomes more difficult. To stabilize the uncertain Nonlinear Discrete-time systems, the fuzzy logic systems are used to approximate the unknown functions, a fuzzy state observer is designed to estimate the immeasurable states, and the effect caused by Discrete-time dead zone can be solved via establishing an adaptation auxiliary signal. Based on the Lyapunov approach, it is proved that all the signals of the closed-loop system are the semiglobal uniformly ultimately bounded, and the tracking error is made within a small neighborhood around zero. The feasibility of the developed control scheme is verified via two simulation examples.
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optimal control based adaptive nn design for a class of Nonlinear Discrete time block triangular systems
IEEE Transactions on Systems Man and Cybernetics, 2016Co-Authors: Yanjun Liu, Shaocheng TongAbstract:In this paper, we propose an optimal control scheme-based adaptive neural network design for a class of unknown Nonlinear Discrete-time systems. The controlled systems are in a block-triangular multi-input–multi-output pure-feedback structure, i.e., there are both state and input couplings and nonaffine functions to be included in every equation of each subsystem. The design objective is to provide a control scheme, which not only guarantees the stability of the systems, but also achieves optimal control performance. The main contribution of this paper is that it is for the first time to achieve the optimal performance for such a class of systems. Owing to the interactions among subsystems, making an optimal control signal is a difficult task. The design ideas are that: 1) the systems are transformed into an output predictor form; 2) for the output predictor, the ideal control signal and the strategic utility function can be approximated by using an action network and a critic network, respectively; and 3) an optimal control signal is constructed with the weight update rules to be designed based on a gradient descent method. The stability of the systems can be proved based on the difference Lyapunov method. Finally, a numerical simulation is given to illustrate the performance of the proposed scheme.
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fuzzy approximation based adaptive backstepping optimal control for a class of Nonlinear Discrete time systems with dead zone
IEEE Transactions on Fuzzy Systems, 2016Co-Authors: Shaocheng Tong, Yongming LiAbstract: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.
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a unified approach to adaptive neural control for Nonlinear Discrete time systems with Nonlinear dead zone input
IEEE Transactions on Neural Networks, 2016Co-Authors: Shaocheng Tong, C Philip L ChenAbstract: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.
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adaptive nn tracking control of uncertain Nonlinear Discrete time systems with nonaffine dead zone input
IEEE Transactions on Systems Man and Cybernetics, 2015Co-Authors: Shaocheng TongAbstract:In the paper, an adaptive tracking control design is studied for a class of Nonlinear Discrete-time systems with dead-zone input. The considered systems are of the nonaffine pure-feedback form and the dead-zone input appears Nonlinearly in the systems. The contributions of the paper are that: 1) it is for the first time to investigate the control problem for this class of Discrete-time systems with dead-zone; 2) there are major difficulties for stabilizing such systems and in order to overcome the difficulties, the systems are transformed into an n -step-ahead predictor but nonaffine function is still existent; and 3) an adaptive compensative term is constructed to compensate for the parameters of the dead-zone. The neural networks are used to approximate the unknown functions in the transformed systems. Based on the Lyapunov theory, it is proven that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error converges to a small neighborhood of zero. Two simulation examples are provided to verify the effectiveness of the control approach in the paper.
Guoliang Wei - One of the best experts on this subject based on the ideXlab platform.
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brief paper h filtering for Nonlinear Discrete time stochastic systems with randomly varying sensor delays
Automatica, 2009Co-Authors: Bo Shen, Zidong Wang, Huisheng Shu, Guoliang WeiAbstract:This paper is concerned with the H"~ filtering problem for a general class of Nonlinear Discrete-time stochastic systems with randomly varying sensor delays, where the delayed sensor measurement is governed by a stochastic variable satisfying the Bernoulli random binary distribution law. In terms of the Hamilton-Jacobi-Isaacs inequalities, preliminary results are first obtained that ensure the addressed system to possess an l"2-gain less than a given positive scalar @c. Next, a sufficient condition is established under which the filtering process is asymptotically stable in the mean square and the filtering error satisfies the H"~ performance constraint for all nonzero exogenous disturbances under the zero-initial condition. Such a sufficient condition is then decoupled into four inequalities for the purpose of easy implementation. Furthermore, it is shown that our main results can be readily specialized to the case of linear stochastic systems. Finally, a numerical simulation example is used to demonstrate the effectiveness of the results derived.
