Partial Persistent Excitation Condition Research Articles

Research and analysis of manipulator control method based on deep learning

Aiming at the stability and accuracy of grasping objects, this paper studies the adaptive neural network control and learning of manipulator control system with unknown system dynamics. First, a stable adaptive neural network (NN) controller is designed, and the unknown closed-loop system dynamics of the manipulator is approximated by using radial basis function (RBF) neural network. The LSTM long and short memory algorithm is introduced, and the RBF based hybrid neural network model is constructed. The LSTM algorithm is used to design the input gate, forgetting gate and output gate structures to suppress the gradient expansion problem during coordinate data training, and accurate trajectory correction instructions are given. Lyapunov stability theorem is used to analyze stability. Partial persistent excitation (PE) conditions of some internal signals in the closed-loop system are satisfied in the control process of tracking the circular reference trajectory. Under the PE condition, the proposed adaptive NN controller can accurately identify the dynamic uncertainties of the manipulator in the stability control process. Then, a new NN learning control method is proposed, which effectively uses the knowledge learned without re adapting to the unknown manipulator control system dynamics to achieve closed-loop stability and improve control performance. The effectiveness of the proposed method is studied through simulation.Keyboard

Deterministic Learning-Based Adaptive Neural Control for Nonlinear Full-State Constrained Systems.

In this article, an adaptive neural learning method is introduced for a category of nonlinear strict-feedback systems with time-varying full-state constraints. The two challenging problems of state constraints and learning capability are investigated and solved in a unified framework. To obtain the learning of unknown functions and satisfy full-state constraints, three main steps are considered. First, an adaptive dynamic surface controller (DSC) based on barrier Lyapunov functions (BLFs) is structured to implement that the closed-loop systems signals are bounded and full-state variables remain within the prescribed time-varying intervals. Moreover, the radial basis function neural networks (RBF NNs) are used to identify unknown functions. The output of the first-order filter, instead of virtual control derivatives, is used to simplify the complexity of the RBF NN input variables. Second, the state transformation is used to obtain a class of linear time-varying subsystems with small perturbations such that the recurrence of the RBF NN input variables and the partial persistent excitation condition are actualized. Therefore, the unknown functions can be accurately approximated, and the learned knowledge is kept as constant NN weights. Third, the obtained constant weights are borrowed into an adaptive learning scheme to achieve the batter control performance. Finally, simulation studies illustrate the advantage of the reported adaptive learning method on higher tracking accuracy, faster convergence rate, and lower computational expense by reusing learned knowledge.

Deterministic learning-based neural control for output-constrained strict-feedback nonlinear systems

This paper studies learning from adaptive neural control of output-constrained strict-feedback uncertain nonlinear systems. To overcome the constraint restriction and achieve learning from the closed-loop control process, there are several significant steps. Firstly, a state transformation is introduced to convert the original constrained system output into an unconstrained one. Then an equivalent n-order affine nonlinear system is constructed based on the transformed unconstrained output state in norm form by the system transformation method. By combining dynamic surface control (DSC) technique, an adaptive neural control scheme is proposed for the transformed system. Then all closed-loop signals are uniformly ultimately bounded and the system output tracks the expected trajectory well with satisfying the constraint requirement. Secondly, the partial persistent excitation condition of the radial basis function neural network (RBF NN) could be verified to achieve. Therefore, the uncertain dynamics can be precisely approximated by RBF NN. Subsequently, the learning ability of RBF NN is achieved, and the knowledge acquired from the neural control process is stored in the form of constant neural networks (NNs). By reutilizing the knowledge, a novel learning controller is established to improve the control performance when facing the similar or same control task. The proposed learning control (LC) scheme can avoid repeating the online adaptation of neural weight estimates, which saves computing resources and improves transient performance. Meanwhile, the LC method significantly raises the tracking accuracy and the speed of error convergence while satisfying of the constraint condition simultaneously. Simulation studies demonstrate the efficiency of this proposed control scheme.

