Second-order Tracking Differentiator Research Articles

Distributed synchronization method of multi-motor driving system’s accelerated backstepping tracking control

This paper proposes a distributed synchronization control method and an accelerated backstepping tracking control scheme for the multi-motor driving system (MMDS). In the first step, we create a dynamic model of the MMDS with complex nonlinear dynamics, encompassing elements such as the dead zone, frictions, and disturbances. Next, in order to tackle the challenge of load tracking, we fuse a speed function, a cosine barrier function, a second-order tracking differentiator (TD), and a disturbance compensator into the backstepping approach. Lastly, to address potential issues related to diverse torque inputs, which could result in the overload occurrences, we put forward a novel distributed synchronization control scheme. This scheme aims to achieve torque synchronization for the MMDS while simultaneously ensuring superior load tracking performance. In the distributed synchronization control, a communication network is built to achieve the local coupling and improve the synchronization efficiency, and a corresponding mean deviation coupling synchronization control scheme is designed. Lyapunov theory is utilized to demonstrate the stability of the introduced control scheme. The simulation experimental results for the MMDS show the effectiveness of the proposed scheme.

Robust adaptive output feedback for the formation control of heterogeneous ships based on a nonlinear extended state observer

This study considers the formation control problem of heterogeneous ships with unknown time-varying disturbances, dynamic uncertainties, and unmeasurable speeds, a robust adaptive output feedback formation control scheme for the heterogeneous ships based on nonlinear extended state observer is developed. In order to solve the heterogeneous ships formation control problem with leader-following structure, transforming the formation control problem into a class of ship trajectory tracking problem by improving the design of the virtual ship. Firstly, a nonlinear extended state observer is designed for estimating ship speeds due to technical limitations and external disturbances. Then, combining the adaptive neural networks with disturbances adaptive law to deal with the unknown time-varying disturbances and dynamic uncertainties. Meanwhile, the second-order tracking differentiator is designed to calculate the derivative of the virtual control law, which has higher precision comparing to the first-order filter. Stability theory is proved that all the signal of closed-loop control system are uniformly ultimately bounded, and the tracking errors can converge into arbitrary small neighborhoods around zero. Finally, comparative simulations were performed to demonstrate the effectiveness of the proposed controller.

Learning-based design optimization of second-order tracking differentiator with application to missile guidance law

Tracking differentiator is widely used to estimate the differential signal of noisy systems with unknown structures. However, there still lacks an efficient approach to tracking differentiator design and optimization, partly due to the nonlinearity by nature, and the high dimension of design parameters. Thus, this paper proposes a learning-based design optimization method. First, neural networks are trained to approximate the multivariate influence on tracking differentiator performance. The resultant learning-based surrogate model is then used to optimize the parameters of tracking differentiator by differential evolution algorithm. The proposed method is applied to Sigmoid-type tracking differentiator and further compared to the unscented Kalman filter with various input signals. The estimation error of the optimized tracking differentiator is reduced by 65.70% compared to that of the benchmark method. The second-order tracking differentiator is integrated into an angular acceleration-based guidance law. Simulation results of tracking moving targets show that the miss distance and control resource are separately lowered by at least 35.70% and 74.12% as opposed to the crude guidance law.

Accelerated Adaptive Backstepping Control of the Chaotic MEMS Gyroscope by Using the Type-2 Sequential FNN

In this paper, we propose an accelerated adaptive backstepping control algorithm based on the type2 sequential fuzzy neural network (T2SFNN) for the microelectromechanical system (MEMS) gyroscope with deadzone and constraints. Firstly, the mathematical model of the MEMS gyroscope is established to perform dynamical analyses and controller design. Then, the phase diagrams and Lyapunov exponents are presented to reveal its chaotic oscillation, which is harmful to system stability. In order to suppress oscillations derived from chaos and deadzone, an accelerated adaptive backstepping controller is proposed wherein an adaptive auxiliary is established to compensate the influence of nonsymmetric deadzone on stability performance, along with the T2SFNN designed to approximate unknown functions of dynamic systems. Furthermore, the speed function is introduced to accelerate convergence speed of the control system, and the problem of complex term explosion in traditional backstepping is successfully solved by a secondorder tracking differentiator. Finally, simulation results show that the proposed control scheme can guarantee asymptotic convergence of all signals in the closedloop system, as well as satisfying states constraints and fulfilling the purposes of chaos suppression and accelerated convergence.

Prescribed Performance Adaptive Fuzzy Containment Control for Nonlinear Multiagent Systems Using Disturbance Observer

This article focuses on the containment control problem for nonlinear multiagent systems (MASs) with unknown disturbance and prescribed performance in the presence of dead-zone output. The fuzzy-logic systems (FLSs) are used to approximate the unknown nonlinear function, and a nonlinear disturbance observer is used to estimate unknown external disturbances. Meanwhile, a new distributed containment control scheme is developed by utilizing the adaptive compensation technique without assumption of the boundary value of unknown disturbance. Furthermore, a Nussbaum function is utilized to cope with the unknown control coefficient, which is caused by the nonlinearity in the output mechanism. Moreover, a second-order tracking differentiator (TD) is introduced to avoid the repeated differentiation of the virtual controller. The outputs of the followers converge to the convex hull spanned by the multiple dynamic leaders. It is shown that all the signals are semiglobally uniformly ultimately bounded (SGUUB), and the local neighborhood containment errors can converge into the prescribed boundary. Finally, the effectiveness of the approach proposed in this article is illustrated by simulation results.

