Dynamic Surface Control Method Research Articles

Event-Triggered Adaptive Bipartite Containment Control for Stochastic Multiagent Systems

In this article, the adaptive bipartite containment control problem is investigated for stochastic nonlinear multiagent systems (MASs) with an event-triggered mechanism. It is known that the dynamic surface control method suffers from the mismatch between the virtual controller and the filter output. To address this issue, a novel error compensator is designed. Meanwhile, motivated by their universal approximation capability, fuzzy-logic systems (FLSs) are employed to identify the plants’ unknown nonlinear characteristics. To reduce the communication overhead, a distributed event-triggered control scheme is designed based on an estimate of unknown gain sign’s reciprocal. Leveraging the stochastic Lyapunov stability theory and backstepping design technique, it is proved that 1) the output responses of followers converge to a convex hull formed by those of the leaders and their symmetric ones; 2) all signals in the closed-loop system are semiglobally uniformly ultimately bounded in probability (SGUUBP); and 3) there is no Zeno behavior. Finally, simulation results are presented to illustrate the effectiveness of the proposed method.

Neural Network Based Adaptive Event-Triggered Control for Quadrotor Unmanned Aircraft Robotics

With the aim of addressing the problem of the trajectory tracking control of quadrotor unmanned aircraft robots (UARs), in this study, we developed a neural network and event-triggering mechanism-based adaptive control scheme for a quadrotor UAR control system. The main technologies included this scheme are as follows. (1) Under the condition that only the quadrotor’s position information can be obtained, a modified high-gain state observer-based adaptive dynamic surface control (DSC) method was applied and the tracking control of quadrotor UARs was acquired. (2) An event-triggered mechanism for UARs was designed, in which the energy consumption was greatly reduced and the communication efficiency between the system and the control terminal was improved. (3) By selecting appropriate parameters, appropriate initial conditions for the adaptive laws, and establishing a high-gain state observer, a tracking performance of L∞ could be achieved. Finally, simulation results of the hardware-in-loop strategy are presented. The control method we propose here outperformed the traditional backstepping sliding mode control (BSMC) scheme.

Resilient anti-disturbance dynamic surface control of uncertain strict-feedback systems subject to partial loss of actuator effectiveness

This paper is concerned with the tracking control of a class of uncertain strict-feedback systems subject to partial loss of actuator effectiveness, in addition to uncertain model dynamics and unknown disturbances. A resilient anti-disturbance dynamic surface control method is proposed to achieve stable tracking regardless of partial actuator faults. First, data-driven adaptive extended state observers are designed based on memory-based identifiers, such that the uncertain model dynamics, external disturbances and the unknown input gains due to actuator faults can be estimated. Next, a resilient anti-disturbance dynamic surface controller is developed based on recovered information from the data-driven adaptive extended state observers. After that, it is proven that the cascade system formed by the observer and controller is input-to-state stable. Finally, comparative studies are performed to validate the efficacy of the resilient anti-disturbance dynamic surface control method for nonlinear strict-feedback systems subject to partial loss of actuator effectiveness.

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.

Adaptive Neural Tracking Control for Nonstrict-Feedback Nonlinear Systems with Unknown Control Gains via Dynamic Surface Control Method

This paper addresses the tracking control problem of nonstrict-feedback systems with unknown control gains. The dynamic surface control method, Nussbaum gain function control technique, and radial basis function neural network are applied for the design of virtual control laws, and adaptive control laws. Then, an adaptive neural tracking control law is proposed in the last step. By using the dynamic surface control method, the “explosion of complexity” problem of conventional backstepping is avoided. Based on the application of the Nussbaum gain function control technique, the unknown control gain problem is well solved. With the help of the radial basis function neural network, the unknown nonlinear dynamics are approximated. Furthermore, through Lyapunov stability analysis, it is proved that the proposed control law can guarantee that all signals in the closed-loop system are bounded and the tracking error can converge to an arbitrarily small domain of zero by adjusting the design parameters. Finally, two examples are provided to illustrate the effectiveness of the proposed control law.