Rapid Sensor Fault Diagnosis for a Class of Nonlinear Systems via Deterministic Learning.

In this article, a rapid sensor fault diagnosis (SFD) method is presented for a class of nonlinear systems. First, by exploiting the linear adaptive observer technology and the deterministic learning method (DLM), an adaptive neural network (NN) observer is constructed to capture the information of the unknown sensor fault function. Second, when the NN input orbit is a period or recurrent one, the partial persistent excitation (PE) condition of the NNs can be guaranteed through the DLM. Based on the partial PE condition and the uniformly completely observable property of a linear time-varying system, the accurate state estimation and the sensor fault identification can be achieved by properly choosing the observer gain. Third, a bank of dynamical observers utilizing the experiential knowledge is constructed to achieve rapid SFD and data recovery. The attractions of the proposed approach are that accurate approximations of sensor faults can be achieved through the DLM, and the data that are destroyed by the sensor faults can be recovered by using the learning results. Simulation studies of a robot system are utilized to show the effectiveness of the proposed method.

Fault Identification for a Class of Nonlinear Systems of Canonical Form via Deterministic Learning.

In this article, through a combination of the deterministic learning (DL) method and the adaptive high gain observer (AHGO) technology, a fault identification approach for a class of nonlinear systems in canonical form is proposed. By using the DL method, the partial persistent excitation condition of the identification system is satisfied, and then, the AHGO technology is exploited to estimate the states and the neural network weights simultaneously. To analyze the convergence of the proposed method, we first analyze the uniformed completely observability (UCO) property of the linear part of the nonlinear identification system. Then, by using the Lipschitz property of the nonlinear item and the Bellman-Gronwall lemma, we show that the UCO property of the nonlinear identification system is depended on the UCO property of the linear part when the observer gain is chosen large. Therefore, by using the UCO property of the nonlinear identification system and the Lyapunov stability theorem, the convergence of the proposed learning observer is proven. The attraction of this article is based on the analysis of the UCO property of the identification system, and the convergence of the proposed learning observer can be directly proven. The simulation example is given to demonstrate the effectiveness of the proposed method.

Dynamic learning from neural network‐based control for sampled‐data strict‐feedback nonlinear systems

AbstractThis article focuses on the dynamic learning and control problem for a class of nonlinear sampled‐data systems in strict‐feedback form. To achieve learning of unknown system dynamics in closed‐loop control, two obstacles need to be overcome: the inherent noncausal problem in the backstepping design of discrete‐time nonlinear systems, and the exponential stability of the sampling closed‐loop error system. First, a novel command filtered adaptive neural control is developed to achieve closed‐loop stability and the convergence of output tracking error based on Lyapunov theory, the noncausal problem is overcome by utilizing the command filter technique, and the ‐step delay is avoided in the recursive process. Second, by combining a state transformation method, the closed‐loop error system is divided into perturbed linear time‐varying (LTV) subsystems. Based on the convergence of the tracking errors, the partial persistent excitation (PE) condition of the radial basis function network is verified and established recursively. By extending the exponential stability result of a class of discrete‐time LTV systems, the convergence of the estimated weights to their optimal values is guaranteed with the PE condition. Subsequently, locally accurate approximation/learning of the unknown closed‐loop sampled dynamics can be obtained and stored in the form of constant neural networks. Finally, by reutilizing the acquired knowledge, a learning‐based control scheme for the sampled‐data system is further proposed to pursue improved control performance. Simulation studies are performed to illustrate the validity of the proposed scheme.

Dynamic Learning From Adaptive Neural Control for Discrete-Time Strict-Feedback Systems.

