Asymptotic Tracking Properties Research Articles

A mean‐field approach for the asymptotic tracking problem of moving continuum target clouds

AbstractWe propose a new coupled kinetic system arising from the asymptotic tracking of a continuum target cloud, and study its asymptotic tracking property. For the proposed kinetic system, we present an energy functional which is monotonic and distance between particle trajectories corresponding to kinetic equations for target, and tracking ensembles tend to zero asymptotically under a suitable sufficient framework. The framework is formulated in terms of system parameters and initial data.

Minimum eigenvalue based adaptive fault compensation for hypersonic vehicles

The attitude tracking control problem is addressed for hypersonic vehicles under actuator faults that may cause an uncertain time-varying control gain matrix. An adaptive compensation scheme is developed to ensure system stability and asymptotic tracking properties, including a kinematic control signal and a dynamic control signal. To deal with the uncertainties of the control gain matrix, a new positive definite one is constructed. The minimum eigenvalue of such a new control gain matrix is estimated. Simulation results of application to an X-33 vehicle model verify the effectiveness of the proposed minimum eigenvalue based adaptive fault compensation scheme.

Dynamical Property of the Shift Map under Group Action

Firstly, we introduced the concept of G ‐ Lipschitz tracking property, G ‐ asymptotic average tracking property, and G ‐ periodic tracking property. Secondly, we studied their dynamical properties and topological structure and obtained the following conclusions: (1) let X , d be compact metric G ‐ space and the metric d be invariant to G . Then, σ has G ¯ ‐ asymptotic average tracking property; (2) let X , d be compact metric G ‐ space and the metric d be invariant to G . Then, σ has G ¯ ‐ Lipschitz tracking property; (3) let X , d be compact metric G ‐ space and the metric d be invariant to G . Then, σ has G ¯ ‐ periodic tracking property. The above results make up for the lack of theory of G ‐ Lipschitz tracking property, G ‐ asymptotic average tracking property, and G ‐ periodic tracking property in infinite product space under group action.

Passive robust control for uncertain Hamiltonian systems by using operator theory

In this study, the passivity-based robust control and tracking for Hamiltonian systems with unknown perturbations by using the operator-based robust right coprime factorisation method is concerned. For the system with unknown perturbations, a design scheme is proposed to guarantee the uncertain non-linear systems to be robustly stable while the equivalent non-linear systems is passive, meanwhile the asymptotic tracking property of the plant output is discussed. Moreover, the design scheme can be also used into the general Hamiltonian systems while the simulation is used to further demonstrate the effectiveness of the proposed method.

Determining Map, Data Assimilation and an Observable Regularity Criterion for the Three-Dimensional Boussinesq System

In this paper, we consider the analysis of a nudging based algorithm for data assimilation for the three-dimensional Boussinesq system, which we call the AOT system. A rigorous analysis of this algorithm for well-posed dissipative partial differential equations was first provided by Azouani, Olson and Titi (J Nonlinear Sci 24:277–304, 2014); thus justifying our terminology for the associated nudging system. We provide a sufficient condition, based solely on the observed velocity data obtained from a Leray-Hopf weak solution, for the global well-posedness, regularity and most crucially, the asymptotic tracking property of solutions of the associated (three-dimensional) nudging system. It is to be noted that neither regularity nor any knowledge of a uniform \({\mathbb {H}}^1\)-norm bound is a priori assumed on the solution of the original three-dimensional Boussinesq system from which the observations are obtained. As a corollary of our result, we obtain a novel observable regularity criterion based on finitely many observational data. Our condition also guarantees the construction of the Lipschitz continuous determining map, which is known to play a crucial role in the construction of the so-called determining form and in statistical data assimilation.

The G -Asymptotic Tracking Property and G -Asymptotic Average Tracking Property in the Inverse Limit Spaces under Group Action

Firstly, we introduce the definitions of G -asymptotic tracking property, G -asymptotic average tracking property, and G -quasi-weak almost-periodic point. Secondly, we study their dynamical properties and characteristics. The results obtained improve the conclusions of asymptotic tracking property, asymptotic average tracking property, and quasi-weak almost-periodic point in the inverse limit space and provide the theoretical basis and scientific foundation for the application of tracking property in computational mathematics, biological mathematics, and computer science.

Minimum eigenvalue-based adaptive compensation of actuator faults for flexible spacecraft

This paper develops an adaptive compensation scheme for flexible spacecraft under actuator faults. System uncertainties caused by faults and flexible uncertainties are first parameterized. To deal with the uncertainty of the control gain matrix caused by faults, a new control gain matrix is constructed. By using the minimum eigenvalue of this new control gain matrix, a nominal control signal is designed. Then an adaptive control signal is designed by estimating the uncertain parameters in the nominal control signal. The developed adaptive control signal guarantees system stability and asymptotic tracking properties. Simulation results are given to verify the effectiveness of the proposed adaptive compensation scheme.

