Discrete-Time Adaptive Control for Three-Phase PWM Rectifier

This paper proposes a dual-loop discrete-time adaptive control (DDAC) method for three-phase PWM rectifiers, which considers inductance-parameter-mismatched and DC load disturbances. A discrete-time model of the three-phase PWM rectifier is established using the forward Euler discretization method, and a dual-loop discrete-time feedback linearization control (DDFLC) is given. Based on the DDFLC, the DDAC is designed. Firstly, an adaptive inductance disturbance observer (AIDO) based on the gradient descent method is proposed in the current control loop. The AIDO is used to estimate lump disturbances caused by mismatched inductance parameters and then compensate for these disturbances in the current controller, ensuring its strong robustness to inductance parameters. Secondly, a load parameter adaptive law (LPAL) based on the discrete-time Lyapunov theory is proposed for the voltage control loop. The LPAL estimates the DC load parameter in real time and subsequently adjusts it in the voltage controller, achieving DC load adaptability. Finally, simulation and experimental results show that the DDAC exhibits better steady and dynamic performances, less current harmonic content than the DDFLC and the dual-loop discrete-time PI control (DDPIC), and a stronger robustness to inductance parameters and DC load disturbances.

H∞Bipartite Synchronization of Double-Layer Markov Switched Cooperation-Competition Neural Networks: A Distributed Dynamic Event-Triggered Mechanism

In this article, the H_∞ bipartite synchronization issue is studied for a class of discrete-time coupled switched neural networks with antagonistic interactions via a distributed dynamic event-triggered control scheme. Essentially different from most current literature, the topology switching of the investigated signed graph is governed by a double-layer switching signal, which integrates a flexible deterministic switching regularity, the persistent dwell-time switching, into a Markov chain to represent the variation of transition probability. Considering the coexistence of cooperative and antagonistic interactions among nodes, the bipartite synchronization of which the dynamics of nodes converge to values with the same modulus but the opposite signs is explored. A distributed control strategy based on the dynamic event-triggered mechanism is utilized to achieve this goal. Under this circumstance, the information update of the controller presents an aperiodic manner, and the frequency of data transmission can be reduced extensively. Thereafter, by constructing a novel Lyapunov function depending on both the switching signal and the internal dynamic nonnegative variable of the triggering mechanism, the exponential stability of bipartite synchronization error systems in the mean-square sense is analyzed. Finally, two simulation examples are provided to illustrate the effectiveness of the derived results.

Event-Triggered Multigradient Recursive Reinforcement Learning Tracking Control for Multiagent Systems

In this article, the tracking control problem of event-triggered multigradient recursive reinforcement learning is investigated for nonlinear multiagent systems (MASs). Attention is focused on the distributed reinforcement learning approach for MASs. The critic neural network (NN) is applied to estimate the long-term strategic utility function, and the actor NN is designed to approximate the uncertain dynamics in MASs. The multigradient recursive (MGR) strategy is tailored to learn the weight vector in NN, which eliminates the local optimal problem inherent in gradient descent method and decreases the dependence of initial value. Furthermore, reinforcement learning and event-triggered mechanism can improve the energy conservation of MASs by decreasing the amplitude of the controller signal and the controller update frequency, respectively. It is proved that all signals in MASs are semiglobal uniformly ultimately bounded (SGUUB) according to the Lyapunov theory. Simulation results are given to demonstrate the effectiveness of the proposed strategy.

Fuzzy adaptive finite-time output feedback control of stochastic nonlinear systems

An adaptive finite-time approach to the feedback control of stochastic nonlinear systems is presented. The fuzzy logic system (FLS) and a state observer are used to estimate the uncertain function and unmeasured state of the controlled system, respectively. A dynamic surface control (DSC) scheme is employed to deal with the "computational explosion" problem, which is inherent in traditional backstepping methods since the repetitive calculation of the derivatives of virtual control signals is avoided. A new output feedback controller is developed to guarantee that all the signals of the controlled system are bounded within a finite time range and the tracking deviation can converge to an arbitrarily small residual set within finite time. Simulations confirm the analytical and theoretical results of the presented algorithm.