Prescribed Performance Guidance Law with Multiple Constraints

In the terminal guidance phase of intercepting aerial target, a guidance law, satisfying impact angle constraint, acceleration constraint, and second-order dynamic characteristic of interceptor autopilot, is designed based on the prescribed performance control and dynamic surface control method. Firstly, a two-dimensional plane interception model considering the dynamic characteristics of autopilot and input constraints is established. Furthermore, for the nonconstrained system, based on the dynamic surface control, the prescribed performance reaching law is used to ensure that the line-of-sight angle and the line-of-sight angle rate can converge to the prescribed range in finite time. At the same time, an adaptive law is used to estimate the uncertainty caused by target maneuver and autopilot. Then, aiming at the acceleration constraint, an auxiliary system is established to convert the restricted system into a nonrestricted system. The finite-time convergence of the terminal line-of-sight tracking error, the line-of-sight rate, and the uniform ultimate boundedness of the system are rigorously proved by Lyapunov stability theory. Finally, the simulation results show that the proposed guidance law can make the interceptor have better interception performance when attacking targets with different maneuvering forms.

Prescribed performance dynamic surface control for nonlinear systems subject to partial and full state constraints

This paper discusses prescribed performance dynamic surface control (DSC) problems for nonlinear systems subject to state constraints. Incorporating the prescribed performance control (PPC) with DSC methods, we present a neural adaptive control method that characterizes the steady-state tracking error and its convergence rate. By constructing a type of funnel error variables, the error variables can be limited in the boundary of funnel functions, and the violations of the conditions of partial and full state constraints are shunned. In the latter case, a new assumption is proposed to handle the circular design problem in the design procedure. Under the control scheme designed, the considered nonlinear systems can be stabilized with the Lyapunov stability theory, and it can be guaranteed that all variables are semi-globally uniformly ultimately bounded (SGUUB). Finally, simulation results verify that the proposed prescribed performance DSC-based control scheme can ensure stability and prescribed performance metrics in the existence of partial and full-state constraints.

Command filter‐based adaptive neural event‐triggered control of MIMO pure‐feedback systems with full‐state time‐varying constraints

SummaryThis article is concerned with the issue of adaptive event‐triggered control for a class of pure‐feedback multi‐input multi‐output (MIMO) nonlinear systems with full‐state time‐varying constraints. By using the hyperbolic tangent as nonlinear mapping technique, the uncertain constrained MIMO non‐affine system is changed into a novel unconstrained MIMO system. Dynamic surface control (DSC) strategy is used to solve the issue of “explosion of complexity.” Command filter is adopted to overcome the insufficient of the DSC method by the error compensation mechanism. Adaptive event‐triggered control scheme is developed for the transformed non‐affine system based on relative threshold mechanism. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions. All the signals in the controlled system are proved to be semi‐globally uniformly ultimately bounded by adding to compensation signals into the whole Lyapunov function. Two simulation examples demonstrate the capability of the proposed control strategy.

Observer‐based distributed fault‐tolerant containment control for stochastic nonlinear multi‐agent systems with asymmetric hysteretic quantization

AbstractThis article investigates the distributed containment control problem for high‐order stochastic nonstrict‐feedback nonlinear multi‐agent systems. To overcome the difficulty of unknown control input gain caused by the asymmetric hysteretic quantization and actuator fault, the properties of Nussbaum function are employed and an auxiliary virtual controller is designed, which does not need to estimate the bounds of the parameters of asymmetric hysteretic quantizer and efficiency factors. Moreover, the unknown terms are estimated by introducing the radial basis function neural networks. Based on the input‐driven filter, an adaptive containment control scheme is designed by using the Nussbaum function technique, the backstepping approach, and the dynamic surface control method. It is shown that the proposed control method can guarantee that all the signals are semi‐globally uniformly ultimately bounded, and the containment control performance can be achieved. Finally, some simulation results are presented to illustrate the effectiveness of the proposed approach.

Decentralized adaptive output feedback dynamic surface control for stochastic nonstrict‐feedback interconnected nonlinear systems with actuator failures and input quantization via command filter

AbstractIn this article, a new decentralized adaptive neural output feedback control scheme based on first‐order command filter is proposed for stochastic nonstrict‐feedback interconnected systems with prescribed performance, input quantization, actuator failures and unmodeled dynamics. The unknown smooth functions are eliminated by using the radial basis function neural networks. The immeasurable states in the system are estimated using the decentralized K‐filters, unmodeled dynamics is processed using dynamic signal, and the hyperbolic tangent function is applied to the construction of the prescribed performance function. The hysteretic quantizer and actuator failure are denoted in the form of linearization, and a smoothing function is introduced to compensate for the effects of quantization and bounded stuck faults. Based on the dynamic surface control (DSC) method and using the properties of Gaussian function to deal with stochastic nonstrict‐feedback interconnected systems, the first‐order command filter is used to replace the first‐order filter in the traditional DSC to eliminate the influence of filtering error on the systems, and an error compensation signal is introduced at the recursive each step of the design to construct a new error dynamic surface, which simplifies the derivation process and the design of the controller. Finally, the Lyapunov method is used to prove that all the signals in the whole controlled system are semiglobally uniformly ultimately bounded in probability and the tracking error is within the time‐varying constraint. The effectiveness of the proposed decentralized adaptive control method is verified by a numerical simulation and an example simulation.

