Neural Network Weight Vector Research Articles

Adaptive position control using backstepping technique for the leader‐follower multiple quadrotor unmanned aerial vehicle formation

SummaryThis article addresses the position control issue of multi‐quadrotor unmanned aerial vehicle (QUAV) formation. Concerning the translational dynamic of a multi‐QUAV system, on the one hand, it is an under‐actuation dynamic; on the other hand, it does not satisfy the matching condition. These features will cause inevitable thorny in the formation position control design. Furthermore, because of the state coupling problem, the formation control of multi‐QUAV system is more challenging and knotty than the control of single QUAV system. To achieve this control, both backstepping technique and neural network (NN) approximation strategy are combined by introducing an intermediary control, where NN is employed to compensate the system uncertainty. However, since the traditional adaptive NN control methods need to train a large number of adaptive parameters for the high approximation accuracy, it will cause the heavy computing burden if traditional adaptive method is used for the QUAV formation control. The proposed adaptive NN strategy in this paper only requires training a scalar adaptive parameter, which is generated from the norm of NN weight vector or matrix, thereby significantly reducing computational burden. Finally, according to Lyapunov stability proof and computer simulation, it is demonstrated that the control tasks can be successfully accomplished.

Decentralized Adaptive Quantized Dynamic Surface Control for a Class of Flexible Hypersonic Flight Vehicles with Input Quantization

A control strategy for a certain class of hypersonic flight aircraft dynamic models with unknown parameters is proposed in this article. The strategy is adaptive dynamic surface input quantization control. To address the issues in conventional inversion control, a first-order low-pass filter and an adaptive parameter minimum learning law are introduced in the control system design process. This method has the following features: (1) it solves the problem of repeated differentiation of the virtual control law in the conventional back-stepping method, greatly simplifying the control law structure; (2) by using the norm of the neural network weight vector as the adaptive adjustment parameter instead of updating each element online, the number of adaptive adjustment parameters is significantly reduced, improving the execution efficiency of the controller; (3) the introduced hysteresis quantizer overcomes the disadvantage of the quantization accuracy deterioration when the input value is too low in the logarithm quantizer, improving the accuracy of the quantizer. Stability analysis has shown that all signals in the closed-loop system are semi-globally uniformly bounded, and simulation results have verified the effectiveness of the proposed adaptive quantized control scheme.

Optimal control for wind turbine based on reinforcement learning

In this conference paper, an optimal control method is designed for a variable speed wind turbine system. Due to the inherent nonlinearity of the wind turbine arising from the aerodynamic torque, a linearized model is derived to handle the system's nonlinearities. An online update cost function is created based on the resulting linearized model. The critic neural network weight vector is updated with the steepest decent algorithm to design an optimal control able to minimize the given cost function. To validate the effectiveness of the optimal control based on reinforcement learning, simulation results with varying wind speed profile for different values of learning parameters are presented.

Observer-based adaptive neural network control design for projective synchronization of uncertain chaotic systems

This paper addresses the design of an observer-based adaptive neural network chaos synchronization scheme for a general class of uncertain chaotic systems. The controller consists of an adaptive neural network control law and an extended state observer. The parameterization of the designed extended observer and the sufficient stability conditions are derived in the light of the singular perturbation theory. The extended observer is incorporated into the controller to reconstruct the synchronization error vector as well as to estimate the error between an ideal control law and the actual control. These estimated error signals are utilized in the adaptation mechanism of the neural network weight vector. In the presented chaos synchronization method, the knowledge of the models of the master–slave systems is not required and the controller only needs the projective synchronization error for its implementation. Numerical simulations are performed along with a comparative study to demonstrate the efficiency and effectiveness of the suggested chaos synchronization approach.

Adaptive finite-time tracking control for full state constrained nonlinear systems with time-varying delays and input saturation

This paper investigates the adaptive finite-time tracking control problem for a class of nonlinear full state constrained systems with time-varying delays and input saturation. Compared with the previously published work, the considered system involves unknown time-varying delays, asymmetric input saturation, and time-varying asymmetric full state constraints. To ensure the state constraint satisfaction, the appropriate time-varying asymmetric Barrier Lyapunov Functions and the backstepping technique are utilized. Meanwhile, the finite covering lemma and the radial basis function neural networks are employed to solve the unknown time-varying delays. The assumption that the time derivative of time-varying delay functions is required to be less than one in traditional Lyapunov–Krasovskii functionals is removed by the proposed method. Moreover, the asymmetric input saturation is handled by an auxiliary design system. Taking the norm of the neural network weight vector as an adaptive parameter, a novel adaptive finite-time tracking controller with minimal learning parameters is constructed. It is proved that the proposed controller can guarantee that all signals in the closed-loop system are bounded, all states are constrained within the predefined sets, and the tracking error converges to a small neighborhood of the origin in a finite time. Finally, a comparison study simulation is given to demonstrate the effectiveness of our proposed strategy. The simulation results show that our proposed strategy has good advantages of high tracking precision and disturbance rejection.

