Stability Of Closed-loop System Research Articles

Backstepping control of hypersonic vehicles under input and output constraints with model uncertainties and disturbances

In this paper, considering the physical restriction of hypersonic vehicle systems in a practical flight environment, the altitude tracking problem is studied with input magnitude, input rate, output constraints, system parameter uncertainties and disturbances, which expands the traditional considerations of control methods in the hypersonic vehicle field. The hyperbolic tangent function is employed to address the system input constraints. Furthermore, the incorporation of barrier Lyapunov function serves to ensure that the system output is limited in the prescribed limitations. In particular, two extended state observers are integrated to eliminate errors from model uncertainties and disturbances. Based on the effective combination of these techniques and auxiliary variable designs, a novel backstepping controller is proposed to simultaneously handle problems of input and output constraints, model uncertainties and disturbances. The closed-loop system stability is demonstrated using the Lyapunov theory. Simulation results show the effectiveness and superiority of the proposed controller compared with the traditional backstepping controller.

Adaptive Visual Control for Robotic Manipulators with Consideration of Rigid-Body Dynamics and Joint-Motor Dynamics

A novel cascade visual control scheme is proposed to tailor for electrically driven robotic manipulators that operate under kinematic and dynamic uncertainties, utilizing an uncalibrated stationary camera. The proposed control approach incorporates adaptive weight radial basis function neural networks (RBFNNs) to learn the behaviors of the uncertain dynamics of the robot and the joint actuators. The controllers are designed to nullify the approximation error and mitigate unknown disturbances through an integrated robust adaptive mechanism. A major advantage of the proposed approach is that prior knowledge of the dynamics of the robotic manipulator and its actuator is no longer required. The controller autonomously assimilates the robot and actuator dynamics online, thereby obviating the need for fussy regression matrix derivation and advance dynamic measurement to establish the adaptive dynamic parameter update algorithm. The proposed scheme ensures closed-loop system stability, bounded system states, and the convergence of tracking errors to zero. Simulation results, employing a PUMA manipulator as a testbed, substantiate the viability of the proposed control policy.

Event-Triggered Adaptive Neural Network Tracking Control for Uncertain Systems With Unknown Input Saturation Based on Command Filters.

This brief presents a modified event-triggered command filter backstepping tracking control scheme for a class of uncertain nonlinear systems with unknown input saturation based on the adaptive neural network (NN) technique. First, the virtual control functions are reconstructed to address the uncertainties in subsystems by using command filters. A piecewise continuous function is employed to deal with the unknown input saturation problem. Next, an event-triggered tracking controller is developed by utilizing the adaptive NN technique. Compared with standard NN control schemes based on multiple-function-approximators, our controller only requires a single NN. The closed-loop system stability is analyzed based on the Lyapunov stability theorem, and it is shown that the Zeno behavior is also avoided under the designed event-triggering mechanism. Simulation studies are performed to validate the effectiveness of our controller.

Output-feedback path-following control of underactuated AUVs via singular perturbation and interconnected-system technique

This paper focuses on the output-feedback control for path-following of underactuated autonomous underwater vehicles subject to multiple uncertainties and unmeasured velocities. First, a novel extended state observer is proposed to estimate the mismatched lumped disturbance and recover the unmeasured velocities. Based on this premise, to overcome the limitation of relying solely on the accurate kinematic model, a disturbance observer-based stabilizing controller is developed. The difference in bandwidths between the observer and the vehicle dynamics allows for a mathematical setup amenable to standard singular perturbation theory. In the fast mode, a kinematic observer is designed to reject system uncertainty caused by unknown attack angular velocity and prohibitive path-tangential angular velocity, using a novel physical perspective. In the slow mode, an interconnected-system control law is proposed by integrating the backstepping technique with the time scale decomposition method. Furthermore, the stability of the overall closed-loop system is established. Finally, simulation results are presented to demonstrate the effectiveness of the proposed method for path-following of underactuated autonomous underwater vehicles in the vertical plane.