This article first investigates the issue on dynamic learning from adaptive neural network (NN) control of discrete-time strict-feedback nonlinear systems. To verify the exponential convergence of estimated NN weights, an extended stability result is presented for a class of discrete-time linear time-varying systems with time delays. Subsequently, by combining the n -step-ahead predictor technology and backstepping, an adaptive NN controller is constructed, which integrates the novel weight updating laws with time delays and without the σ modification. After ensuring the convergence of system output to a recurrent reference signal, the radial basis function (RBF) NN is verified to satisfy the partial persistent excitation condition. By the combination of the extended stability result, the estimated NN weights can be verified to exponentially converge to their ideal values. The convergent weight sequences are comprehensively represented and stored by constructing some elegant learning rules with some novel sequences and the mod function. The stored knowledge is used again to develop a neural learning control scheme. Compared with the traditional adaptive NN control, the proposed scheme can not only accomplish the same or similar tracking tasks but also greatly improve the transient control performance and alleviate the online computation. Finally, the validity of the presented scheme is illustrated by numerical and practical examples.

Dynamic learning‐based event‐triggered control of strict‐feedback systems with finite‐time prescribed performance

AbstractThis paper is concerned with the event‐triggered neural learning control for strict‐feedback nonlinear systems (SFNSs) subject to predefined tracking performance. A system transformation approach is utilized to transform the original SFNSs into the normal form, which makes it easily to verify the convergence of neural weights since only one neural network (NN) approximator is employed. Then, a novel finite‐time performance function is first proposed to characterize the performance constraints of tracking error, thus guaranteeing the prescribed tracking performance. On this basis, a new lemma is given, which is crucial to ensure the stability of the closed‐loop system. By using the error transformation technique, the constrained tracking control problem is converted into the stabilization problem of unconstrained error system. Subsequently, by introducing the first‐order sliding mode differentiator into the backstepping procedure and with the help of the high‐gain observer, a novel adaptive neural tracking control scheme is presented to ensure that the prescribed tracking performance is satisfied and all closed‐loop signals are ultimately bounded. After ensuring the satisfaction of the partial persistent excitation condition for radial basis function NN, the neural weight estimates are verified to converge to the ideal values, and then the convergent weights are stored as the constant values. By utilizing the stored knowledge, an event‐triggered neural learning controller is constructed to accomplish the same or similar control tasks, which can effectively improve the transient control performance, save the communication resource, and relieve the online computation at the same time. Finally, the effectiveness of the presented scheme is testified by numerical and practical examples.

Composite-Learning-Based Adaptive Neural Control for Dual-Arm Robots With Relative Motion.

This article presents an adaptive control method for dual-arm robot systems to perform bimanual tasks under modeling uncertainties. Different from the traditional symmetric bimanual robot control, we study the dual-arm robot control with relative motions between robotic arms and a grasped object. The robot system is first divided into two subsystems: a settled manipulator system and a tool-used manipulator system. Then, a command filtered control technique is developed for trajectory tracking and contact force control. In addition, to deal with the inevitable dynamic uncertainties, a radial basis function neural network (RBFNN) is employed for the robot, with a novel composite learning law to update the NN weights. The composite learning is mainly based on an integration of the historic data of NN regression such that information of the estimate error can be utilized to improve the convergence. Moreover, a partial persistent excitation condition is employed to ensure estimation convergence. The stability analysis is performed by using the Lyapunov theorem. Numerical simulation results demonstrate the validity of the proposed control and learning algorithm.

Deterministic learning from neural control for uncertain nonlinear pure‐feedback systems by output feedback

SummaryThe essence of intelligence lies in the acquisition/learning and utilization of knowledge. However, how to implement learning in dynamical environments for nonlinear systems is a challenging issue. This article investigates the deterministic learning (DL) control problem for uncertain pure‐feedback systems by output feedback, which achieves the human‐like learning and control in a simple way. To reduce the complexity of control design and analysis, first, by combining an appropriate system transformation, the original pure‐feedback system is transformed into a simple normal nonaffine system. An observer is then introduced to estimate the transformed system states. Based on the backstepping and dynamic surface control techniques, a simple adaptive neural control scheme is first developed to guarantee the finite time convergence of the tracking error using only one neural network (NN) approximator. Second, through DL, the exponential convergence of the NN weights is obtained with the satisfaction of partial persistent excitation condition. Thus, locally accurate approximation/learning of the transformed unknown system dynamics is achieved and stored as constant NNs. Finally, by utilizing the stored knowledge, an experience‐based controller is constructed and a novel learning control scheme is further proposed to improve the control performance without any further adaptation online for the estimate neural weights. Simulation results have been given to illustrate that the proposed scheme not only can learn and memorize knowledge like humans but also can utilize experience to achieve superior control performance.