Adaptive neural network control for time-varying state constrained nonlinear stochastic systems with input saturation

This paper investigates the tracking control issue of nonlinear stochastic systems subject to time-varying full state constraints and input saturation. By employing both neural network-based approximator and backstepping technique, an adaptive neural network (NN) control approach is presented on the basis of the time-varying barrier Lyapunov function. To surmount the influence of saturation nonlinearity, a Gaussian error function-based continuous differentiable saturation model is introduced such that the actual control in the final backstepping step can be achieved. The designed controller can not only achieve the tracking control objective, but also surmount the impact of input saturation to stochastic system performance. Meanwhile, the norm of NN weight vector is taken as estimated parameter, and it can alleviate computation burden. The presented controller can ensure that all the signals in the closed-loop system are bounded in probability and all state variables are restricted the predefined regions. Finally, simulation results are given to illustrate the effectiveness of the established controller.

Adaptive Neural Boundary Control Design for Nonlinear Flexible Distributed Parameter Systems

This paper proposes an adaptive neural boundary feedback control design for a nonlinear flexible distributed parameter system described by a nonuniform wave equation containing an unknown nonlinear function in the boundary conditions. In the proposed design method, a radial-basis-function neural network (NN) with an adaptive weight update law is used to approximate the unknown nonlinear term. By using this adaptive NN, an adaptive boundary feedback controller is constructed to ensure that the resulting closed-loop system is practically exponentially stable. The closed-loop stability of the system is analyzed by the Lyapunov direct method and technique of integration by parts, and the update law of an NN weight vector is determined simultaneously. The closed-loop well-posedness analysis is also provided by applying the C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> -semigroup approach. Moreover, the proposed design method is extended for a nonlinear flexible distributed parameter system modeled by a nonuniform Euler-Bernoulli beam equation containing an unknown nonlinear function in the boundary conditions. Finally, extensive numerical simulation results are given to demonstrate the performance of the proposed adaptive neural boundary control design method.

RBF Neural Network Backstepping Sliding Mode Adaptive Control for Dynamic Pressure Cylinder Electrohydraulic Servo Pressure System

According to the hydraulic principle diagram of the subgrade test device, the dynamic pressure cylinder electrohydraulic servo pressure system math model and AMESim simulation model are established. The system is divided into two parts of the dynamic pressure cylinder displacement subsystem and the dynamic pressure cylinder output pressure subsystem. On this basis, a RBF neural network backstepping sliding mode adaptive control algorithm is designed: using the double sliding mode structure, the two RBF neural networks are used to approximate the uncertainties in the two subsystems, provide design methods of RBF sliding mode adaptive controller of the dynamic pressure cylinder displacement subsystem and RBF backstepping sliding mode adaptive controller of the dynamic pressure cylinder output pressure subsystem, and give the two RBF neural network weight vector adaptive laws, and the stability of the algorithm is proved. Finally, the algorithm is applied to the dynamic pressure cylinder electrohydraulic servo pressure system AMESim model; simulation results show that this algorithm can not only effectively estimate the system uncertainties, but also achieve accurate tracking of the target variables and have a simpler structure, better control performance, and better robust performance than the backstepping sliding mode adaptive control (BSAC).

Neural Network Learning and Robust Stabilization of Nonlinear Systems With Dynamic Uncertainties.

Due to the existence of dynamical uncertainties, it is important to pay attention to the robustness of nonlinear control systems, especially when designing adaptive critic control strategies. In this paper, based on the neural network learning component, the robust stabilization scheme of nonlinear systems with general uncertainties is developed. Through system transformation and employing adaptive critic technique, the approximate optimal controller of the nominal plant can be applied to accomplish robust stabilization for the original uncertain dynamics. The neural network weight vector is very convenient to initialize by virtue of the improved critic learning formulation. Under the action of the approximate optimal control law, the stability issues for the closed-loop form of nominal and uncertain plants are analyzed, respectively. Simulation illustrations via a typical nonlinear system and a practical power system are included to verify the control performance.

