Neural Dynamic Surface Research Articles

A yaw stability-guaranteed hierarchical coordination control strategy for four-wheel drive electric vehicles using an unscented Kalman filter

A novel hierarchical coordination control strategy (HCCS) is offered to guarantee the stability of four-wheel drive electric vehicles (4WD-EVs) combining the Unscented Kalman filter (UKF). First, a dynamics model of the 4WD-EVs is established, and the UKF-based estimator of sideslip angle and yaw rate is constructed concurrently. Second, the equivalent cornering stiffness coefficients are jointly estimated to consider the impact of vehicle uncertainty parameters on the estimator design. Afterwards, a HCCS with two-level controller is presented. The sideslip angle and yaw rate are controlled by an adaptive backstepping-based yaw moment controller, and the computational burden is relieved by an improved adaptive neural dynamic surface control technology in the upper-level controller. Simultaneously, the optimal torque distribution controller of hub motors is developed to optimize the adhesion utilization ratio of tire in the lower-level controller. Finally, the proposed HCCS has shown effective improvement in the trajectory tracking capability and yaw stability of the 4WD-EVs under various maneuver conditions compared with the traditional Luenberger observer-based and the federal-cubature Kalman filter-based hierarchical controller.

Predictor-Based Neural Dynamic Surface Control for Strict-Feedback Nonlinear Systems With Unknown Control Gains.

Neural dynamic surface control (NDSC) is an effective technique for the tracking control of nonlinear systems. The objective of this article is to improve closed-loop transient performance and reduce the number of learning parameters for a strict-feedback nonlinear system with unknown control gains. For this purpose, a predictor-based NDSC (PNDSC) approach is presented. It introduces Nussbaum functions and predictors into the traditional NDSC for nonlinear systems with unknown control gains. Unlike NDSC that uses surface errors to update the learning parameters of neural networks (NNs), the PNDSC employs prediction errors for the same purpose, leading to improved transient performance of closed-loop control systems. To reduce the number of learning parameters, the PNDSC is further embedded with the technique of the minimal number of learning parameters (MNLPs). This avoids the problem of the ``explosion of learning parameters'' as the order of the system increases. A Lyapunov-based stability analysis shows that all signals are bounded in the closed-loop systems under PNDSC embedded with MNLPs. Simulations are conducted to demonstrate the effectiveness of the PNDSC approach presented in this article.

Robust adaptive synchronized event-triggered formation control of USVs with the fault amendment strategy

In this paper, the formation control of the underactuated surface vehicles (USVs) is studied in the presence of the condition of actuator fault and limited communication resources. Considering the performance characteristics of the underactuated surface vehicle (USV), a robust adaptive synchronized event-triggered formation control method is proposed under the usage of the event-triggered control (ETC) and robust neural damping technique. In consideration of the constant energy expenditure of the law of adaptation, the formulated control method is set in the mechanism of triggering by both the controller and the gain related adaptive law, which could cause the communication to reduce more much power consumption. The robust adaptive rule is fault compensated in the way of combining robust neural damping and dynamic surface control (DSC) techniques. Since the fault amendment strategy compresses inconclusive bias fault parameters and model uncertainty parameters, system stability can be enhanced under the premise of reducing the influence of adaptive parameters. A huge volume of work has taken place to ensure semi-global uniform ultimate bounded (SGUUB) stability. To conclude, the effectiveness of the algorithm is verified by two arithmetic examples.

Design of Photovoltaic Power Generation Servo System Based on Discrete Adaptive Network Dynamic Surface Control Technology