Neuro-adaptive trajectory tracking control of underactuated autonomous surface vehicles with high-gain observer

This paper addresses the trajectory tracking control of underactuated autonomous surface vehicles subject to immeasurable velocities and parameter uncertainties. An adaptive control scheme is proposed based on backstepping method, neural network and low-frequency techniques. In addition, the overall signals of closed-loop system are ensured uniformly ultimate boundness based on Lyapunov stability theory. The advantages are highlighted as follows: (i) To avoid explosion of complexity of conventional backstepping method, the derivations of virtual control signals are obtained through second-order tracking differentiator. (ii) The proposed controller does not require any previous knowledge about hydrodynamic damping and external disturbances, which is easily applied into practice. (iii) To solve the problem of immeasurable velocities, the controller does not acquire velocity signals by employing high-gain observer. Finally, simulation results are provided to verify strong robustness and tracking effectiveness of proposed control scheme

Adaptive neural finite-time containment control for nonlower triangular nonlinear multi-agent systems with dynamics uncertainties

This paper considers the finite-time containment control problem for nonstrict-feedback nonlinear multi-agent systems (MASs) in the presence of unmodeled dynamics. A new variable separation approach is developed to overcome the difficulty of unknown functions with nonstrict-feedback structure in the backstepping design process. The second-order tracking differentiator is extended to the nonstrict-feedback nonlinear MASs for avoiding the problem of “explosion of complexity”. Neural networks are used to approximate the unknown nonlinear functions. With introducing a dynamic signal, the difficulty from the unmodeled dynamics is successfully solved. And, by introducing a finite-time stability criterion, an new adaptive finite-time containment control scheme is designed, which ensures all signals are bounded. Moreover, the output signals of all followers converge to a convex hull spanned by the outputs of the leaders. Finally, a simulation example illustrates the effectiveness of the developed control scheme.

Cooperative Adaptive Event-Triggered Control for Multiagent Systems With Actuator Failures

This paper investigates the leaderless and leader-following problems for the nonlinear multiagent systems based on event-triggered communication scheduling. It should be pointed out that the input coefficient of every actuator is a stochastic function related to Markovian variables. A more general event-triggered mechanism is designed to decrease communication burden from the controller to the actuator. Furthermore, Barrier Lyapunov function is used to restrict the bound of tracking error in advance. To reduce the amount of calculations, a second-order tracking differentiator is introduced to avoid repeated derivative. Based on Lyapunov stability theory, it is proved that the designed controllers can guarantee the outputs of all agents eventually converge to agreement and all the signals in the systems are bounded in probability. Finally, the numerical simulation results are presented to illustrate the effectiveness of the approach proposed.

Adaptive cooperative control for a class of nonlinear multi-agent systems with dead zone and input delay

This paper studies the adaptive fuzzy control problem for multi-agent systems (MASs) with dead zone and input delay. Second-order tracking differentiator is introduced to avoid the repeated differentiations of the virtual control. The problem of dead zone is solved by using dead-zone slope and boundary value theory. Based on the Pade approximation method, the influence of input delay is eliminated of the MASs. The designed controller can guarantee all the signals in the closed-loop system are semi-globally uniformly ultimately bounded, and tracking errors converge to a neighbourhood around the origin. Finally, the simulation results show the effectiveness of the proposed method.

Adaptive Dynamic Surface Control for Spacecraft Terminal Safe Approach with Input Saturation Based on Tracking Differentiator

This thesis studies the spacecraft terminal safe approach control problem considering input saturation. Based on the spacecraft relative motion model and sphere collision avoidance potential function, an anti-saturation controller and an adaptive finite-time anti-saturation controller using dynamic surface control(DSC) are presented for the situations of known and unknown upper bound of external disturbances respectively, which can guarantee that no collisions happen in the tracking process. The second-order tracking differentiator is introduced to design the controllers, which avoids the differential of the virtual control signal and ensures the tracking performance of system output signals. Meanwhile, the auxiliary system is introduced to handle input saturation. Lyapunov stability theory is adopted to prove that the states of system under the designed controllers are uniformly ultimately bounded and practical finite-time stable respectively, and the chaser spacecraft can approach to the desired position without collision. The numerical simulation results demonstrate that the chaser spacecraft using the designed controllers can realize terminal safe approach to target spacecraft, which further illustrate the effectiveness of the proposed controllers.

Performance enhanced design of chaos controller for the mechanical centrifugal flywheel governor system via adaptive dynamic surface control

This paper addresses chaos suppression of the mechanical centrifugal flywheel governor system with output constraint and fully unknown parameters via adaptive dynamic surface control. To have a certain understanding of chaotic nature of the mechanical centrifugal flywheel governor system and subsequently design its controller, the useful tools like the phase diagrams and corresponding time histories are employed. By using tangent barrier Lyapunov function, a dynamic surface control scheme with neural network and tracking differentiator is developed to transform chaos oscillation into regular motion and the output constraint rule is not broken in whole process. Plugging second-order tracking differentiator into chaos controller tackles the “explosion of complexity” of backstepping and improves the accuracy in contrast with the first-order filter. Meanwhile, Chebyshev neural network with adaptive law whose input only depends on a subset of Chebyshev polynomials is derived to learn the behavior of unknown dynamics. The boundedness of all signals of the closed-loop system is verified in stability analysis. Finally, the results of numerical simulations illustrate effectiveness and exhibit the superior performance of the proposed scheme by comparing with the existing ADSC method.