Dynamic Surface Control Method Research Articles

Position constrained adaptive time-varying formation control of autonomous surface vessels with uncertain dynamics

This paper investigates the adaptive time-varying formation control problem of autonomous surface vessels (ASVs) with position constraints, uncertain dynamics and external disturbances under directed communication topology. Different from the existing studies, the nonlinear error transformation function is combined with formation control to achieve position constraints of ASVs. Based on dynamic surface control and backstepping method, a virtual control law is designed for each vessel. Radial basis function neural networks are employed to approximate the unknown nonlinear continuous function caused by ASVs’ model uncertainties, and the minimum learning parameter (MLP) method is applied to reduce computational complexity. Then, a time-varying formation position constrained controller and an adaptive law are proposed for each ASV. By using the Lyapunov stability theory, it is proved that all signals of the closed-loop ASV system are semi-global uniformly ultimately bounded and the position constrained objective can be achieved. Finally, simulation analyses are given to verify the effectiveness of theoretical results.

Adaptive neural dynamic surface control for nonstrict feedback systems with state delays

AbstractThis article focuses on a class of nonstrict feedback systems with input delay, state delays and time‐varying full‐state constraints by proposing an adaptive neural control scheme. To overcome the problems of all state variables effected by time‐varying constraints, the asymmetric time‐varying barrier Lyapunov functions are constructed. The influence of state delays and input delay is eliminated by employing suitable Lyapunov–Krasovskii functionals. Additionally, the process of controller design is based on backstepping method and the unknown functions can be approximated by radial basis function neural networks. Moreover, the problem of repeated differentiations for nonlinear components during controller design is hugely simplified by taking advantage of the dynamic surface control method. The boundness of all the closed‐loop signals can be ensured by the designed controller. Finally, two numerical simulations illustrate that the proposed adaptive neural control scheme is effective.

Active suspension hierarchical control with parameter uncertainty and external disturbance of electro-hydraulic actuators

In order to improve the ride comfort and handling stability of the electro-hydraulic active suspension system, a hierarchical control strategy is proposed. For the active suspension system with body mass uncertainty and safety constraints, an enhanced constraint adaptive backstepping controller is designed to generate the target force of body vertical motion. When dealing with constraints, nonlinear filters are introduced, backstepping technology and quadratic Lyapunov function are used to combine the control target and domain constraints, and the vertical displacement of the body and the suspension deflection control index are synthesized into a single controlled variable, so that the control variable converging to zero meets the suspension dynamic displacement limit. The ride comfort and safety of the active suspension system are improved. Secondly, stability analysis is conducted on the zero dynamic error system to ensure that all safety performance indicators are bounded. The effects of external disturbances, parameter uncertainties and modelling errors on the force tracking accuracy of asymmetric cylinder electrohydraulic systems are addressed. A backstepping dynamic surface control method based on a nonlinear perturbation observer is proposed, which estimates the composite perturbation terms such as modelling error and external perturbation, and uses the estimated value of the nonlinear observer to design a feedforward compensating control term to offset the effect of the composite perturbation on the system performance. In addition, the dynamic surface control method is used to calculate the derivative of the target force input, which avoids the derivative explosion phenomenon and reduces the computational complexity of the system. Simulation test results show that this method reduces the computational complexity of the system and improves the control performance. And under random and bumpy road conditions, the root-mean-square value of sprung mass acceleration performance index is reduced by 48.354 % and 72.677 % compared with passive suspension, which improves the ride comfort of the vehicle.

Distributed adaptive finite-time output feedback containment control for nonstrict-feedback stochastic multi-agent systems via command filters

In this paper, distributed adaptive finite-time output feedback containment control based on command filters is proposed for nonstrict-feedback stochastic multi-agent systems (SMASs) with unmodeled dynamics, input quantization and prescribed performance. The unknown states are estimated using a high-gain observer, the unmodeled dynamics is handled by introducing a measurable dynamic signal, and the input signal is processed using an integrated quantizer that combines the advantages of uniform quantizer and hysteretic quantizer. The hyperbolic tangent function and time-varying function are applied to construct the performance function, and the constrained containment error is transformed into an unconstrained system through nonlinear mapping (NM). Unknown smooth functions are handled with the superb approximation capability of radial basis function neural networks (RBFNNs). Based on stochastic finite-time theory and dynamic surface control (DSC) method, nonlinear command filters are introduced to reduce the use of black-box functions and simplify the controller design. Finally, the theoretical analysis and two sets of experimental results demonstrate that all signals in the controlled system are semi-global finite-time stability in probability (SGFSP) and the designed controller works well.