In recent years, under the development of the dual carbon goal, the energy crisis has become increasingly serious, and China has also experienced serious power rationing. However, the research on dynamic surface control technology in solar tracking systems in nonlinear control systems is mostly based on continuous-time systems, while adaptive dynamic surface control based on discrete-time nonlinear control systems can describe an actual control system more accurately in the production process. It can effectively suppress interference with extremely high stability and safety. To solve the problem of low efficiency in photovoltaic power generation, this research first built a photovoltaic power generation servo system model based on the parameter of uncertainty. Then, a discrete adaptive neural network dynamic surface (DANNDS) controller was designed to solve the problems in the design of the traditional backstepping method. Finally, based on the designed method of a dynamic surface controller, a discrete adaptive neural network quantization controller (DANNQC) for the photovoltaic power generation servo system was designed by introducing external disturbance. The control parameters and their studied ranges were as follows: The reference signals were or1=sin(0.1t) and or2=cos(0.1t). The parameters of the virtual control law and the final control law were m11=0.01, m22=0.01, m12=0.02, m13=0.02, and m23=0.02. The time constant of the low-pass filter was ζ12=ζ13=ζ22=ζ23=0.005. The parameters of the parameter regulation law were ρ12=ρ13=ρ22=ρ23=0.0005 and a12=a13=20, a22=a23=22. The research results show that the MTE, RMSTE, and 2NTE scores of the height angle servo motor of the DANNDS control method were 0.0026, 7.0279 × 10−4, and 0.3552, respectively. The scores for each index of the azimuth servo motor were 0.0028, 8.9237 × 10−4, and 0.4511, respectively. The height angle tracking error for the DANNQC control method was [−0.02,0.022]. The azimuth tracking error was [−0.03,0.03]. In summary, the photovoltaic power generation servo system based on the DANNQC has a better control performance. By controlling the height angle and azimuth angles, it can better track the position of the sun and adjust the position of the photovoltaic panel in real time. The sun’s rays illuminate the photovoltaic panel at an appropriate angle to achieve maximum power generation efficiency, which is of great practical significance for the development of solar technology.

BLF-based neural dynamic surface control for stochastic nonlinear systems with time delays and full-state constraints

This paper investigates the adaptive neural tracking control problem for a class of stochastic nonlinear systems with time delays and full-state constraints in a unified framework for the first time. The time-delay terms of the controlled systems are compensated by novel Lyapunov–Krasovskii functionals. The asymmetric barrier Lyapunov function (BLF) is adopted to guarantee that the full states are always restricted within prescribed constraints. RBF neural networks are utilised to approximate the lumped unknown functions in the design process. Furthermore, the dynamic surface control (DSC) technique is employed to simplify the process of control design significantly. Stability analysis shows all closed-loop signals are SGUUB, and full-state constraints are not violated. Finally, simulation results confirm the effectiveness of the proposed control scheme.

Adaptive Neural Control of Nonlinear Cyber–Physical Systems Against Randomly Occurring False Data Injection Attacks

In this article, the main contribution is to introduce the adaptive backstepping technique into nonlinear cyber–physical systems against randomly occurring false data injection (ROFDI) attacks. And a new defense strategy based on nonlinear disturbance observer (NDO) is developed, which can not only effectively estimate the external compound disturbance in the presence of the attack, but also improve the robustness of the controlled system. Different from FDI attacks, it is a special case of ROFDI attacks, and the proposed method can deal with ROFDI attacks injected by attackers. Meanwhile, multiple Nussbaum functions are introduced, which overcomes the design difficulty of unknown control directions caused by ROFDI attacks. Furthermore, the approximation of the unknown nonlinear function and the exponential growth problem in the traditional backstepping calculation process are handled by radial basis function neural network and dynamic surface control, respectively. Finally, a new adaptive neural control method based on NDO is proposed to make all signals bounded. Meanwhile, tracking errors and disturbance estimation errors converge on the neighborhood of zero. Numerical and practical examples further illustrate the rationality of the method.

Neural dynamic surface control for stochastic nonlinear systems with unknown control directions and unmodelled dynamics

AbstractThe control problem for a class of stochastic nonlinear systems with both unknown control directions and unmodelled dynamics is investigated here for the first time. The technique of dynamics signal is adopted to cope with the unmodelled dynamics in the considered system. The unknown control directions problem are addressed by Nussbaum function. RBF neural networks are employed to approximate the lumped unknown functions, and regardless of the number of neural networks used and the order of the system, only one adaptive parameter requires to be adjusted. Dynamic surface control(DSC) is utilized to cope with the complexity explosion of the backstepping design. Hence, a novel neural control scheme is proposed by means of dynamics signal method, DSC technique and Nussbaum function. Stability analysis proves all closed‐loop signals are SGUUB by choosing the parameters appropriately, and the simulation results demonstrate the correctness and effectiveness of the proposed scheme.