Distributed Fast Fault Diagnosis for Multimachine Power Systems via Deterministic Learning

In this paper, a distributed fast fault diagnosis approach is proposed for multimachine power systems based on deterministic learning (DL) theory. First, a learning estimator is constructed to accumulate the knowledge of transient fault dynamics in power systems. Through DL, a partial persistent excitation condition of the local neurons is satisfied and convergence of the neural weights is achieved. Thus, a knowledge bank can be established and gradually updated. To deal with the high dimensional data, only the neurons centered in a neighborhood of the system trajectory are activated. In this manner, the computation load is mitigated. Second, by using the learnt knowledge, a distributed fault diagnosis scheme is designed to monitor the power system. The memory of the transient fault dynamics can be quickly recalled and a fast fault diagnosis decision is made. Finally, based on the concepts of mismatch interval and duty ratio, the diagnosis capabilities of the proposed scheme are investigated. The effectiveness of the proposed diagnosis scheme is demonstrated by computer simulation and the hardware-in-loop experimental test based on the RT-LAB realtime simulator.

Learning from neural control for non-affine systems with full state constraints using command filtering

ABSTRACT This paper focusses on learning from command filtering-based adaptive neural control for non-affine nonlinear systems with full state constraints. This paper utilises a novel transformed function to convert the origin full-state constrained problem into an equivalent unconstrained one. By combining command-filtered backstepping, a novel adaptive neural control scheme is proposed to guarantee that all closed-loop signals are uniformly ultimately bounded and all states stay in the predefined bounded regions. Subsequently, by verifying the partial persistent excitation condition of the radial basis function neural network, neural weight estimates are proven to converge to the ideal weights and the convergent weights are stored in the constant values. Using the stored knowledge, a neural learning control scheme is developed for similar control tasks, which can improve control performances without the violation of full state constraints. Simulation studies are performed to illustrate the validity of the proposed scheme.

Dynamic learning from adaptive neural control for flexible joint robot with tracking error constraints using high-gain observer

ABSTRACTThis paper presents dynamic learning from adaptive neural control with prescribed tracking error performance for flexible joint robot (FJR) included unknown dynamics. Firstly, a system transformation method is introduced to convert the original FJR system into a normal system. As a result, only one neural network (NN) approximator is used to identify the uncertain system nonlinear dynamics and the verification on the convergence of neural weights is simplified extremely. To further solve the predefined performance issue, a performance function is introduced to describe a tracking error constraint and a error transformation technique is used to convert the constrained tracking control problem into the unconstrained stabilization of error system. By combining a high-gain observer and the backsteppig method, the adaptive neural controller is presented to stabilize the unconstrained error system. Under the satisfaction of the partial persistent excitation condition, the adaptive neural controller is shown to be capable of achieving unknown dynamics acquisition, expression and storage. Furthermore, a neural learning control with using the stored NN weights is proposed for the same or similar control task so that a time-consuming NN online adjustment process can be avoided and a better control performance can be obtained. Simulation results demonstrate the effectiveness of the proposed control method.