Adaptive Neural Dynamic Surface Control With Prespecified Tracking Accuracy of Uncertain Stochastic Nonstrict-Feedback Systems

This article addresses the adaptive neural tracking control problem for a class of uncertain stochastic nonlinear systems with nonstrict-feedback form and prespecified tracking accuracy. Some radial basis function neural networks (RBF NNs) are used to approximate the unknown continuous functions online, and the desired controller is designed via the adaptive dynamic surface control (DSC) method and the gain suppressing inequality technique. Different from the reported works on uncertain stochastic systems, by combining some non-negative switching functions and dynamic surface method with the nonlinear filter, the design difficulty is overcome, and the control performance is analyzed by employing stochastic Barbalat's lemma. Under the constructed controller, the tracking error converges to the accuracy defined a priori in probability. The simulation results are shown to verify the availability of the presented control scheme.

Optimal Design of High-Order Control for Fuzzy Dynamical Systems Based on the Cooperative Game Theory

In this article, we propose a high-order robust control for fuzzy dynamical systems. The time varying but bounded uncertainty in this system is described by the fuzzy set theory. The control is deterministic and is not based on IF-THEN fuzzy rules. By the Lyapunov approach, we prove that the control is able to guarantee uniform boundedness and uniform ultimate boundedness. In addition, the tunable parameters in the high-order control are regarded as two players in a cooperative game. Two cost functions are also proposed based on the two players. These two cost functions are related to system performance and control cost. Then, the optimal design problem is solved by finding the Pareto-optimality parameters. Numerical simulations are performed for verification.

TSM-Based Adaptive Fuzzy Control of Robotic Manipulators with Output Constraints

This paper proposes an adaptive control scheme based on terminal sliding mode (TSM) for robotic manipulators with output constraints and unknown disturbances. The fuzzy logic system (FLS) is developed to approximate unknown dynamics of robotic manipulators. An error transformation technique is used in the process of controller design to ensure that the output constraints are not violated. The advantage of the error transformation compared to traditional barrier Lyapunov functions (BLFs) is that there is no need to design a virtual controller. Thus, the design complexity of the controller is reduced. Through Lyapunov stability analysis, the system state can be proved to converge to the neighborhood near the balanced point in finite time. Extensive simulation results illustrated the validity of the proposed controller.

MTN output feedback tracking control for MIMO discrete-time uncertain nonlinear systems

An adaptive controller is developed that is based on the multidimensional Taylor network (MTN). This controller is used for multi-input and multi-output (MIMO) uncertain discrete-time nonlinear systems. This newly developed MTN is dissimilar with the neural network, in which only multiplication and addition are needed for this controller. Thus, real-time control is more easily to be achieved. The theoretical analysis shows that the output errors of the system are convergent and the output signals are semi-globally, uniformly and ultimately bounded. To illustrate the validity of MTN-based adaptive controller (MTNAC), a numerical example is given. The simulation data demonstrate that this MNTAC has better real-time performance and higher robustness compared with neural networks.

Gradient-Sensitive Optimization for Convolutional Neural Networks

Convolutional neural networks (CNNs) are effective models for image classification and recognition. Gradient descent optimization (GD) is the basic algorithm for CNN model optimization. Since GD appeared, a series of improved algorithms have been derived. Among these algorithms, adaptive moment estimation (Adam) has been widely recognized. However, local changes are ignored in Adam to some extent. In this paper, we introduce an adaptive learning rate factor based on current and recent gradients. According to this factor, we can dynamically adjust the learning rate of each independent parameter to adaptively adjust the global convergence process. We use the factor to adjust the learning rate for each parameter. The convergence of the proposed algorithm is proven by using the regret bound approach of the online learning framework. In the experimental section, comparisons are conducted between the proposed algorithm and other existing algorithms, such as AdaGrad, RMSprop, Adam, diffGrad, and AdaHMG, on test functions and the MNIST dataset. The results show that Adam and RMSprop combined with our algorithm can not only find the global minimum faster in the experiment using the test function but also have a better convergence curve and higher test set accuracy in experiments using datasets. Our algorithm is a supplement to the existing gradient descent algorithms, which can be combined with many other existing gradient descent algorithms to improve the efficiency of iteration, speed up the convergence of the cost function, and improve the final recognition rate.