Adaptive neural dynamic surface control with fixed-time prescribed performance for uncertain nonstrict-feedback stochastic switched systems

An adaptive neural dynamic surface control (DSC) problem with fixed-time prescribed performance (FTPP) is investigated for a class of nonstrict-feedback stochastic switched systems. Differently from the existing works for FTPP problem, the stochastic switched systems with nonstrict-feedback form and completely unknown systems are considered in this paper, and the unknown functions are approximated by some radial basis function (RBF) neural networks (NNs). The desired adaptive neural controller is designed by using common Lyapunov function method and defining fixed-time prescribed performance function (PPF). And based on the adaptive DSC scheme with the nonlinear filter, the “explosion of complexity” problem is avoided. Besides, the constructed fixed-time PPF just need to meet the requirement of second derivative exists. According to the Lyapunov stability theory, the FTPP of output tracking error is achieved, and all signals of closed-loop system remain bounded in probability. Finally, simulation results are presented to verify the availability of the designed control strategy.

Neural Predictor-Based Dynamic Surface Predictive Control for Power Converters

In this letter, a neural predictor-based dynamic surface predictive control framework, endowed with the merits of adaptive dynamic surface control and finite control-set model predictive control, is proposed where the estimation of neural predictor is incorporated to identify the system dynamics and lumped unknown uncertainties. The key features of the proposal are that, first, the issue of “explosion of complexity” inherent in the classical back-stepping control is avoided, second, the model uncertainties and disturbances are explicitly dealt with, and, third, the tedious determination procedure of weighting factors is removed. These features lead to a much simpler adaptive predictive control solution, which is convenient to implement in applications. Furthermore, a Lyapunov function is constructed, and the stability analysis is given. It demonstrates that all signals in the closed-loop system are uniformly ultimately bounded. Finally, this proposal is experimentally assessed, where the performance evaluation of steady-state and transient-state confirms the availability of the proposed solution for modular multilevel converter.

Learning-Based Neural Dynamic Surface Predictive Control for MMC

Reinforcement learning technique was developed recently as an interesting topic in designing adaptive optimal controllers. This technique explicitly provided a feasible solution to circumvent the “curse of dimensionality” and requiring a system model inherent in the classical dynamic programming algorithm. By virtue of this property, in our work, by introducing this technique into a predictor-based online adaptive neural dynamic surface predictive control architecture, we concentrate on a novel robust predictive control framework subject to system uncertainties. To be specific, in this presented framework, an adaptive dynamic programming control strategy utilizing a critic neural network point of view is developed to learn the optimal control policy. Our modification is able to facilitate the alleviation of performance deterioration caused by system uncertainties and enable the smooth and fast learning, while keeping the merits of the finite control-set model predictive control. Finally, the interest and applicability of the proposed control methodology are verified by performance evaluation.

Robust Adaptive Neural Control for Wing-Sail-Assisted Vehicle via the Multiport Event-Triggered Approach.

This article presents a robust adaptive neural control algorithm for the wing-sail-assisted vehicle to track the desired waypoint-based route, where the event-triggered mechanism is with the multiport form. The main features of the proposed algorithm are three-fold: 1) the communication burden, in the channel from the sensor to the controller as well as the actuator, has been reduced for the merits of the multiport event-triggered approach. The feedback error signals and the control input will be updated only on the event-triggered time point; 2) for the wing-sail-assisted vehicle, the thrust force is provided by devices with the propeller and the sail. From this consideration, the proper sail force compensation is derived on the basis of information about the current heading angle and the wind direction. The corresponding control law can guarantee the energy-saving for the propeller; and 3) in the algorithm, the system uncertainties are remodeled by the neural-network approximator. Furthermore, by fusion of the robust neural damping and dynamic surface control (DSC) techniques, the corresponding gain-related adaptive law is developed to address constraints of the gain uncertainty and the environmental disturbances. Through the Lyapunov theorem, all signals of the closed-loop control system have been proved to be with the semiglobal uniform ultimate bounded (SGUUB) stability, including the triggered time point and the intermediate triggered interval. Finally, the numerical simulation and the practical experiment are illustrated to verify the effectiveness of the proposed strategy.

Neural adaptive finite-time dynamic surface control for the PMSM system with time delays and asymmetric time-varying output constraint

This paper presents a neural adaptive finite-time dynamic surface control for the permanent magnet synchronous motor system with time delays and asymmetric time-varying output constraint. The core challenge is how to address the time delays and asymmetric output constraint when designing a finite-time control scheme. Given this, a proper Lyapunov–Krasovskii functional is introduced to address time delays, and a nonlinear transformation function is considered to convert the output-constrained problem into an unconstrained one. Then, a neural adaptive finite-time dynamic surface control approach is devised in the finite-time backstepping framework, which applies neural networks to estimate the unknown nonlinear functions and introduces first-order filters to solve the “explosion of complexity” problems. Furthermore, it is demonstrated that all the signals of the resulting system are finite-time stable and the tracking error converges to a neighborhood of origin in finite time without violating the output constraint. Finally, the simulation results show that the integration of squared error results, the integral of time and absolute error results as well as the integration of absolute value error results of the proposed scheme is smaller than the tested scheme by 0.3458 , 22.2977 , and 2.2513 , respectively, when the time delays are considered. It further elucidates the availability and superiority of the developed method.