Robust optimal control for uncertain wheeled mobile robot based on reinforcement learning: ADP approach

This paper presents a robust optimal control approach for the wheel mobile robot system, which considers the effects of external disturbances, uncertainties, and wheel slipping. The proposed method utilizes an adaptive dynamic programming (ADP) technique in conjunction with a disturbance observer. Initially, the system's state space model is formulated through the utilization of kinematic and dynamic models. Subsequently, the ADP method is employed to establish an online adaptive optimal controller, which solely relies on a single neural network for the purpose of function approximation. The utilization of the disturbance observer in conjunction with the compensation controller serves to alleviate the effects of disturbances. The Lyapunov theorem establishes the stability of the complete closed-loop system and the convergence of the weights of the neural network. The proposed approach has been shown to be effective through simulation under the effect of the disturbances and the change of the desired trajectory.

Robust distributed fixed-time cooperative hunting control for multi-quadrotor with obstacles avoidance

This paper addressed the robust distributed fixed-time cooperative hunting problem of multiple quadrotors subject to disturbances in obstacles environment. To handle the underactuated issue inherent in quadrotor dynamics, an inner–outer (attitude-position) loop cascade control configuration is proposed to achieve the cooperative flight control of quadrotors. For position subsystem, as the information of target cannot be accessible to all quadrotors, a distributed fixed-time observer is devised to estimate the target’s information. To improve the system’s robustness, a fixed-time extended state observer is designed to reject disturbances actively. Based on two observers, the sliding mode position encirclement control protocol with repulsive force is presented to avoid obstacles and encircle the target within a fixed time. For attitude subsystem, a sliding mode attitude tracking control protocol is proposed such that tracking errors can converge to zero even under disturbances. The stability analysis is performed to show the stabilization of the whole closed-loop system with fixed-time convergence. Finally, two sets of comparison simulation are provided to show the superiority of the developed control strategy.

Fuzzy PD-sliding mode control design for networked system with time delays

This research specifically addresses the problem of sliding mode control (SMC) in a particular group of T–S fuzzy systems that experience output disturbances and time delays using a networked control system. First, a model for a proportional–derivative sliding mode observer (SMO) is established, subsequently followed by the design of a controller based on SMO to maintain closed-loop system stability. The authors establish a novel mechanism to optimize the bandwidth utilization of the communication network by introducing a newly adjusted event-triggering parameter. After that, addressed a linear matrix inequality (LMI) problem to determine the controller gain and observer coefficients. This was done to guarantee the asymptotic stability of the closed-loop plant. Furthermore, the authors were able to directly identify the disturbances for these plants using the proposed descriptor SMO. Moreover, a parameter-based novel event-triggered scheme, along with a new resultant closed-loop system, will be employed to modify trigger frequency parameters within a unified framework. The controller gains will be determined by solving a linear matrix inequality, subject to certain conditions that ensure sufficiency. These conditions will be deduced to ensure asymptotic stability. In the final section, the authors presented examples from the Wind Energy System (WES) that illustrate the feasibility and effectiveness of our proposed methodology.

Distributed finite-time adaptive consensus output-feedback control of multi-agent systems under switching topologies

The paper investigates the finite-time adaptive consensus control of nonlinear multi-agent systems (MASs) by output-feedback. During the process of control design, the fuzzy logic system (FLS) is employed to approximate nonlinear function, as well as constructing a fuzzy state observer to estimate unmeasured states. Combining the dynamic surface control (DSC) with adaptive backstepping method conquers the complexity explosion issue. Then, semi-global practical finite-time stability (SGPFS) for closed-loop system is obtained under arbitrary switching communication topologies. All the signals of the overall system are uniformly ultimately bounded (UUB). Finally, the availability of developed control approach will be demonstrated through a simulation.

Trajectory tracking controller design for wheeled Mobile robot with velocity and torque constraints

This article investigates the trajectory tracking control problem for wheeled mobile robot (WMR) subject to both velocity and torque constraints. Firstly, a more general model is established by considering the displacement between the centre of mass and the midpoint of the driving wheels of the WMR, based on which, a new bounded kinematic controller is proposed by combining the first-order filtering approach to keep the trajectory tracking error asymptotically stable. Then the dynamic controller is designed and the stability of the overall closed-loop system is proved by the Lyapunov stability theory and Barbalat's lemma. Some conditions are given to ensure that both the velocity constraints and torque constraints are satisfied. Finally, some numerical examples are given to show the effectiveness and advantages of the method proposed in this paper.

Sliding Mode Fuzzy Control of Stochastic Nonlinear Systems Under Cyber-Attacks.