Adaptive Fault-Tolerant Tracking Control for Discrete-Time Multiagent Systems via Reinforcement Learning Algorithm

This article investigates the adaptive fault-tolerant tracking control problem for a class of discrete-time multiagent systems via a reinforcement learning algorithm. The action neural networks (NNs) are used to approximate unknown and desired control input signals, and the critic NNs are employed to estimate the cost function in the design procedure. Furthermore, the direct adaptive optimal controllers are designed by combining the backstepping technique with the reinforcement learning algorithm. Comparing the existing reinforcement learning algorithm, the computational burden can be effectively reduced by using the method of less learning parameters. The adaptive auxiliary signals are established to compensate for the influence of the dead zones and actuator faults on the control performance. Based on the Lyapunov stability theory, it is proved that all signals of the closed-loop system are semiglobally uniformly ultimately bounded. Finally, some simulation results are presented to illustrate the effectiveness of the proposed approach.

Adaptive Consensus Tracking Control of Uncertain Nonlinear Multiagent Systems With Predefined Accuracy

In this article, we consider the leader-follower consensus control problem of uncertain multiagent systems, aiming to achieve the improvement of system steady state and transient performance. To this end, a new adaptive neural control approach is proposed with a novel design of the Lyapunov function, which is generated with a class of positive functions. Guided by this idea, a series of smooth functions is incorporated into backstepping design and Lyapunov analysis to develop a performance-oriented controller. It is proved that the proposed controller achieves a perfect asymptotic consensus performance and a tunable L₂ transient performance of synchronization errors, whereas most existing results can only ensure the stability. Simulation demonstrates the obtained results.

Relative Degrees and Implicit Function-Based Control of Discrete-Time Noncanonical Form Neural Network Systems

This paper studies the relative degrees of discrete-time neural network systems in a general noncanonical form, and develops a new feedback control scheme for such systems, based on implicit function theory and feedback linearization. After time-advance operation on output of such systems, the output dynamics nonlinearly depends on the control input. To address this issue, we use implicit function theory to define the relative degrees, and to establish a normal form. Then, an implicit function equation solution-based control scheme and an iterative solution-based control scheme are proposed, which ensure not only the closed-loop stability but also the output tracking for the controlled plant. An adaptive control framework for the controlled plant with uncertainties is also presented to illustrate the basic design procedure. The simulation results are given to demonstrate the desired system performance.

Adaptive Discrete-Time Flight Control Using Disturbance Observer and Neural Networks

This paper studies the adaptive neural control (ANC)-based tracking problem for discrete-time nonlinear dynamics of an unmanned aerial vehicle subject to system uncertainties, bounded time-varying disturbances, and input saturation by using a discrete-time disturbance observer (DTDO). Based on the approximation approach of neural network, system uncertainties are tackled approximately. To restrain the negative effects of bounded disturbances, a nonlinear DTDO is designed. Then, a backstepping technique-based ANC strategy is proposed by utilizing a constructed auxiliary system and a discrete-time tracking differentiator. The boundness of all signals is proven in the closed-loop system under the discrete-time Lyapunov analysis. Finally, the feasibility of the proposed ANC technique is further specified based on numerical simulation results.

Design and Adaptive Control for an Upper Limb Robotic Exoskeleton in Presence of Input Saturation

This paper addresses the control design for an upper limb exoskeleton in the presence of input saturation. An adaptive controller employing the neural network technology is proposed to approximate the uncertain robotic dynamics. Also, an auxiliary system is designed to deal with the effect of input saturation. Furthermore, we develop both the state feedback and the output feedback control strategies, which effectively estimates the uncertainties online from the measured feedback errors, instead of the model-based control. In addition to the proposed control, a disturbance observer is designed to reject the unknown disturbance online for achieving the trajectory tracking. The method requires a minimal amount of a priori knowledge of system dynamics. Subsequently, the principle of Lyapunov synthesis ensures the stability of the closed-loop system. Finally, the experimental studies are carried out on this robotic exoskeleton.

Adaptive Neural Control for Robotic Manipulators With Output Constraints and Uncertainties

This paper investigates adaptive neural control methods for robotic manipulators, subject to uncertain plant dynamics and constraints on the joint position. The barrier Lyapunov function is employed to guarantee that the joint constraints are not violated, in which the Moore-Penrose pseudo-inverse term is used in the control design. To handle the unmodeled dynamics, the neural network (NN) is adopted to approximate the uncertain dynamics. The NN control based on full-state feedback for robots is proposed when all states of the closed loop are known. Subsequently, only the robot joint is measurable in practice; output feedback control is designed with a high-gain observer to estimate unmeasurable states. Through the Lyapunov stability analysis, system stability is achieved with the proposed control, and the system output achieves convergence without violation of the joint constraints. Simulation is conducted to approve the feasibility and superiority of the proposed NN control.