Neural adaptive dynamic surface control for position tracking of electrohydraulic servo systems based on extended state observer

High-performance motion tracking of electro-hydraulic servo systems plays an important role in developing industrial technology. However, the system itself has parameter uncertainty, uncertain nonlinearity, and measurement noise, significantly decreasing the performance of conventional controllers designed based on nominal models. To improve the tracking performance of electro-hydraulic servo systems, an adaptive dynamic surface control method combining extended state observer and radial basis function neural network is proposed. Firstly, an extended state observer combining neural network output and parameter adaptation technology is designed without the need for speed and pressure feedback to observe the system’s unknown state variables and nonlinear matched disturbance. The design of neural networks is used to approximate mismatched disturbance with significant nonlinearity online. Then, the proposed extended state observer is introduced into the neural adaptive backstepping design, effectively compensating for simultaneous matched and mismatched disturbances, thereby suppressing most of the uncertain nonlinearity of the system. Meanwhile, online update of uncertain parameters further improves the tracking performance of the controller. In addition, the introduction of dynamic surface overcomes the “explosion of complexity” issue in backstepping design. The rigorous stability of the closed-loop system is proved by the Lyapunov stability theory. Finally, the effectiveness of the proposed controller is validated through comparative experiments on valve-controlled hydraulic cylinder.

Adaptive command filtered control for a class of nonlinear time delay systems with extreme learning machine

AbstractIn this paper, an extreme learning machine (ELM)‐based adaptive command filtered control method is investigated for a class of strict feedback nonlinear systems with unknown external disturbances and time delay. To begin with, the original system state equation is transformed into a new form on account of coordinate transformation. Subsequently, an ELM is adopted to approximate unknown functions which exist in the whole system states, without any prior knowledges of the ideal weight vectors and approximation errors. Secondly, a command filter is developed for the system under consideration, which can avoid the probem of “explosion of complexity” caused by repeated derivation of virtual control signals in traditional backstepping control. Meanwhile, error compensation signals are designed to conquer the shortcoming of a dynamic surface control (DSC) method. The combination of ELM and command filter technique has been used to construct corresponding controllers and adaptive laws. Effective handling of the impact of time delay terms is ensured through designing a novel Lyapunov–Krasovskii functional. The proposed strategy guarantees boundedness of all signals in the closed‐loop system and the tracking error asymptotically converges to a compact set around the origin. In the end, two continuous stirred tank reactors (CSTRs) are taken as example to further verify the efficiency of the put forward control method.

Decentralized Output-Feedback Adaptive Event-Triggered Control for Interconnected Nonlinear Delay Systems with Actuator Failures

This paper investigates decentralized adaptive event-triggered fault-tolerant control for interconnected nonlinear delay systems with actuator failures. The actuator failures suffered include loss of effectiveness and bias faults. A control scheme based on the K-filter is proposed, which effectively compensates for the effects of unknown actuator failures. A hyperbolic tangent function and neural network are introduced to approximate the unknown interconnection function and nonlinear delay function. By introducing the dynamic surface control method, the “explosion of complexity” issue is addressed. Furthermore, our proposed controller can ensure that all states of the corresponding closed-loop system are semi-globally uniformly ultimately bounded and that the tracking error can converge to a small neighborhood of zero. Meanwhile, Zeno behavior can be effectively avoided. Finally, the validity of the proposed control scheme is verified using a simulation example.

