Dynamic Surface Control Technology Research Articles

Finite-Time Adaptive Fuzzy Backstepping Control for Quadrotor UAV With Stochastic Disturbance

This paper proposes an adaptive fuzzy output feedback control approach for quadrotor unmanned aerial vehicles (QUAV) with stochastic disturbances, besides which we consider the unmeasurable states and unknown nonlinear functions. The QUAV system contains stochastic terms which are not bounded and not differentiable. By combining the It <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\hat{\rm \textbf{o}}$</tex-math> </inline-formula> differential equation with finite-time theory, a novel stochastic finite-time stability controller for QUAV is raised for the first time. The fuzzy logic system (FLS) is utilized to approximate the unknown nonlinear functions in the model. Dynamic surface control technology is introduced to reduce the complexity of differential. Furthermore, an observer with FLS is designed through the adaptive backstepping technique to estimate the immeasurable states. It is proved that this control approach can ensure that all states of the closed-loop QUAV system are semi-global and finite-time stable in probability. Meanwhile, the errors of system outputs and observer converge to a small neighborhood of origin. The simulation results show the effectiveness of the proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —In practical applications, many systems are often affected by internal and external disturbances, and not all of them can be described by mathematical models, so they are called stochastic disturbances. Taking the QUAV as an example, when the system is disturbed by internal parameters, external environment, system input, sensor error, and other stochastic factors, the deterministic system can no longer accurately describe the controlled object. In this paper, the QUAV is regarded as a stochastic system for the first time, and a novel controller is designed to solve the above problems. In addition, the QUAV needs fast action in some applications, such as emergency collision avoidance, which has high requirements for the convergence performance of the controller. Therefore, studying the finite-time control for QUAV systems with stochastic disturbances is necessary. At the same time, this paper also considers the problem that the state is not measurable and the system contains unknown nonlinear equations.

Neural-Network-Based Adaptive Event-Triggered Asymptotically Consensus Tracking Control for Nonlinear Nonstrict-Feedback MASs: An Improved Dynamic Surface Approach.

In this article, the asymptotic tracking control problem for a class of nonlinear multi-agent systems (MASs) is researched by the combination of radial basis function neural networks (RBF NNs) and an improved dynamic surface control (DSC) technology. It's important to emphasize that the MASs studied in this article are nonlinear and nonstrict-feedback systems, where the nonlinear functions are unknown. In order to satisfy the requirement that all items in the controller must be available, the unknown nonlinearities in the system are flexibly approximated by utilizing RBF NNs technique. Moreover, the issue of ``complexity explosion'' in the backstepping procedure is handled by improving the traditional DSC technology, and meanwhile, the influences of the boundary layers caused by the filters in the DSC procedure are eliminated skillfully through the compensation terms. In addition, the relative threshold event-triggered strategy is developed for the designed controllers to reduce the waste of communication resources, where Zeno phenomenon is successfully avoided. It is observed that the new presented control strategy ensures that all the closed-loop systems variables are uniformly ultimately bounded (UUB), and furthermore all the outputs of followers are able to track the output of the leader with zero tracking errors. Finally, the simulation results are presented to show the effectiveness of the obtained design scheme.

High-order disturbance observer-based safe tracking control for a class of uncertain MIMO nonlinear systems with time-varying full state constraints

This paper investigates a high-order disturbance observer-based safe tracking control scheme for a class of uncertain multiple-input and multiple-output systems under time-varying full state constraints and disturbances. To achieve the safe tracking objective, a boundary protection algorithm is introduced to generate new safe desired signals which are within corresponding state constraints. An improved second-order dynamic surface control technology is developed to deal with the piecewise differentiability of safe desired signals and the phenomenon of repeatedly differentiation, simultaneously. To handle the negative effects of system uncertainties and obtain better estimation effect of high order time-varying disturbances, the radial basis function neural networks and high-order disturbance observer methods are developed. The safety and performance of the closed-loop nonlinear system under the proposed control scheme have been rigorous proved and discussed by Lyapunov stability analysis. Finally, a two-link manipulator model has been given as an example, and the numerical simulations are given to express the availability of the proposed controller.