Dynamic Surface Control with High-Order LESO Compensation for Near-Space Vehicle

Aimed at the flight control problem of a near-space vehicle (NSV) with uncertainties such as parameter perturbation and external disturbance, a novel dynamic surface control (DSC) method with high-order linear extended state observer (HLESO) compensation is proposed in this paper. In the proposed method, a tracking differentiator (TD) based on an inverse hyperbolic sine function is firstly designed, and the convergence of TD is also analysed with the Lyapunov stability theory. Furthermore, the numerical simulations are detailed to demonstrate the superiority of the proposed TD compared with others. Then, a dynamic surface controller based on the traditional backstepping control technique is designed, where the TD is adopted to obtain the differential signal of the virtual control law, in order to solve the “differential expansion,” and the HLESO is adopted to accurately estimate the “lumped disturbance” so as to realize the dynamic compensation of the controller and enhance the disturbance suppression ability of the system. The simulation results demonstrate the validity of the proposed method.

Variable Structure Disturbance Observer Based Dynamic Surface Control of Electrohydraulic Systems with Parametric Uncertainty

This paper focuses on the position tracking control issue of electrohydraulic systems (EHS). The dynamical model of EHS is introduced in the first place, based on which a type of Variable Structure Disturbance Observer (VSDO) is constructed for EHS to estimate the parametric uncertainty the EHS possesses. Then, a backstepping controller is designed under VSDO to realize the high precision position tracking purpose. To avoid the phenomenon of differential explosion, a dynamic surface control method is adopted in this paper, which improved the position tracking control performance of EHS. The proposed theoretical results are verified by numerical simulation and experiment to illustrate the feasibility.

High‐gain observer‐based adaptive fuzzy finite‐time prescribed performance tracking control for linear stepping motor with event‐triggered strategy

AbstractThis paper considers the tracking problem of linear stepping motor system with unmeasurable states, and a finite‐time prescribed performance controller is designed with dynamic surface control scheme and event‐triggered strategy. In the adaptive backstepping recursive design, fuzzy logic system is used to approximate the nonlinear function, and a high‐gain observer is introduced to estimate the unmeasured states. A finite‐time performance function is developed to improve the transient and transient performance of the system, and a relative threshold event‐triggered strategy is proposed to reduce the communication burden. In addition, the inherent complexity explosion problem of the backstepping process is solved by the dynamic surface control method. Finally, the simulation results prove the effectiveness of the scheme.

Neural-networks-based adaptive asymptotic tracking control of MIMO stochastic non-strict-feedback nonlinear systems with full state constraints and unknown control gains

The neural-networks-based adaptive asymptotic tracking control problem is considered for a class of multiple input multiple output (MIMO) stochastic non-strict-feedback nonlinear systems with unknown control gains and full state constraints. Firstly, barrier Lyapunov functions (BLFs) are designed to avoid the violation of the state constraints, the dynamic surface control (DSC) method is adopted to ensure the computation burden is greatly reduced, and the introduced auxiliary virtual controllers solve the design obstacle arised from unknown control gains. Then, by introducing a specific gain suppression inequality, a new adaptive asymptotic tracking control scheme is proposed and its correctness and validity are rigorously proved, which can not only effectively guarantee that all the signals of the closed-loop system are bounded in probability, but also makes the tracking error converge to zero in the fourth moment. At the same time, the impact of the full state constraints on the system performance is also tackled. Finally, the feasibility and practicability of the proposed control scheme are verified by the simulation results.

Finite-time fuzzy dynamic surface control for permanent magnet synchronous motor stochastic systems with input constraint and load disturbance

In this paper, a finite-time adaptive fuzzy dynamic surface control (DSC) method is proposed for the position tracking control of permanent magnet synchronous motors (PMSMs) stochastic nonlinear system with input constraint and load disturbance. First, the stochastic disturbance of PMSMs is considered in operation, and the fuzzy control method is applied to cope with the stochastic nonlinear function in the motor model. Second, the DSC technique is applied to avoid the “explosion of complexity” in the backstepping design. Moreover, the finite-time control is applied to the stochastic nonlinear system of PMSMs to improve the convergence speed of the system, tracking accuracy, and anti-interference ability. Conclusive, simulation results are given to verify the method that can achieve fast tracking of the desired signal.