Event-Based Adaptive NN Tracking Control of Nonlinear Discrete-Time Systems

This paper is concerned with the simultaneous design of a neural network (NN)-based adaptive control law and an event-triggering condition for a class of strict feedback nonlinear discrete-time systems. The stability and tracking performance of the closed-loop network control system under the event-triggering strategy is formally proven based on the Lyapunov theory in a hybrid framework. The proposed Lyapunov formulation yields an event-triggered algorithm to update the control input and NN weights based on conditions involving the closed-loop state. Different from the existing traditional NN control schemes where the feedback signals are transmitted and executed periodically, the feedback signals are transmitted and executed only when the event-trigger error exceeds the specified threshold, which can largely reduce the communication load. The effectiveness of the approach is evaluated through a simulation example.

A Reinforcement Learning Neural Network for Robotic Manipulator Control

We propose a neural network model for reinforcement learning to control a robotic manipulator with unknown parameters and dead zones. The model is composed of three networks. The state of the robotic manipulator is predicted by the state network of the model, the action policy is learned by the action network, and the performance index of the action policy is estimated by a critic network. The three networks work together to optimize the performance index based on the reinforcement learning control scheme. The convergence of the learning methods is analyzed. Application of the proposed model on a simulated two-link robotic manipulator demonstrates the effectiveness and the stability of the model.

Adaptive Neural Control of Uncertain Nonlinear Systems Using Disturbance Observer

This paper studies the problem of prescribed performance adaptive neural control for a class of uncertain multi-input and multi-output (MIMO) nonlinear systems in the presence of external disturbances and input saturation based on a disturbance observer. The system uncertainties are tackled by neural network (NN) approximation. To handle unknown disturbances, a Nussbaum disturbance observer is presented. By incorporating the disturbance observer and NNs, an adaptive prescribed performance neural control scheme is further developed. Then, the expected asymptotically convergent tracking errors between system output signals and desired signals are achieved. Numerical simulation results demonstrate the effectiveness of the proposed control scheme.

An Approach to Stable Gradient-Descent Adaptation of Higher Order Neural Units

Stability evaluation of a weight-update system of higher order neural units (HONUs) with polynomial aggregation of neural inputs (also known as classes of polynomial neural networks) for adaptation of both feedforward and recurrent HONUs by a gradient descent method is introduced. An essential core of the approach is based on the spectral radius of a weight-update system, and it allows stability monitoring and its maintenance at every adaptation step individually. Assuring the stability of the weight-update system (at every single adaptation step) naturally results in the adaptation stability of the whole neural architecture that adapts to the target data. As an aside, the used approach highlights the fact that the weight optimization of HONU is a linear problem, so the proposed approach can be generally extended to any neural architecture that is linear in its adaptable parameters.

Adaptive Neural Network Control of a Marine Vessel With Constraints Using the Asymmetric Barrier Lyapunov Function

In this paper, we consider the trajectory tracking of a marine surface vessel in the presence of output constraints and uncertainties. An asymmetric barrier Lyapunov function is employed to cope with the output constraints. To handle the system uncertainties, we apply adaptive neural networks to approximate the unknown model parameters of a vessel. Both full state feedback control and output feedback control are proposed in this paper. The state feedback control law is designed by using the Moore-Penrose pseudoinverse in case that all states are known, and the output feedback control is designed using a high-gain observer. Under the proposed method the controller is able to achieve the constrained output. Meanwhile, the signals of the closed loop system are semiglobally uniformly bounded. Finally, numerical simulations are carried out to verify the feasibility of the proposed controller.

Adaptive Neural Network Based Control of Noncanonical Nonlinear Systems

This paper presents a new study on the adaptive neural network-based control of a class of noncanonical nonlinear systems with large parametric uncertainties. Unlike commonly studied canonical form nonlinear systems whose neural network approximation system models have explicit relative degree structures, which can directly be used to derive parameterized controllers for adaptation, noncanonical form nonlinear systems usually do not have explicit relative degrees, and thus their approximation system models are also in noncanonical forms. It is well-known that the adaptive control of noncanonical form nonlinear systems involves the parameterization of system dynamics. As demonstrated in this paper, it is also the case for noncanonical neural network approximation system models. Effective control of such systems is an open research problem, especially in the presence of uncertain parameters. This paper shows that it is necessary to reparameterize such neural network system models for adaptive control design, and that such reparameterization can be realized using a relative degree formulation, a concept yet to be studied for general neural network system models. This paper then derives the parameterized controllers that guarantee closed-loop stability and asymptotic output tracking for noncanonical form neural network system models. An illustrative example is presented with the simulation results to demonstrate the control design procedure, and to verify the effectiveness of such a new design method.