Dynamic Learning From Adaptive Neural Control of Robot Manipulators With Prescribed Performance

This paper presents dynamic learning from adaptive neural control (ANC) with prescribed tracking error performance for an $ {n}$ -link robot manipulator subjected to unknown system dynamics and external disturbances. To achieve the prescribed performance, a performance function is introduced to describe the performance restrictions on tracking errors, and then specific performance requirements are served as a priori condition of tracking control design. By an error transformation method, the constrained tracking control problem of the original robot manipulator is transformed into the stabilization problem of an unconstrained augmented system. Then, a novel ANC scheme is proposed for the unconstrained system by combining a filter tracking error with radial basis function (RBF) neural network (NN) approximator, and all the signals in the closed-loop system are semi-globally uniformly ultimately bounded. The external disturbances might make it difficult to achieve the accurate convergence of NN weight estimates. To overcome this difficulty, an appropriate state transformation is introduced to transform the closed-loop system into a linear time-varying system with small perturbed terms. Under partial persistent excitation condition of RBF NNs, the convergence of NN weight estimates is guaranteed, and then the experienced knowledge on the unknown robot manipulator dynamics can be stored with NN constant weights. Using the experienced knowledge, a static neural learning control is proposed to improve the system performances without time-consuming online parameter adjustment process, and the proposed learning control can also guarantee the prescribed transient and steady-state tracking control performance. Simulation results demonstrate the effectiveness of the proposed method.

Dynamic Learning From Neural Control for Strict-Feedback Systems With Guaranteed Predefined Performance.

This paper focuses on dynamic learning from neural control for a class of nonlinear strict-feedback systems with predefined tracking performance attributes. To reduce the number of neural network (NN) approximators used and make the convergence of neural weights verified easily, state variables are introduced to transform the state-feedback control of the original strict-feedback systems into the output-feedback control of the system in the normal form. Then, using the output error transformation based on performance functions, the constrained tracking control problem of the normal systems is transformed into the stabilization problem of an equivalent unconstrained one. By combining the backstepping method, a high-gain observer with radial basis function (RBF) NNs, a novel adaptive neural control (ANC) scheme is proposed to guarantee the predefined tracking error performance as well as the ultimate boundedness of all other closed-loop signals. In particular, only one NN is employed to approximate the lumped unknown system dynamics during the controller design. Under the satisfaction of the partial persistent excitation condition for RBF NNs, the proposed stable ANC scheme is shown to be capable of achieving knowledge acquisition, expression, and storage of unknown system dynamics. The stored knowledge is reused to develop a neural learning controller for improving the control performance of the closed-loop system. When the initial condition satisfies the predefined performance, the proposed neural learning control can still guarantee the predefined tracking performance. Simulation results on a third-order one-link robot are given to show the effectiveness of the proposed method.

Neural learning control of pure-feedback nonlinear systems

This paper is concerned with the problem of learning control for a class of pure-feedback systems with unknown non-affine terms in dynamical environments. The implicit function theorem and the mean value theorem are firstly used to transform the closed-loop system into a semi-affine form. By combining the quadratic-type Lyapunov function and the appropriate inequality technology, a concise adaptive neural control scheme is developed to simplify the system stability analysis and guarantee the convergence of the tracking error in a finite time. After the stable control design, we decompose the closed-loop system into a series of linear time-varying perturbed subsystems with the help of the linear state transformation. Using a recursive design, the partial persistent excitation (PE) condition for the radial basis function neural network is satisfied during tracking control to a recurrent reference trajectory. Under the PE condition, accurate approximations of the implicit desired control dynamics are recursively achieved in a local region along recurrent orbits of closed-loop signals. Subsequently, a neural learning control method which effectively utilizes the learned knowledge without re-adapting to the unknown system dynamics is proposed to achieve the closed-loop stability and improved control performance. Simulation studies are performed to demonstrate that the proposed learning control scheme not only can approximate accurately the implicit desired control dynamics, but also can reuse the learned knowledge to achieve the better control performance with the faster tracking convergence rate and the smaller tracking error.

Learning from adaptive neural dynamic surface control of strict-feedback systems.