Appointed-Time Prescribed Performance Fault Tolerant Control for QUAV With Actuator Fault and Model Parameters Uncertainties

In this paper, an appointed-time prescribed performance fault-tolerant control (ATPPFTC) method for quadrotor unmanned aerial vehicle (QUAV) system is studied in the presence of model parameters uncertainties, actuator faults and external disturbances. For the position loop and the attitude loop, the proposed method overcomes the model parameters uncertainties caused by the changes of rotary inertia, the mass and aerodynamic damping coefficients. Meanwhile, unknown actuator faults and unknown external disturbances are investigated by using adaptive method. Moreover, a new appointed-time prescribed performance function and coordinate transformation are introduced to impose performance characteristics on the tracking errors. Based on the Lyapunov stability theory, an adaptive dynamic surface control method is proposed to ensure that the position and attitude tracking errors of the closed-loop system can achieve the appointed-time convergence and prescribed transient and steady-state performance. Incidentally, the convergence speed and convergence time of the system tracking error can be set flexibly. Finally, the simulation verifies the effectiveness and superiority of the proposed control scheme from both qualitative and quantitative aspects.

Adaptive Asymptotic Regulation for Uncertain Nonlinear Stochastic Systems with Time-Varying Delays

In this paper, for a class of uncertain stochastic nonlinear systems with input time-varying delays, an adaptive neural dynamic surface control (DSC) method is proposed. To approximate the unknown continuous functions online, the neural network approximation technique was applied, and based on the DSC scheme, the desired controller was constructed. A compensation system is presented to compensate for the effect of the input delay. The Lyapunov–Krasovskii functionals (LKFs) were employed to compensate for the effect of the state delay. Compared with the existing works, based on using the DSC scheme with the nonlinear filter and stochastic Barbalat’s lemma, the asymptotic regulation performance of this closed-loop system can be guaranteed under the developed controller. To certify the availability for the designed control method, some simulation results are presented.

Prescribed Performance Control with Sliding-Mode Dynamic Surface for a Glue Pump Motor Based on Extended State Observers

The actuator of a particleboard glue-dosing system, the glue pump motor, is affected by external disturbances and unknown uncertainty. In order to achieve accurate glue-flow tracking, in this paper, a glue pump motor compound control method was designed. First, the prescribed performance control method is used to improve the transient behaviors, and the error of the glue flow tracking is guaranteed to converge to a preset range, as a result of the design of an appropriate performance function. Second, two extended state observers were designed to estimate the state vector and the disturbance, in order to improve the robustness of the controlled system. To further strengthen the steady-state performance of the system, the sliding-mode dynamic surface control method was introduced to compensate for uncertainties and disturbances. Finally, a Lyapunov stability analysis was conducted, in order to prove that all of the signals are bounded in a closed-loop system, and the effectiveness and feasibility of the proposed method were verified through numerical simulation.

Distributed adaptive fault-tolerant supervisory control for leader-following systems with actuator faults

This paper investigates an adaptive cooperative fault-tolerant supervisory control problem for nonlinear strict-feedback leader-following systems with unknown control coefficients and actuator faults under the fixed directed graph. Radial basis function neural networks are used to approximate system uncertainties. The Nussbaum gain technique is introduced to address unknown signs of control gains. Then, based on the dynamic surface control method, a distributed adaptive fault-tolerant control scheme is presented to compensate for the actuator faults of followers. For neural networks approximation theory, the unknown smooth function can only be approximated on a compact set due to the approximation errors. By theoretic analysis, the supervisory-based adaptive controllers are proposed to guarantee that system state signals can converge to compact sets and the leader-following systems can achieve the practical output consensus. Finally, the simulation results are provided to show the validity of the proposed consensus scheme.

Adaptive fuzzy finite‐time decentralized control for large‐scale stochastic nonlinear systems

SummaryAn adaptive finite‐time decentralized control algorithm for a class of large‐scale stochastic nonlinear systems is presented. The fuzzy logic system is used to estimate uncertain nonlinearities. One advantage of the developed scheme is that each subsystem only needs to update one adaptive parameter, which alleviates the burden of online estimation. The dynamic surface control method is employed to reduce the “complexity explosion” caused by the repetitive derivation of the intermediate variable function in the backstepping control scheme. A new decentralized controller is designed so that all signals of the controlled system are bounded and the tracking error converges to a small residual set around the origin within a finite time. The simulation results of a numerical example illustrate the effectiveness of the method.