Predictor-Based Neural Dynamic Surface Control of a Nontriangular System With Unknown Disturbances

For a class of nontriangular nonlinear systems in presence of unknown disturbances, we propose a predictor-based neural dynamic surface control (PNDSC) strategy in this paper. This nontriangular system is transformed via the mean value theorem, and a predictor is then constructed. To avoid an algebraic loop problem, partial state vectors are employed as input signals of neural networks (NNs) for approximating unknown dynamics, and compensation items are designed to compensate for approximation errors from NNs. Different from the traditional NDSC, the PNDSC in this paper utilizes prediction errors to update learning parameters for improving NNs’ learning behaviors with overlarge adaptive gains. On the basis of improved NNs’ approximation behaviors, a predictor-based NNs disturbance observer (PNNDO) is constructed for compensation for external disturbances and approximation errors from NNs. Furthermore, with predictors, a normalization method of weights is developed to reduce the number of online learning parameters. On the basis of the aforementioned result, measurement noises are taken into account in our predictor-based neural control strategy. We employ predictor states, rather than measurement information paralyzed by noises, in design of our control strategy. This reduces high-frequency oscillations in control input. A Lyapunov-based stability analysis shows that all signals are ultimately bounded in the closed-loop system. Finally, the effectiveness of the proposed control strategy is verified by a numerical example and a permanent magnet brushless DC motor system.

Neural Adaptive Funnel Dynamic Surface Control with Disturbance-Observer for the PMSM with Time Delays.

This paper suggests an adaptive funnel dynamic surface control method with a disturbance observer for the permanent magnet synchronous motor with time delays. An improved prescribed performance function is integrated with a modified funnel variable at the beginning of the controller design to coordinate the permanent magnet synchronous motor with the output constrained into an unconstrained one, which has a faster convergence rate than ordinary barrier Lyapunov functions. Then, the specific controller is devised by the dynamic surface control technique with first-order filters to the unconstrained system. Therein, a disturbance-observer and the radial basis function neural networks are introduced to estimate unmatched disturbances and multiple unknown nonlinearities, respectively. Several Lyapunov-Krasovskii functionals are constructed to make up for time delays, enhancing control performance. The first-order filters are implemented to overcome the “complexity explosion” caused by general backstepping methods. Additionally, the boundedness and binding ranges of all the signals are ensured through the detailed stability analysis. Ultimately, simulation results and comparison experiments confirm the superiority of the controller designed in this paper.

Neural network dynamic surface position control of n‐joint robot driven by PMSM with unknown load observer

To solve the problems of low accuracy and poor stability due to modeling error, external disturbance and unknown load, which exist in the position servo control of permanent magnet synchronous motor (PMSM) driven joint robot, this article is to propose the radial basis function (RBF) neural networks dynamic surface control strategy with the Sage-Husa adaptive Kalman filter load torque observer. For the unknown load torque of the robot, the PMSM load torque observer is established by using the Sage-Huga adaptive Kalman filter. The RBF neural network dynamic surface controller is designed using the online approximation capability of the neural network, which is used to approximate the modeling error, external interference and filtering error generated by the dynamic surface control of the joint robot online. Combining the above strategies, the n-joint robot position controller is designed. The stability of this control strategy is demonstrated by stability analysis. Simulations and experiments on the two-joint robot show that the control strategy ensures the accuracy and stability of the joint robot position control.