Learning plays an essential role in autonomous control systems. However, how to achieve learning in the nonstationary environment for nonlinear systems is a challenging problem. In this paper, we present learning method for a class of n th-order strict-feedback systems by adaptive dynamic surface control (DSC) technology, which achieves the human-like ability of learning by doing and doing with learned knowledge. To achieve the learning, this paper first proposes stable adaptive DSC with auxiliary first-order filters, which ensures the boundedness of all the signals in the closed-loop system and the convergence of tracking errors in a finite time. With the help of DSC, the derivative of the filter output variable is used as the neural network (NN) input instead of traditional intermediate variables. As a result, the proposed adaptive DSC method reduces greatly the dimension of NN inputs, especially for high-order systems. After the stable DSC design, we decompose the stable closed-loop system into a series of linear time-varying perturbed subsystems. Using a recursive design, the recurrent property of NN input variables is easily verified since the complexity is overcome using DSC. Subsequently, the partial persistent excitation condition of the radial basis function NN is satisfied. By combining a state transformation, accurate approximations of the closed-loop system dynamics are recursively achieved in a local region along recurrent orbits. Then, the learning control method using the learned knowledge is proposed to achieve the closed-loop stability and the improved control performance. Simulation studies are performed to demonstrate the proposed scheme can not only reuse the learned knowledge to achieve the better control performance with the faster tracking convergence rate and the smaller tracking error but also greatly alleviate the computational burden because of reducing the number and complexity of NN input variables.

Dynamic learning from adaptive neural network control of a class of nonaffine nonlinear systems.

This paper studies the problem of learning from adaptive neural network (NN) control of a class of nonaffine nonlinear systems in uncertain dynamic environments. In the control design process, a stable adaptive NN tracking control design technique is proposed for the nonaffine nonlinear systems with a mild assumption by combining a filtered tracking error with the implicit function theorem, input-to-state stability, and the small-gain theorem. The proposed stable control design technique not only overcomes the difficulty in controlling nonaffine nonlinear systems but also relaxes constraint conditions of the considered systems. In the learning process, the partial persistent excitation (PE) condition of radial basis function NNs is satisfied during tracking control to a recurrent reference trajectory. Under the PE condition and an appropriate state transformation, the proposed adaptive NN control is shown to be capable of acquiring knowledge on the implicit desired control input dynamics in the stable control process and of storing the learned knowledge in memory. Subsequently, an NN learning control design technique that effectively exploits the learned knowledge without re-adapting to the controller parameters is proposed to achieve closed-loop stability and improved control performance. Simulation studies are performed to demonstrate the effectiveness of the proposed design techniques.

Reinforcement learning output feedback NN control using deterministic learning technique.

In this brief, a novel adaptive-critic-based neural network (NN) controller is investigated for nonlinear pure-feedback systems. The controller design is based on the transformed predictor form, and the actor-critic NN control architecture includes two NNs, whereas the critic NN is used to approximate the strategic utility function, and the action NN is employed to minimize both the strategic utility function and the tracking error. A deterministic learning technique has been employed to guarantee that the partial persistent excitation condition of internal states is satisfied during tracking control to a periodic reference orbit. The uniformly ultimate boundedness of closed-loop signals is shown via Lyapunov stability analysis. Simulation results are presented to demonstrate the effectiveness of the proposed control.

Adaptive neural control and learning of affine nonlinear systems

This paper presents deterministic learning from adaptive neural network control of affine nonlinear systems with completely unknown system dynamics. Thanks to the learning capability of radial basis function, neural network (NN), stable adaptive NN controller is designed for the unknown affine nonlinear systems. The designed adaptive NN controller is rigorously shown that learning of the unknown closed-loop system dynamics can be achieved during the stable control process because partial persistent excitation condition of some internal signals in the closed-loop system is satisfied. Subsequently, neural learning controller using the knowledge obtained from deterministic learning is constructed to achieve closed-loop stability and improve control performance. Numerical simulation is provided to show the effectiveness of the proposed control scheme.