Adaptive dynamic surface control of MIMO nonlinear systems: A hybrid event triggering mechanism

SummaryThis paper addresses the event‐triggered stabilization control for multi‐input and multi‐output (MIMO) nonlinear systems. To handle the “explosion of complexity”, the dynamic surface control (DSC) technology is introduced to the proposed control scheme. In addition, the event‐driven idea is adopted to mitigate the data transmission pressure in sensor‐to‐controller and controller‐to‐actuator channels. Considering that the non‐derivable virtual controllers are commonly constructed in the event‐triggered control schemes aiming at saving dual‐channel resources, in this paper, a hybrid event‐triggering mechanism with multiple event detectors is developed to obtain differentiable virtual control signals, thereby providing a suitable application environment for the DSC technology. Meanwhile, an output‐based adaptive threshold is designed to obtain more communication benefits compared with the fixed threshold strategy. Finally, all signals in the closed‐loop system are ensured to be bounded under a standard Lyapunov stability analysis framework, and the effectiveness of the proposed control scheme is validated by a simulation example.

Adaptive Finite-Time Fuzzy Control for Uncertain Nonlinear Systems with Asymmetric Full-State Constraints

This paper studies the adaptive finite-time fuzzy control issue associated with uncertain nonlinear systems that exhibit asymmetric constraints on the full state. A distinct function, constrained by nonlinear states, is designed to mitigate the excessive breach of these full-state boundaries. Unlike the standard barrier Lyapunov function (BLF) method, this approach solves symmetric and asymmetric full-state constraints without modifying the controller structure, and it does not require any additional assumptions about virtual control to be met. Simultaneously employing approximating functions using fuzzy logic systems and incorporating dynamic surface control technology integrated with a first-order filter, the unknown nonlinear functions emanating from the suggested controller strategy are estimated. Additionally, this approach addresses the prevalent problem of complexity explosion observed in conventional backstepping techniques. An adaptive finite-time fuzzy tracking control strategy is introduced, ensuring that all signals and tracking errors of the controlled system remain bounded in finite time. Finally, two simulation examples are given to illustrate the effectiveness of the proposed control scheme, confirming that all states remain within the predefined regions.

Adaptive neural optimal tracking control of stochastic nonstrict-feedback nonlinear systems with output constraints

In this article, a novel adaptive optimal control method is proposed for constrained stochastic nonlinear systems in the form of nonstrict-feedback. The output constraints are handled by employing nonlinear mapping, and the controller is composed of feedforward and optimal parts. The feedforward controller is designed based on dynamic surface control technology with Gaussian properties, where a dynamic signal and linearly parametrized neural networks are employed to approximate the unknown dynamics and unavailable nonlinear functions, respectively. Using the mean value theorem and Young’s inequality, only one parameter must be online tweaked at each step. In the optimal part, the cost function is approximately obtained using adaptive dynamic programming for the optimal control law. All signals in the closed-loop systems are analytically proved to be semi-globally uniformly ultimately bounded in the probabilistic space. Numerical simulations are provided to verify the effectiveness of the proposed approach.

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.

Distributed convex optimization of higher order nonlinear uncertain multi-agent systems with switched parameters and topologies

This paper investigates the distributed optimization problem for a class of nonlinear uncertain multi-agent systems with unmeasured states, switched parameters, and directed communication topologies changing in the control process. To achieve the goal of optimizing the global objective function, a penalty function is constructed through making up of a sum of local objective functions and integrating consensus conditions of the multi-agent systems to utilize local and neighboring information. Radial basis function neural-networks and neural-networks state observer are applied to approximate the unknown nonlinear functions and obtain the unmeasured states, respectively. To avoid “explosion of complexity” and obtain derivatives for virtual control functions continuously, dynamic surface control technology is proposed to develop a distributed adaptive backstepping neural network control protocol to ensure that all the agents’ outputs asymptotically reach consensus to the optimal solution of the global objective function. Simulations demonstrate the effectiveness of the proposed control scheme.

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.

Fixed-time self-structuring neural network fault-tolerant tracking control of underactuated surface vessels with state constraints

In this paper, a fixed-time fault-tolerant control strategy is proposed for trajectory tracking of underactuated surface vessels (USVs) with input saturation. A predefined region boundary function is proposed, which has all predefined fixed-time convergence properties and provides predefined specifications for tracking errors. To achieve the predetermined tracking performance, a fixed-time adaptive neural network state constrained fault-tolerant controller is proposed based on dynamic surface control technology, a back-stepping program, and an asymmetric time-varying tangent barrier Lyapunov function (ATVTBLF). The unknown external environment disturbances and complex continuous unknown nonlinear terms are approximated by a self-structuring neural network (SSNN), which can improve the robustness of the control system to unknown parameters and guarantee the tracking performance of the control system. The number of neurons of the SSNN can be adjusted online according to the approximation efficiency, which can reduce the amount of calculation of the control system. Based on Lyapunov stability theory, it is proven that the closed-loop system is bounded and stable in a fixed time, and the tracking error is always kept within the constraint range. The simulation results show that the underactuated surface vessel control system has good tracking performance.