Robust adaptive dynamic surface control of high-order strict feedback systems based on fully actuated system approach

In this study, the authors propose a robust adaptive dynamic surface control method by using the fully actuated system approach for high-order strict-feedback systems (SFSs) with parameter uncertainty and disturbance. Each subsystem of the SFSs is a high-order system with a full actuation structure. In contrast to the traditional first-order state space method, the proposed control method directly treats each high-order subsystem as a whole without transforming it into a first-order system, which is a concise and efficient treatment. By introducing a series of first-order low-pass filters in each step of the design, the high-order derivatives of the virtual control law are obtained, and the complex and multiple derivation operations are transformed into simple algebraic operations. Adaptive control and robust control are combined to address parameter uncertainty and external disturbances in the system. The Lyapunov stability theory is utilised to demonstrate that all signals in the closed-loop system are uniformly ultimately bounded. The system output can effectively track the desired reference signal under specific constraints, and the tracking error can be adjusted by tweaking the parameters to converge to a sufficiently small neighbourhood around zero. Ultimately, the efficiency of the proposed control method is validated through simulations on a flexible joint manipulator system.

Command filter‐based adaptive event‐triggered control for switched nonlinear systems with full state constraints

AbstractAn adaptive event‐triggered control issue based on command filter and dynamic surface control is studied for switched nonlinear systems with full state time‐varying constraints in this article. To handle state constraints, the nonlinear mapping conversion technique is used. Radial basis function neural networks (RBFNNs) are utilized to approximate unknown nonlinear continuous functions. Adaptive control algorithm is designed based on command filtered backstepping technology. Novel even triggered control is constructed for two different cases in the switching interval. Furthermore, all signals in the switched system are proved to be semi‐globally uniformly ultimate bounded (SGUUB) by the aid of dynamic surface control method under arbitrary switching. Meanwhile, all states do not violate the preset constraints and Zeno phenomenon is avoided. The validity of the presented approach is confirmed through a numerical simulation result.

Anti-deadzone adaptive fuzzy dynamic surface control for planar space robot with elastic base and flexible links

In order to combat the impact of the dead zone and reduce vibration of the space robot's elastic base and flexible links, the trajectory tracking and vibration suppression of a multi-flexible-link free-floating space robot system are addressed. First, the elastic connection between the base and the link is considered as a linear spring. Then the assumed mode approach is used to derive the dynamic model of the flexible system. Secondly, a slow subsystem characterizing the rigid motion and a fast subsystem relating to vibration of the elastic base and multiple flexible links are generated utilizing two-time scale hypotheses of singular perturbation. For the slow subsystem with a dead zone in joint input torque, a dynamic surface control method with adaptive fuzzy approximator is designed. Dynamic surface control scheme is adopted to avoid calculation expansion and to simplify calculation. The fuzzy logic function is applied to approximate uncertain terms of the dynamic equation including the dead zone errors. For the fast subsystem, an optimal linear quadratic regulator controller is used to suppress the vibration of the multiple flexible links and elastic base, ensuring the stability and tracking accuracy of the system. Lastly, the simulation results verify the effectiveness of the proposed control strategy.

Adaptive Fuzzy Fault-Tolerant Control of Uncertain Fractional-Order Nonlinear Systems with Sensor and Actuator Faults

In this work, an adaptive fuzzy backstepping fault-tolerant control (FTC) issue is tackled for uncertain fractional-order (FO) nonlinear systems with sensor and actuator faults. A fuzzy logic system is exploited to manage unknown nonlinearity. In addition, a novel FO nonlinear filter-based dynamic surface control (DSC) method is constructed, effectively avoiding the inherent complexity explosion problem in the backstepping recursive process, and in the light of the construction of auxiliary functions, compensating the coupling term introduced by faults. On account of certain assumptions, the stability criterion of the FO Lyapunov function is applied to guarantee the stability of the closed-loop system. Finally, the simulation example verifies the validity of the presented control strategy.

Observer-Based Adaptive NN Security Control for Switched Nonlinear Systems Against DoS Attacks: An ADT Approach.

In this article, a novel switched observer-based neural network (NN) adaptive control algorithm is established, which addresses the security control problem of switched nonlinear systems (SNSs) under denial-of-service (DoS) attacks. The considered SNSs are described in lower triangular form with external disturbances and unmodeled dynamics. Note that when an attack is launched in the sensor-controller channel, the controller will not receive any message, which makes the standard backstepping controller not workable. To tackle the challenge, a set of NN adaptive observers are designed under two different situations, which can switch adaptively depending on the DoS attack on/off. Further, an NN adaptive controller is constructed and the dynamic surface control method is borrowed to surmount the complexity explosion phenomenon. To eliminate double damage from DoS attacks and switches, a set of switching laws with average dwell time are designed via the multiple Lyapunov function method, which in combination with the proposed controllers, guarantees that all the signals in the closed-loop system are bounded. Finally, an illustrative example is offered to verify the availability of the proposed control algorithm.