In this article, the problem of integral sliding mode control (ISMC) for a class of nonlinear systems with stochastic characteristics under cyber-attack is investigated. The control system and the cyber-attack are modeled as an Itô-type stochastic differential equation. The stochastic nonlinear systems are approached by the Takagi-Sugeno fuzzy model. A dynamic ISMC scheme is applied and the states and control input are analyzed within a universal dynamic model. It is demonstrated that trajectory of the system can be confined to the integral sliding surface within finite time, and the stability of closed-loop system under cyber-attack will be guaranteed by using a set of linear matrix inequalities. Following a standard procedure of universal fuzzy ISMC, it is shown that all signals in the closed-loop system will be guaranteed bounded, and the states are asymptotic stochastic stable if some conditions are met. An inverted pendulum is applied to show the effectiveness of our control scheme.

Endogenous advanced oxidation process with peracetic acid for recycling spent LiFePO4 batteries

LiFePO4 batteries are becoming more widely used due to their low cost and high stability advantages, which means that many spent batteries are generated. Designing green and efficient recycling methods for used batteries is strategically significant for the sustainable development of the new energy industry. This study innovatively proposes a self-activated advanced oxidation process with peroxyacetic acid for recycling spent LiFePO4, selectively releasing Li+ while converting LiFePO4 to FePO4. Quenching tests show that the de-embedding of Li+ is mainly caused by the rapid attack from HO• and R-O• radicals. Furthermore, the recycled products Li2CO3 and FePO4 are employed to regenerate LiFePO4 cathode materials, forming a closed-loop recycling process. Compared with traditional hydrometallurgy and hydrogen peroxide oxidation methods, this technology has obvious advantages in terms of process complexity, energy consumption, reagent consumption, recovery profit, and environmental friendliness. This work opens up a new way for the recycling of spent lithium-ion batteries.

Model-free anti-disturbance tracking control for high-order discrete-time nonlinear system based on concurrent learning extended state observer

The research objective of this paper is to address the tracking control problem of high-order discrete-time nonlinear systems in the presence of completely unknown internal uncertainties, unknown external disturbances, and unknown control input gain. To address this challenge, the paper proposes a high-order discrete-time model-free anti-disturbance tracking control method without relying on prior knowledge of system parameters. The core of the approach is the development of a data-driven concurrent learning extended state observer. The uniqueness of this observer lies in its ability to estimate unknown control input gains without the persistent excitation and ensure the convergence of the estimates. Based on the concurrent learning extended state observer, a high-order discrete-time tracking control law is designed to precisely track the reference signal, ensuring the stability of the nonlinear closed-loop system. The effectiveness of this method was verified by applying simulation verification to the heading tracking control of surface automatic vehicles.

Reinforcement learning-based moving-target enclosing control for an unmanned surface vehicle in multi-obstacle environments

This paper investigates the moving-target enclosing problem in multi-obstacle environments for an unmanned surface vehicle (USV) with complex unknown factors, including target dynamics, vehicle dynamics, and disturbances. A reinforcement learning-based moving-target enclosing control scheme is proposed to ensure collision-free behavior and bolster the enclosing capability. Specifically, an extended state observer is deployed to estimate the target dynamics. Leveraging the estimated data and control obstacle functions, a virtual safety control law is formulated to dynamically harmonize obstacle avoidance and target enclosing control. Then, a novel controller is constructed to track this control law utilizing a Nussbaum-type function in conjunction with actor–critic neural networks (NNs). The actor and critic NNs are employed to approximate unknown dynamics encapsulating vehicle dynamics and disturbances, and value function, respectively. The Nussbaum-type function is embedded to adaptively identify unknown inertia mass, regulating the control input of the USV with the actor NN online. The proposed scheme effectively decouples obstacle avoidance and target enclosing control and only relies on the measurable variables. A rigorous theoretical analysis is further employed to ensure the closed-loop stability of the USV system. Eventually, Simulations are demonstrated to validate the effectiveness and superiority of the proposed scheme for the USV in multi-obstacle environments.