Multi-step heuristic dynamic programming for optimal control of nonlinear discrete-time systems

Policy iteration and value iteration are two main iterative adaptive dynamic programming frameworks for solving optimal control problems. Policy iteration converges fast while requiring an initial stabilizing control policy, which is a strict constraint in practice. Value iteration avoids the requirement of initial admissible control policy while converging much slowly. This paper tries to utilize the advantages of policy iteration and value iteration, and avoids their drawbacks at the same time. Therefore, a multi-step heuristic dynamic programming (MsHDP) method is developed for solving the optimal control problem of nonlinear discrete-time systems. MsHDP speeds up value iteration and avoids the requirement of initial admissible control policy in policy iteration at the same time. The convergence theory of MsHDP is established by proving that it converges to the solution of the Bellman equation. For implementation purpose, the actor-critic neural network (NN) structure is developed. The critic NN is employed to estimate the value function and its NN weight vector is computed with a least-square scheme. The actor NN is used to estimate the control policy and a gradient descent method is proposed for updating its NN weight vector. According to the comparative simulation studies on two examples, the effectiveness and advantages of MsHDP are verified.

Adaptive Neural Synchronization Control for Bilateral Teleoperation Systems With Time Delay and Backlash-Like Hysteresis.

This paper considers the master and slave synchronization control for bilateral teleoperation systems with time delay and backlash-like hysteresis. Based on radial basis functions neural networks' approximation capabilities, two improved adaptive neural control approaches are developed. By Lyapunov stability analysis, the position and velocity tracking errors are guaranteed to converge to a small neighborhood of the origin. The contributions of this paper can be summarized as follows: 1) by using the matrix norm established using the weight vector of neural networks as the estimated parameters, two novel control schemes are developed and 2) the hysteresis inverse is not required in the proposed controllers. The simulations are performed, and the results show the effectiveness of the proposed method.

A Model Predictive Algorithm for Active Control of Nonlinear Noise Processes

In this paper, an improved nonlinear Active Noise Control (ANC) system is achieved by introducing an appropriate secondary source. For ANC system to be successfully implemented, the nonlinearity of the primary path and time delay of the secondary path must be overcome. A nonlinear Model Predictive Control (MPC) strategy is introduced to deal with the time delay in the secondary path and the nonlinearity in the primary path of the ANC system. An overall online modeling technique is utilized for online secondary path and primary path estimation. The secondary path is estimated using an adaptive FIR filter, and the primary path is estimated using a Neural Network (NN). The two models are connected in parallel with the two paths. In this system, the mutual disturbances between the operation of the nonlinear ANC controller and modeling of the secondary can be greatly reduced. The coefficients of the adaptive FIR filter and weight vector of NN are adjusted online. Computer simulations are carried out to compare the proposed nonlinear MPC method with the nonlinear Filter‐x Least Mean Square (FXLMS) algorithm. The results showed that the convergence speed of the proposed nonlinear MPC algorithm is faster than that of nonlinear FXLMS algorithm. For testing the robust performance of the proposed nonlinear ANC system, the sudden changes in the secondary path and primary path of the ANC system are considered. Results indicated that the proposed nonlinear ANC system can rapidly track the sudden changes in the acoustic paths of the nonlinear ANC system, and ensure the adaptive algorithm stable when the nonlinear ANC system is time variable.

A design method of adaptive H∞ control for servo system with friction compensation: using dead-zone modification strategy

This paper considers a tracking control of a servo mechanism with friction. It is assumed that the static and dynamic characteristics of friction are captured by the dynamic LuGre model. Based on notion of H∞ optimality, an adaptive friction compensation strategy is proposed. Neural-Network (NN) is used to parameterize the nonlinear characteristic function of the friction model. In this proposed method, unknown friction parameters and NN weight vector are updated by estimating strategy. Moreover, an approximation error in NN is regarded as an exogenous disturbance to the system, the L2 gains from the disturbance to generalized outputs are made less than prescribed positive constants. To cope with the practical applications, dead-zone modification method is also applied to the unknown parameter estimating strategies. Experimental results are shown to illustrate the effectiveness of our proposed method.

TD Learning with Neural Networks

Temporal difference (TD) learning (TD learning), proposed by Sutton in the late 1980s, is very interesting prediction using obtained predictions for future prediction. Applying this learning to neural networks helps improve prediction performance using neural networks, after certain problems are solved. Major problems are as follows: 1) Prediction Pt at time t is assumed to be scalar in Sutton's original paper, raising the problem of ""what is the rule for updating weight vector of the neural network if the neural network has multiple outputs?"" 2) How do we derive individual components of gradient vector ∇wPt for weight vector w? This paper proposes how to handle these problems when TD learning is used in a neural network, focusing on the TD(0) algorithm, often used in TD learning. It proposes the rule for updating the neural network weight vector for a two-out neural network under problem 1) above, and explains the rule's validity. It then proposes computing every components of ∇wPt.