Dynamic surface adaptive RBF neural network control for a class of non‐linear uncertain systems

AbstractAn adaptive neural network dynamic surface control method for strict feedback non‐linear systems with model uncertainty is proposed in this paper. The uncertain parts are approached by RBF neural network; meanwhile, the virtual controller is designed to make system stable according to dynamic surface control. The method of Lyapunov is used to prove the stability and convergence of the system. The simulation results prove the feasibility of this controller and prove that the controller has an advantage to approach the uncertain non‐linear system and make system have well convergence and traceability.

Attitude tracking control of hypersonic vehicle based on an improved prescribed performance dynamic surface control

AbstractIn this paper, we investigate the constrained attitude control problem of hypersonic vehicles (HVs). An improved prescribed performance dynamic surface control method is proposed based on an adaptive scaling strategy. Because of the uncertain time-varying disturbances, the controlled state may violate the constraint in the prescribed performance control (PPC) framework. An adaptive scaling strategy is introduced in the PPC method to avoid state violation. The performance function is scaled with respect to the state adaptively. Moreover, a nonlinear disturbance observer is used to compensate the sum of external and other internal disturbances of the system. The proposed method improves the system dynamic performance while ensuring the system robustness. Furthermore, the stability of the closed-loop system is proved by Lyapunov analysis. Finally, numerical simulations are implemented to verify the effectiveness of the PPC method and superiority over other methods.

High-order adaptive dynamic surface control for output-constrained non-linear systems based on fully actuated system approach

In this study, the authors propose a high-order adaptive dynamic surface control (HOADSC) method by using the fully actuated system-based approach for uncertain high-order strict-feedback systems (SFSs) with an output constraint. Each subsystem of the SFSs is a high-order system with a full actuation structure. In contrast to the traditional first-order state space method, the proposed control method directly treats each high-order subsystem as a whole without transforming it into a first-order system, which is a concise and efficient treatment. By introducing a series of first-order low-pass filters in each step of the design, the high-order derivatives of the virtual control law are obtained, and the complex and multiple derivation operations are transformed into simple algebraic operations. The Barrier Lyapunov function is combined to ensure that the output of the system satisfies the given constraints. And the Lyapunov theory is used to prove that all signals in the closed-loop system are ultimately uniformly bounded, and its output can accurately track the desired reference signal without violating the given constraints. The effectiveness of the proposed control method is verified by simulations of an actual manipulator system.

A novel adaptive coordinated tracking control scheme for a morphing aircraft with telescopic wings

Inspired by flight biology, morphing flight technology has great potential to improve the adaptability and maneuverability of aircraft. This paper is devoted to the flight control problem of morphing aircraft, and aimed at safe and fuel-saving flight through morphing actively. Specifically, the longitudinal dynamics of a morphing aircraft with telescopic wings is modelled as a strict-feedback nonlinear system. Through fitting the expression of aerodynamic parameters by the morphing ratio, the model uncertainties induced by morphing errors are embedded in the dynamics. To meet the safety and fuel-saving requirements, an Adaptive Coordinated Tracking Control Scheme (ACTCS) is then proposed, which consists of a morphing control module and a tracking control module. For the morphing control module, an on-line morphing decision model is given in an optimization process with respect to the morphing ratio, and a second-order tracking filter is introduced to smooth the decision output and ensure the physical realizability. For the tracking control module, the novel adaptive controllers for the velocity and altitude subsystems are proposed based on the dynamic surface control method, in which adaptive mechanisms are designed to compensate for the model uncertainties. Finally, the proposed ACTCS is simulated in nine different cases of the test flight mission, to verify its effectiveness, robustness and fuel-saving effect.