Neural Network-Based Control of Networked Trilateral Teleoperation With Geometrically Unknown Constraints

Most studies on bilateral teleoperation assume known system kinematics and only consider dynamical uncertainties. However, many practical applications involve tasks with both kinematics and dynamics uncertainties. In this paper, trilateral teleoperation systems with dual-master-single-slave framework are investigated, where a single robotic manipulator constrained by an unknown geometrical environment is controlled by dual masters. The network delay in the teleoperation system is modeled as Markov chain-based stochastic delay, then asymmetric stochastic time-varying delays, kinematics and dynamics uncertainties are all considered in the force-motion control design. First, a unified dynamical model is introduced by incorporating unknown environmental constraints. Then, by exact identification of constraint Jacobian matrix, adaptive neural network approximation method is employed, and the motion/force synchronization with time delays are achieved without persistency of excitation condition. The neural networks and parameter adaptive mechanism are combined to deal with the system uncertainties and unknown kinematics. It is shown that the system is stable with the strict linear matrix inequality-based controllers. Finally, the extensive simulation experiment studies are provided to demonstrate the performance of the proposed approach.

Robust Adaptive Neural Tracking Control for a Class of Stochastic Nonlinear Interconnected Systems

In this paper, an adaptive neural decentralized control approach is proposed for a class of multiple input and multiple output uncertain stochastic nonlinear strong interconnected systems. Radial basis function neural networks are used to approximate the packaged unknown nonlinearities, and backstepping technique is utilized to construct an adaptive neural decentralized controller. The proposed control scheme can guarantee that all signals of the resulting closed-loop system are semiglobally uniformly ultimately bounded in the sense of fourth moment, and the tracking errors eventually converge to a small neighborhood around the origin. The main feature of this paper is that the proposed approach is capable of controlling the stochastic systems with strong interconnected nonlinearities both in the drift and diffusion terms that are the functions of all states of the overall system. Simulation results are used to illustrate the effectiveness of the suggested approach.

Adaptive Neural Network Control of an Uncertain Robot With Full-State Constraints

This paper studies the tracking control problem for an uncertain n -link robot with full-state constraints. The rigid robotic manipulator is described as a multiinput and multioutput system. Adaptive neural network (NN) control for the robotic system with full-state constraints is designed. In the control design, the adaptive NNs are adopted to handle system uncertainties and disturbances. The Moore-Penrose inverse term is employed in order to prevent the violation of the full-state constraints. A barrier Lyapunov function is used to guarantee the uniform ultimate boundedness of the closed-loop system. The control performance of the closed-loop system is guaranteed by appropriately choosing the design parameters. Simulation studies are performed to illustrate the effectiveness of the proposed control.

Neural Controller Design-Based Adaptive Control for Nonlinear MIMO Systems With Unknown Hysteresis Inputs

This paper studies an adaptive neural control for nonlinear multiple-input multiple-output systems in interconnected form. The studied systems are composed of N subsystems in pure feedback structure and the interconnection terms are contained in every equation of each subsystem. Moreover, the studied systems consider the effects of Prandtl-Ishlinskii (PI) hysteresis model. It is for the first time to study the control problem for such a class of systems. In addition, the proposed scheme removes an important assumption imposed on the previous works that the bounds of the parameters in PI hysteresis are known. The radial basis functions neural networks are employed to approximate unknown functions. The adaptation laws and the controllers are designed by employing the backstepping technique. The closed-loop system can be proven to be stable by using Lyapunov theorem. A simulation example is studied to validate the effectiveness of the scheme.