Adaptive disturbance rejection neural output feedback control of hydraulic manipulator systems

This paper proposes an adaptive disturbance rejection neural output feedback control (ADRNC) scheme for multi-degree-of-freedom (n-DOF) hydraulic manipulator systems, subjected to unknown nonlinearities, external disturbances and unmeasured system states. The controller design is formulated by integrating Radial Basis Function Neural Networks (RBFNNs) with state and disturbance observers using the backstepping method. The RBFNNs are synthesized to handle unknown nonlinear functions and the residual estimate error, coupled with external disturbances, is estimated through the combination of state observer and disturbance observer. The unique features of the proposed controller lies in its capability to estimate both matched and unmatched lumped disturbances. The auxiliary disturbance estimation law is guided by the neural learning weights and estimated system states provided by state observers. By effectively utilizing neural networks to approximate and mitigate most nonlinear uncertainties, the workload of the disturbance observer is substantially reduced. High-gain feedback is therefore avoided and improved tracking performance can be expected. Moreover, to avoid the tedious analysis and the problem of “explosion of complexity” in the conventional backstepping method, we employ a first-order sliding-mode differentiator. Rigorous analysis via Lyapunov methods establishes the stability of the entire closed-loop system, ensuring guaranteed and satisfactory tracking performance under the integrated influence of unknown nonlinearities, unmeasured states, and external disturbances. Extensive simulations are conducted to verify the effectiveness of the nested control strategy.

Robust H∞ consensus for uncertain linear multi-agent systems on directed topologies: A dynamic event-triggered strategy

Considering the asymmetry of the system matrix caused by directed communication networks, a dynamic event-triggered control protocol for the robust [Formula: see text] consensus of uncertain linear multi-agent systems accompanied by external disturbances on directed topologies is proposed. Through the introduction of the controlled output and generalized algebraic connectivity for directed graphs, the consensus problem is converted to the event-triggered stabilization of the uncertain linear closed-loop system with disturbance. On the basis of the relative state of neighbor agents at event-times and the introduced dynamic variables, a dynamic event-triggered control protocol is put forward, and the linear matrix inequality sufficient conditions for the system to achieve robust [Formula: see text] consensus are obtained after a rigorous proof. Then, linear matrix inequalities are further decoupled to greatly reduce the computational complexity, and the parameters of the control protocol are determined by solving the decoupled linear matrix inequalities. Finally, simulations are applied for the verification of conclusions.

Adaptive backstepping controller based on a novel framework for dynamic solution of an ankle rehabilitation spherical parallel robot

AbstractThis research offers an adaptive model-based methodology for autonomous control of 3-RRR spherical parallel manipulator (RSPM) based on a novel modeling framework. RSPM is an overconstrained parallel mechanism that has a variety of applications in medical procedures such as ankle rehabilitation because of its precision and accuracy. However, obtaining a complete explicit dynamic model of these mechanisms for tracking purposes has been a problematic challenge due to their inherent singularities, coupling effects of the limbs, and redundant constraints imposed by the intermediate joints. This paper presents a novel algorithm to obtain the analytical kinematic solutions of RSPMs based on the closed-loop vector method, which includes constraint analysis. By incorporating constrained kinematics into the dynamic model, a comprehensive explicit dynamic solution of the non-overconstrained version 3-RCC of RSPM is developed in task space, based on screw theory and the linear homogeneous property of algebraic equations on the manipulator twist. Based on the proposed computational framework, a robust self-tuning backstepping control (STBC) strategy is applied to the robot to overcome the effect of external disturbances and time-varying uncertainties. Furthermore, an observer-based compensation (OBC) method is presented for dealing with the nonlinear hysteresis loops of the ankle during trajectory tracking purposes. The closed-loop stability of the whole system including STBC and OBC is theoretically performed by Lyapunov methods. The proposed methodologies are validated by realistic co-simulations in different scenarios. For instant, in the presence of external disturbances, the maximum tracking error norm of STBC is 37.5% less than the sliding mode approach.

Predictor-based constrained fixed-time sliding mode control of multi-UAV formation flight

In this work, a predictor-based fixed-time sliding mode control is designed to tackle the problem of achieving precise trajectory tracking control of multiple unmanned aerial vehicle formation flight. The proposed approach simultaneously addresses various practical requirements, such as optimality, constraints, fixed-time convergence, external interferences, and computational burden. Initially, using the Taylor series concept, we derive the predictive models for the fixed-time sliding surface and reaching law. Subsequently, we formulate a constrained performance index by integrating these predictions with the control input. Ultimately, the optimal control input is computed through solving the constrained quadratic optimization problem. An outstanding feature of this study is the theoretical guarantee of closed-loop fixed-time system stability in the presence of external disturbances and constraints. Furthermore, the comparative analysis with sliding mode predictive control law and fixed-time sliding mode control methods demonstrates that the proposed approach achieves a straightforward control method with improved performance and acceptable accuracy. Finally, an experimental test is conducted to demonstrate the algorithm's potential for hardware implementation by employing the Hardware-in-the-Loop test.