Adaptive neural dynamic surface control of load/grid connected voltage source inverters with LC/LCL filters

Utilizing passive filters such as L, LC and LCL is preferred to cancel out high-frequency harmonics caused by pulse width modulation of voltage source inverters. However, the LC and LCL filters have shown better harmonic attenuation than the conventional L filter. Nevertheless, the control process of LC and LCL filters is more complicated due to their higher-order dynamics. The problem gets more challenging in the presence of uncertainties such as load and grid impedance variations. To overcome these challenges, two novel adaptive neural dynamic surface controllers are proposed for LC and LCL filters in the load and grid-connected modes, respectively. Meanwhile, the issue of computational complexity inherent in the conventional backstepping method is avoided here by utilizing the dynamic surface control technique. Furthermore, the matched and unmatched uncertainties of LC/LCL filters are approximated via multi-input multi-output radial basis function neural networks. Stability of the closed-loop systems is guaranteed by converging the tracking errors to a small neighborhood of the origin. Simulations are given to illustrate the effectiveness and potential of the proposed adaptive neural dynamic surface control methods under the load and grid impedance changes.

Research on Variable-Swept Hybrid Aerial Underwater Vehicle Plunge-Diving Control Based on Adaptive Dynamic Surface Control

The variation in aerodynamic parameters during the process of a variable sweepback hybrid aerial underwater vehicle (HAUV) affects flight stability. During the air–water trans-media locomotion, there are medium mutations and solid–liquid gas coupling phenomena, resulting in the complex dynamic process of HAUV. To ensure stable control during the trans-media process of a variable sweepback vehicle, this study proposes a neural-network-based adaptive dynamic surface control method for aircraft flight-path angle. This method aims to establish an effective control model for the entire process of air to media transition, in response to the characteristics of uncertainty and external disturbances in the process of variable backsweeping in the air and media transition. By utilizing the multibody dynamics method, the dynamic equations for variable-swept vehicles are established and transformed into a rigorous feedback system with model uncertainty. The adaptive dynamic surface method in this paper introduces a first-order filter, which overcomes the “differential explosion” problem in traditional backstepping control design through differential filtering; the unknown parameters present in the model are estimated online through adaptive laws, and the uncertain parts of the system are overcome through nonlinear damping items. By analyzing Lyapunov stability, the semi-global stability of the required closed-loop system can be obtained, and adjusting the controller parameters can make the tracking error infinitely small. Numerical simulations are conducted to illustrate the tracking control of flight-path angles for different plunge-diving angle rates and strategy of ingress. The results show that HAUV with variable-swept configuration with different strategy has a great effect on the stability of plunge-diving locomotion; the designed controller can effectively track the target trajectory and has a certain degree of robustness and adaptability.

Disturbance observer-based adaptive neural control for underactuated surface vehicle with constraint of input saturation

In this paper, a robust adaptive neural control algorithm is provided to solve the problem of path-following control for underactuated surface vehicle (USV) subject to input saturation, in the presence of model uncertainties and unknown marine environmental disturbance.In the algorithm, through the application of neural network (NN), an adaptive disturbance observer (ADO) is proposed to observe the unknown disturbance, which does not need the precise information of the upper bound of the disturbance, and the model uncertainty can be appropriated simultaneously. Specially, since the ADO and control law share the same set of NN, the number of adaptive parameters of the controller can be greatly reduced. After that, dynamic surface control (DSC) method is used to avoid repeated derivative in the process of back-stepping, which solve the “calculation explosion” problem. An auxiliary system is designed to compensate errors caused by input saturation, which solve the input saturation problem of actuators. Through Lyapunov stability analysis, it is proved that all signals of the closed-loop system are semi-globally ultimately uniformly bounded (SGUUB). Finally, some experiments are conducted to demonstrate the effectiveness of the algorithm.

Adaptive dynamic programming based composite control for profile tracking with multiple constraints

A composite control method based on adaptive dynamic programming (ADP) is developed to solve the profile tracking problem of the hypersonic gliding vehicle (HGV) with multiple constraints (flight and input constraints). First, based on the framework of the standard profile guidance method, a standard drag acceleration–velocity profile is planned as the tracking target, which satisfies the flight constraints. Second, a composite controller based on ADP and dynamic surface control (DSC) is proposed to track the planned profile and satisfy both the terminal conditions and the input constraint. An ADP method is developed to realize the optimal control through a critic neural network (NN) approximation for the solution of Hamilton–Jacobi–Bellman (HJB) equation. By using DSC method, the steady control is realized. Finally, the states of the closed-loop system and the weight estimation error are proved to be uniformly ultimately bounded, and the effectiveness of the proposed composite control method is verified via simulations.