Adaptive neural dynamic surface control for uniform energy exploitation of floating wind turbine

To avoid the harmful effects of global warming on the earth planet and its atmosphere, the expansion of wind energy consumption based on new control techniques leads to improved energy capacity. The development of wind power plants on the sea is more efficient owing to the stronger wind flows in comparison with the onshore structure. Furthermore, stable installation of the offshore wind energy base meets the energy management requirements of today's consumers. As a result, dependency on fossil fuels as the main source of global warming decreases. The feedback control system and on-line sensor signals provide the stability and increased efficiency of the floating wind turbine. The aggressive environment and large size structure of the turbine lead to entering uncertainty in the turbine model and exogenous noises that should not be effectively compensated by conventional control methods. Therefore, a radial based functional neural network (RBFNN) controller is proposed to estimate and compensate the effect of uncertainty on feedback control of the wind turbine. For comparison purposes, a linear quadratic regulator (LQR) state feedback is also developed for optimal control of the floating wind turbines. The neural network adaptively determines the upper bound of uncertainty/noise. Therefore, conservative high-gain control actions to achieve robustness of the classical feedback controllers against structural deviations of the turbine body are decreased. In our newly proposed adaptive control algorithm, using a basic raised cosine function guides to restore the computational efficiency of RBFNN. With the Lyapunov-based stability analysis, the final limits of the closed-loop system and the convergence caused by the terminal sliding mode (TSM) tracking error are determined. Detailed software simulations of both the LQR and the designed RBFNN control systems indicate the superiority of the neural network-based approach.

Adaptive neural network dynamic surface control of uncertain strict-feedback nonlinear systems with unknown control direction and unknown actuator fault

In this paper, the tracking control problem of a class of uncertain strict-feedback nonlinear systems with unknown control direction and unknown actuator fault is studied. By using the neural network control approach and dynamic surface control technique, an adaptive neural network dynamic surface control law is designed. Based on the neural network approximator, the uncertain nonlinear dynamics are approximated. Using the dynamic surface control technique, the complexity explosion problems in the design of virtual control laws and adaptive updating laws can be overcome. Moreover, to solve the unknown control direction and unknown actuator fault problems, a type of Nussbaum gain function is incorporated into the recursive design of dynamic surface control. Based on the designed adaptive control law, it can be confirmed that all of the signals in the closed-loop system are semi-global bounded, and the convergence of the tracking error to the specified small neighborhood of the origin could be ensured by adjusting the designing parameters. Finally, two examples are provided to demonstrate the effectiveness of the proposed adaptive control law.

Observer‐based adaptive neural network dynamic surface bipartite containment control for switched fractional order multi‐agent systems

SummaryThis article studies the bipartite containment control problem for a class of fractional order nonlinear multi‐agent systems in the presence of arbitrary switchings and unmeasured states. Under the framework of Lyapunov function theory, this article proposes an adaptive neural network dynamic surface controller, in which dynamic surface control technology can avoid “explosion of complexity” and obtain fractional derivatives for virtual control functions continuously. Radial basis function neural networks are used to approximate the unknown nonlinear functions and an observer is designed to obtain the unmeasured states. The proposed distributed protocol can ensure all the signals remain semi‐global uniformly ultimately bounded in the closed‐loop system and all followers can converge to the convex hull containing each leader's trajectory as well as its opposite trajectory different in sign. Example and simulation results confirm the feasibility of the proposed control method.

Predictor-Based Neural Dynamic Surface Control for Bipartite Tracking of a Class of Nonlinear Multiagent Systems.

This article is concerned with bipartite tracking for a class of nonlinear multiagent systems under a signed directed graph, where the followers are with unknown virtual control gains. In the predictor-based neural dynamic surface control (NDSC) framework, a bipartite tracking control strategy is proposed by the introduction of predictors and the minimal number of learning parameters (MNLPs) technology along with the graph theory. Different from the traditional NDSC, the predictor-based NDSC utilizes prediction errors to update the neural network for improving system transient performance. The MNLPs technology is employed to avoid the problem of "explosion of learning parameters". It is proved that all closed-loop signals steered by the proposed control strategy are bounded, and the system achieves bipartite consensus. Simulation results verify the efficiency and effectiveness of the strategy.

Secure predictor-based neural dynamic surface control of nonlinear cyber–physical systems against sensor and actuator attacks

This paper addresses a secure predictor-based neural dynamic surface control (SPNDSC) issue for a cyber–physical system in a nontriangular form suffering from both sensor and actuator deception attacks. To avoid the algebraic loop problem, only partial states are employed as input vectors of neural networks (NNs) for approximating unknown dynamics, and compensation terms are further developed to offset approximation errors from NNs. With introduction of nonlinear gain functions and attack compensators, adverse effects of an intelligent adversary are alleviated effectively. Furthermore, we present stability analysis and prove the ultimate boundedness of all signals in the closed-loop system. The effectiveness of the proposed control strategy is illustrated by two examples.