Continuous Data Assimilation for the Three-Dimensional Navier--Stokes Equations

In this paper, we identify conditions, based solely on the observed data, for the global well-posedness, regularity, and the asymptotic tracking property of solutions of the Newtonian relaxation (n...

Higher-order tracking properties of nonlinear adaptive control systems

While the asymptotic output tracking property has been proven for many nonlinear adaptive control systems, their higher-order output tracking property has not been reported. In this paper, the higher-order derivative convergence of the output tracking error e ( t ) is studied for nonlinear adaptive control systems using the feedback linearization design. It is proven that not only each error component e j ( t ) from e ( t ) = [ e 1 ( t ) , e 2 ( t ) , … , e m ( t ) ] T converges to zero asymptotically but also its up to k th-order time-derivative e j ( k ) ( t ) converges to zero, for k = 1 , 2 , … , ρ j , where ρ j , j = 1 , 2 , … , m , are the control relative degrees of the nonlinear system with m inputs.

Stability analysis of single area power system considering parameter uncertainties

ABSTRACT In this work, the stability of a single area power system AVR loop is analysed in terms of specified gain and phase margin standpoint, by utilising an extended reduced-order observer (EROO). The design approach utilises a full-state feedback as well as an estimated signal for external disturbance (parametric uncertainties and disturbances due to change in load demands) to form the control law. Symmetric root locus (SRL) technique is used to assign the closed-loop poles (CLPs) of the system at desired locations by considering the stability margins. Parametric model uncertainty has been considered to demonstrate the robustness of control achieved by assigning a bound on the deviations in plant parameters. The proposed observer provides the estimates of unavailable states and state of the disturbance model in order to compensate system in the presence of external disturbances. The control scheme achieves performances satisfying the specified stability margins with asymptotic tracking and disturbance rejection property. The methodology provides control over peak values of the terminal voltage (with guaranteed zero steady-state errors) and control signal deviations which may be utilised to meet hardware constraints. Step by step design procedures with illustrative examples have been provided using MATLAB commands.

A decoupling control for quadrotor UAV using dynamic surface control and sliding mode disturbance observer

This paper proposes a decoupling tracking controller for quadrotors using dynamic surface control (DSC) and second-order sliding mode disturbance observer (SMDO). The DSC used in this paper is improved with the sliding mode differentiators that replace the original low-pass filter, and the SMDO is utilized to restrain the influence of system uncertainties and external disturbances. In addition, instead of the roll attitude angle ( $$\varphi $$ ) and pitch attitude angle ( $$\theta $$ ), applying $$\sin {\varphi }$$ and $$\sin {\theta }$$ as control variables simplifies the analysis of stability. Moreover, a fuzzy logic-based method is utilized to compensate the influence of battery voltage changing during the procedure of thrust generation. The asymptotic tracking property of the closed-loop system is proven via the Lyapunov-based stability theory. Finally, the real-time experiment results, which contain a hovering case and rectangular path tracking case, are given to validate the practicability of the proposed method.

Distributed Fault-Tolerant Control of Multiagent Systems: An Adaptive Learning Approach.

This paper focuses on developing a distributed leader-following fault-tolerant tracking control scheme for a class of high-order nonlinear uncertain multiagent systems. Neural network-based adaptive learning algorithms are developed to learn unknown fault functions, guaranteeing the system stability and cooperative tracking even in the presence of multiple simultaneous process and actuator faults in the distributed agents. The time-varying leader's command is only communicated to a small portion of follower agents through directed links, and each follower agent exchanges local measurement information only with its neighbors through a bidirectional but asymmetric topology. Adaptive fault-tolerant algorithms are developed for two cases, i.e., with full-state measurement and with only limited output measurement, respectively. Under certain assumptions, the closed-loop stability and asymptotic leader-follower tracking properties are rigorously established.

Direct parametric attitude tracking control for generic hypersonic vehicle

ABSTRACTThis paper considers the attitude tracking problem for the generic hypersonic vehicle (GHV). First, the second-order nonlinear GHV attitude model is introduced. Second, by utilising the direct parametric approach, a modified parametric controller composed of the parametric state proportional plus derivative feedback controller and the feedforward controller is proposed. With application of the first part, the closed-loop system is a constant linear system with desired eigenstructures, and the second part is used to ensure the asymptotic tracking property of the outputs of the GHV attitude system. Since the control input of the established GHV attitude model is moment command, an algorithm that transforms the moment commands into the fins deflection command is proposed. Finally, the effectiveness of the proposed parametric controller and transform algorithm is illustrated by the numerical simulation results.