Adaptive Neural Control of a Class of Output-Constrained Nonaffine Systems

In this paper, we present a novel tracking controller for a class of uncertain nonaffine systems with time-varying asymmetric output constraints. Firstly, the original nonaffine constrained (in the sense of the output signal) control system is transformed into a output-feedback control problem of an unconstrained affine system in normal form. As a result, stabilization of the transformed system is sufficient to ensure constraint satisfaction. It is subsequently shown that the output tracking is achieved without violation of the predefined asymmetric time-varying output constraints. Therefore, we are capable of quantifying the system performance bounds as functions of time on both transient and steady-state stages. Furthermore, the transformed system is linear with respect to a new input signal and the traditional backstepping scheme is avoided, which makes the synthesis extremely simplified. All the signals in the closed-loop system are proved to be semi-globally, uniformly, and ultimately bounded via Lyapunov synthesis. Finally, the simulation results are presented to illustrate the performance of the proposed controller.

Consensus Control With Failure--Wait or Abandon?

This paper introduces and solves a decision-making problem under the context of consensus control with failure. We study an optimal consensus control problem in which n autonomous agents try to arrive at a target at the same time. One of the agents suddenly fails and the rest n - 1 agents can either wait or abandon the failed agent. If they wait, they must slow down and delay the consensus time. If they abandon the failed agent, they can reach consensus earlier at the cost of losing one agent at consensus. This cost is an added delay to the consensus time. The decision problem is to decide whether to wait or abandon and, if abandon, when? To solve this problem, we derive analytical expressions and establish structural properties for target distance functions. We use numerical examples and simulation examples to demonstrate the applications of the derived formulas and results.

Observer-Based Adaptive Neural Network Control for Nonlinear Systems in Nonstrict-Feedback Form

This paper focuses on the problem of adaptive neural network (NN) control for a class of nonlinear nonstrict-feedback systems via output feedback. A novel adaptive NN backstepping output-feedback control approach is first proposed for nonlinear nonstrict-feedback systems. The monotonicity of system bounding functions and the structure character of radial basis function (RBF) NNs are used to overcome the difficulties that arise from nonstrict-feedback structure. A state observer is constructed to estimate the immeasurable state variables. By combining adaptive backstepping technique with approximation capability of radial basis function NNs, an output-feedback adaptive NN controller is designed through backstepping approach. It is shown that the proposed controller guarantees semiglobal boundedness of all the signals in the closed-loop systems. Two examples are used to illustrate the effectiveness of the proposed approach.

Adaptive Fuzzy Tracking Control for a Class of MIMO Nonlinear Systems in Nonstrict-Feedback Form

This paper focuses on the problem of fuzzy adaptive control for a class of multiinput and multioutput (MIMO) nonlinear systems in nonstrict-feedback form, which contains the strict-feedback form as a special case. By the condition of variable partition, a new fuzzy adaptive backstepping is proposed for such a class of nonlinear MIMO systems. The suggested fuzzy adaptive controller guarantees that the proposed control scheme can guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking errors eventually converge to a small neighborhood around the origin. The main advantage of this paper is that a control approach is systematically derived for nonlinear systems with strong interconnected terms which are the functions of all states of the whole system. Simulation results further illustrate the effectiveness of the suggested approach.

Introducing an Evolving Local Neuro-Fuzzy Model--Application to modeling of car-following behavior

This paper proposes an Evolving Local Linear Neuro-Fuzzy Model for modeling and identification of nonlinear time-variant systems which change their nature and character over time. The proposed approach evolves through time to follow the structural changes in the time-variant dynamic systems. The evolution process is managed by a distance-based extended hierarchical binary tree algorithm, which decides whether the proposed evolving model should be adapted to the system variations or evolution is necessary. To represent an interesting but challenging example of the systems with changing dynamics, the proposed evolving model is applied to model car-following process in a traffic flow, as an online identification problem. Results of simulations demonstrate effectiveness of the proposed approach in modeling of the time-variant systems.

Neural networks for tracking of unknown SISO discrete-time nonlinear dynamic systems

This article presents a Lyapunov function based neural network tracking (LNT) strategy for single-input, single-output (SISO) discrete-time nonlinear dynamic systems. The proposed LNT architecture is composed of two feedforward neural networks operating as controller and estimator. A Lyapunov function based back propagation learning algorithm is used for online adjustment of the controller and estimator parameters. The controller and estimator error convergence and closed-loop system stability analysis is performed by Lyapunov stability theory. Moreover, two simulation examples and one real-time experiment are investigated as case studies. The achieved results successfully validate the controller performance.