FTC Design for Switched Fractional-Order Nonlinear Systems: An Application in a Permanent Magnet Synchronous Motor System.

In this article, an adaptive fault-tolerant control (FTC) method and a fractional-order dynamic surface control (DSC) algorithm are jointly proposed to deal with the stabilization problem for a class of multiple-input-multiple-output (MIMO) switched fractional-order nonlinear systems with actuator faults and arbitrary switching. In each MIMO subsystem and each switched subsystem, the neural networks (NNs) are utilized to identify the complicated unknown nonlinearities. A fractional filter DSC technology is adopted to conquer the issue of "explosion of complexity," which may occur when some functions are repeatedly derived. The common Lyapunov function method is used to restrain arbitrary switching problems in the system, and the actuator compensation technique is introduced to tackle the failure faults and bias faults in the actuators. By combining the backstepping DSC design technique and fractional-order stability theory, a novel NN adaptive switching FTC algorithm is proposed. Under the operation of the proposed algorithm, the stability and control performance of the fractional-order systems can be guaranteed. Finally, a simulation example of a permanent magnet synchronous motor (PMSM) system reveals the feasibility and effectiveness of the developed scheme.

Adaptive fuzzy fixed-time dynamic surface control for stochastic nonstrict nonlinear systems with unknown dead-zones

This paper focuses on an adaptive fuzzy fixed-time control problem for stochastic nonstrict nonlinear systems with unknown dead-zones by using dynamic surface control (DSC) technology. Fuzzy logic systems (FLSs) and DSC technology are used to approximate nonlinear functions and reduce the computational complexity, respectively. At the same time, the influence of the dead-zone disturbance is offset by transforming the dead-zone model into the nonlinear model that can be approximated by the FLSs. Then, based on the fixed-time stability theory, an adaptive fuzzy fixed-time tracking control strategy is proposed, which can ensure semi-global practical fixed-time stability of the system and the tracking error converging to a small neighborhood near the origin. Finally, two simulation examples are given to prove the effectiveness of the proposed control strategy.

An Event-Triggered Predefined Time Decentralized Output Feedback Fuzzy Adaptive Control Method for Interconnected Systems

This article investigates the event-triggered predefined time output feedback control design problem for nonlinear interconnected systems with nonstrict feedback control structures. Compared with the existing event-triggered output feedback control design schemes, the most significant contribution of this article is that the system stability time can be preset directly. Fuzzy logic systems (FLSs) and FLSs-based state observer deal with unknown nonlinear dynamics and unmeasured states. Combining with dynamic surface control technology and event-triggered mechanism based on switching threshold strategy, an event-triggered predefined time decentralized output feedback control method is proposed, in which a predefined time filter is designed to solve the computational complexity problem. In addition, the algebraic loop problem and control singular problem are also solved, respectively, by applying the property of fuzzy basis function and L’Hospital’s rule. Utilizing the predefined time Lyapunov stability theory, the system stability analysis is given. Finally, the effectiveness and practicability of the proposed control method are verified by practical system simulation cases.

Ship Collision Avoidance Based on the Vulnerability Assessment for Small Vessels in Bad Weather

In the conditions of bad weather, the small vessels maneuvering ability of collision avoidance is seriously reduced and the vulnerability to maritime accidents increases due to the influence of strong wind and wave. This paper proposes a collision avoidance decision-making and control method for small vessels using the integrated collision risk assessment based on fuzzy logic. First, the speed of wind and height of wave in the bad weather conditions are fuzzified. Then, the collision risk indices are selected for fuzzy inference to get the basic collision risk which will be integrated with the vulnerability to collision accidents and it helps to improve the accuracy of collision risk assessment. According to the current multi-ships encounter situations, the similar cases are retrieved from the case database, and the collision avoidance decision is given after fuzzy adjustments. To implement collision avoidance actions, a fuzzy algorithm for nonlinear ship heading dynamic surface control (DSC) control considering input saturation and uncertainties is designed. The problem of "computational expansion" that may occur in high-order systems is avoided by using DSC technology. Finally, simulation experiments are implemented to verify the effectiveness of the collision avoidance method.