Asymptotic tracking control of strict‐feedback non‐linear systems with output constraints in the presence of input saturation

In this study, the asymptotic tracking control problem is addressed for known and unknown non-linear systems in the strict-feedback form with time-varying output constraints, input saturation, and external disturbances. A barrier Lyapunov function is employed to prevent transgression of the output constraints. Neural networks are applied to approximate the unknown functions. To deal with the input saturation effects and/or neural networks reconstruction errors, the Nussbaum gain technique is suggested. The proposed approach guarantees the boundedness of all the closed-loop signals, and for the first time, the asymptotic tracking property is achieved for the strict-feedback non-linear systems, while the actual output remains in the output constraints, despite input saturation and external disturbances. Two simulation examples have validated the effectiveness of the proposed results.

Actuator failure compensation for two linked 2WD mobile robots based on multiple-model control

Abstract This paper develops a new actuator failure compensation scheme for two linked two-wheel drive (2WD) mobile robots based on multiple-model control. First, a configuration of two linked 2WD robots is described, and their kinematics and dynamics are modeled. Then, a multiple-model based failure compensation scheme is developed to compensate for actuator failures, consisting of a kinematic controller, multiple dynamic controllers and a control switching mechanism, which ensures system stability and asymptotic tracking properties. Finally, simulation results verify the effectiveness of the proposed failure compensation control system.

Adaptive Compensation of Multiple Actuator Faults for Two Physically Linked 2WD Robots

This short paper develops an adaptive compensation control scheme for two physically linked two-wheel-drive mobile robots with multiple actuator faults. Kinematic and dynamic models are first proposed. Then, an adaptive control scheme is designed, which ensures system stability and asymptotic tracking properties. Simulation results verify its effectiveness.

Multidesign Integration Based Adaptive Actuator Failure Compensation Control for Two Linked 2WD Mobile Robots

This paper develops an actuator failure compensation control scheme for two linked mobile robots. The kinematic and dynamic models of two robots with a physical link that is employed to deal with actuator failures for two-wheel drive mobile robots are proposed. Then, a kinematic controller is designed, which is a virtual one. Based on this controller, multiple adaptive dynamic control signals are designed to cover all possible failure cases. By combining these dynamic control signals, the dynamic controller is designed, which ensures desired system stability and asymptotic tracking properties. Finally, simulation results verify the effectiveness of the proposed adaptive actuator failure compensation scheme.

An adaptive actuator failure compensation scheme for two linked 2WD mobile robots

This paper develops a new adaptive compensation control scheme for two linked mobile robots with actuator failurs. A configuration with two linked two-wheel drive (2WD) mobile robots is proposed, and the modelling of its kinematics and dynamics are given. An adaptive failure compensation scheme is developed to compensate actuator failures, consisting of a kinematic controller and a multi-design integration based dynamic controller. The kinematic controller is a virtual one, and based on which, multiple adaptive dynamic control signals are designed which covers all possible failure cases. By combing these dynamic control signals, the dynamic controller is designed, which ensures system stability and asymptotic tracking properties. Simulation results verify the effectiveness of the proposed adaptive failure compensation scheme.

Event‐Triggered Iterative Learning Control for Multi‐Agent Systems with Quantization

AbstractThe emergence of networked control systems urges the digital control design to integrate communication constraints efficiently. In order to accommodate this requirement, this paper investigates the joint design of tracking problem for multi‐agent system (MAS) in the presence of resource‐limited communication channel and quantization. An event‐triggered robust learning control with quantization is firstly proposed and employed for MAS in this paper. The new event‐triggered distributed robust learning control system with the introduction of logarithmic quantization guarantees the asymptotic tracking property on the finite interval. Convergence analysis is given based on the Lyapunov direct method. Finally, numerical simulations are given to illustrate the efficacy of the event‐triggered approach compared with time‐triggered controllers.

Constrained Tracking Control by Gain-Scheduled Feedback With Optimal State Resets: A General Servo Problem and an Online Optimization Method

In this paper, a tracking control problem for discrete-time linear systems with actuator saturation is addressed. The reference signal is assumed to be generated by an external dynamics. First, a design condition of a controller parameterized by a single scheduling parameter is introduced. The controller includes a servo compensator to achieve zero steady-state error. Then, a control algorithm that guarantees closed-loop stability and makes the tracking error converge to zero is given. In the control algorithm, the controller state as well as the scheduling parameter is updated online so that the tracking control performance is improved. Then, it is shown that the decision problem of the scheduling parameter and the controller state can be transformed into a convex optimization problem with respect to a scalar parameter. Based on this fact, we propose a numerically efficient algorithm for solving the optimization problem. Further, we propose a method of modifying the control algorithm so that the asymptotic tracking property is ensured even when the numerical error exists in the optimal solution. A numerical example and an experimental result are provided to illustrate effectiveness of the proposed control method.