Resilient coordination of multi-agent systems in the presence of unknown heterogeneous actuation efficiency and coupled dynamics: distributed approaches

To guarantee the stability and performance of an overall heterogeneous multi-agent system, feedback control structures must be capable of addressing the presence of heterogeneous agent-based nonlinear uncertainties, unknown actuation performance, and coupling effects. Additionally, some tasks require agents to track the leader's state and reach different states in a distributed way. Therefore, this paper proposes a distributed adaptive controller that drives a set of agents to user-assigned positions in the presence of the mentioned heterogeneous system anomalies. To address actuator dynamics, a hedging-based reference model is used to decouple adaptive updating from the actuator dynamics. To deal with the coupled dynamics, an observer-based estimation algorithm is proposed. Finally, the low-frequency learning method is used to deal with the high-frequency control response and, therefore, to obtain a better transient performance. The overall closed-loop system's stability is investigated using the Lyapunov Stability Theory, and the Linear Matrix Inequalities (LMI) technique is employed to identify stability limits regarding the actuator bandwidths of each agent. Illustrative numerical examples are presented to demonstrate the designed controller's performance in a heterogeneous uncertain multi-agent system's dynamics with unknown actuation capabilities and coupled dynamics.

Online learning of stable robust adaptive controllers design based on data-dependent feedback linearization with application to rotary inverted pendulum

This study introduces an online (supervised) learning method to design nonlinear auto-regressive moving average (NARMA) controllers for feedback-linearized nonlinear single-input single-output (SISO) systems. The algorithm ensures Schur stability of the overall closed-loop system and provides adaptiveness and robustness for the NARMA controllers. The first stage of the method derives, in a data-dependent way, a feedback-linearized model of the nonlinear plant by using its input and output sample pairs. The method’s second stage, which constitutes the novel part of the presented study, builds up an online learning scheme for the linear auto-regressive moving average (ARMA) controller based on an already learned feedback-linearized model of the nonlinear plant. During online supervised learning, ARMA parameters of the feedback-linearized SISO plant model and the closed-loop ARMA model are computed by minimizing the plant identification and the closed-loop system tracking errors. Both errors are defined as ℓ1,ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\ell}}_{1,{\\varvec{\\varepsilon}}}$$\\end{document}, namely ε-insensitive loss functions that provide NARMA controller the robustness against noise and outliers. The proposed online learning control algorithm is applied to a rotary inverted pendulum model and to a real rotary inverted pendulum setup. The tracking performance of the developed controller is compared with those of the linear quadratic regulator and coupled sliding mode controller in terms of mean square error.

Fast Finite-Time Composite Controller for Vehicle Steer-by-Wire Systems with Communication Delays

The modern steer-by-wire (SBW) systems represent a revolutionary departure from traditional automotive designs, replacing mechanical linkages with electronic control mechanisms. However, the integration of such cutting-edge technologies is not without its challenges, and one critical aspect that demands thorough consideration is the presence of nonlinear dynamics and communication network time delays. Therefore, to handle the tracking error caused by the challenge of time delays and to overcome the parameter uncertainties and external perturbations, a robust fast finite-time composite controller (FFTCC) is proposed for improving the performance and safety of the SBW systems in the present article. By lumping the uncertainties, parameter variations, and exterior disturbance with input and output time delays as the generalized state, a scaling finite-time extended state observer (SFTESO) is constructed with a scaling gain for quickly estimating the unmeasured velocity and the generalized disturbances within a finite time. With the aid of the SFTESO, the robust FFTCC with the scaling gain is designed not only for ensuring finite-time convergence and strong robustness against time delays and disturbances but also for improving the speed of the convergence as a main novelty. Based on the Lyapunov theorem, the closed-loop stability of the overall SBW system is proven as a global uniform finite-time. Through examination across three specific scenarios, a comprehensive evaluation is aimed to assess the efficiency of the suggested controller strategy, compared with active disturbance rejection control (ADRC) and scaling ADRC (SADRC) methods across these three distinct driving scenarios. The simulated results have confirmed the merits of the proposed control in terms of a fast-tracking rate, small tracking error, and strong system robustness.