Neural adaptive dynamic event‐triggered practical fixed‐time dynamic surface control for non‐strict feedback nonlinear systems

SummaryIn this article, a dynamic surface practical fixed‐time control scheme is proposed based on dynamic event‐triggered mechanism for a class of non‐strict feedback systems. Dynamic surface control (DSC) technology was introduced to solve computational complexity problems. Dynamic triggering technology is implemented to solve the problem of transmitting data burden. Dynamic triggers have fewer triggers than static triggers. Nonlinear filters are introduced to combine DSC technology with fixed‐time adaptive control technology. Theoretical analysis shows that all signals in the closed‐loop system are bounded at a fixed time. Finally, two numerical simulation examples are given to prove the feasibility of the proposed method.

Distributed Optimization for Fractional-Order Multi-Agent Systems Based on Adaptive Backstepping Dynamic Surface Control Technology

In this article, the distributed optimization problem is studied for a class of fractional-order nonlinear uncertain multi-agent systems (MASs) with unmeasured states. Each agent is represented through a system with unknown nonlinearities, unmeasurable states and a local objective function described by a quadratic polynomial function. A penalty function is constructed by a sum of local objective functions and integrating consensus conditions of the MASs. Radial basis function Neural-networks (RBFNNs) and Neural networks (NN) state observer are applied to approximate the unknown nonlinear dynamics and estimate unmeasured states, respectively. By combining the NN state observer and the penalty function, and the stability theory of the Lyapunov function, the distributed observer-based adaptive optimized backstepping dynamic surface control protocol is proposed to ensure the outputs of all agents asymptotically reach consensus to the optimal solution of the global objective function. Simulations demonstrate the effectiveness of the proposed control scheme.

Prescribed performance dynamic surface fuzzy control for strict‐feedback nonlinear system with actuator fault

In this paper, an adaptive fuzzy control scheme for strict-feedback nonlinear system with finite-time prescribed performance and actuator fault is studied. First, we consider a prescribed performance function that enables the tracking error to converge within a preset interval in a finite time. Subsequently, the fuzzy logic system and dynamic surface control technology are embedded in the backstepping design process, and the purpose of the dynamic surface control technique is to settle the problem of computational explosion when processing the backstepping design. The fuzzy logic system is used to approximate the unknown functions that appear in the system. Finally, a new controller is designed in combination with an updated law which ensures that all the signals in the closed-loop is bounded. Two simulation examples are taken to illustrate the feasibility of the presented control scheme.

Command filter and dynamic surface control technology based adaptive optimal control of uncertain nonlinear systems in strict‐feedback form

AbstractIn this article, the problem of command filter and event‐triggered mechanism based adaptive neural optimal control is discussed for a class of nonlinear systems in the presence of unmodeled dynamics in strict‐feedback form. The overall controller design is composed of feedforward controller and feedback controller as well as event‐triggered controller design. In the first part, the feedforward controller is constructed by exploiting command filter and introducing the compensation error, and the first‐order filter in the classical dynamic surface control technology is replaced by utilizing the second‐order filter. In the second part, adaptive dynamic programming algorithm is used to estimate the unknown optimal index function and optimal control signal by the aid of the capability of neural networks. In the third part, based on the feedforward and feedback controllers, an adaptive event‐triggered control is developed to avoid the occurrence of Zeno behavior. All the signals in the controlled system are proved to be semi‐globally uniformly ultimately bounded through theoretical analysis. Two numerical examples are employed to verify the availability of the proposed method.

Trajectory Control Algorithm of Flexible Joint Manipulator Based on Random Matrix and Screw Theory

Flexible articulated manipulators are often used for the task of tracking reference trajectories in space and have attracted much attention. Aiming at the uncertainty of the robot system, based on random matrix and screw theory, this paper constructs a trajectory control model of a flexible joint manipulator. In order to reduce the steady-state tracking error, a random matrix variable structure control method is introduced into the model, and a nonlinear spinor-like random matrix function is designed to improve the traditional random matrix surface. In the simulation process, the dynamic model of the series robot is firstly obtained according to the screw and random matrix equation, and the dynamic characteristics are analyzed. Combined with dynamic surface control technology, a neural network controller is designed to solve the problem of dimensional explosion and ensure that the tracking error converges to a small neighborhood of zero. The experimental results show that by using the observation value to replace the unmeasurable state of the system, combining it with the random matrix network to identify the unknown dynamics of the system, and designing the random matrix network controller, the tracking control of the system can be realized, and the tracking error can be ensured to converge to a small neighborhood of zero. The control system has a better control effect than traditional PID, the peak time is shortened by 45.83%, the adjustment time is shortened by 46.91%, the maximum overshoot is reduced by 51.35%, and the steady-state error after filtering is only 0.049, which is reduced by 47.31%. Effective interference signal and measurement noise are suppressed, and the quantitative observation performance of the flexible joint manipulator system is improved.

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.