Virtual Control Signals Research Articles

Adaptive output feedback command filter control based on extreme learning machine for nonaffine time delay systems with input saturation

This paper is concerned with the tracking control problem of nonlinear time delay systems. For time delay systems, we consider nonaffine pure-feedback structure. Additionally, the case where the time delay systems are subject to input saturation and unknown states is also taken into account. To begin with, a mean value theorem and an implicit function theorem are exploited to transform the systems into an affine form. Afterwards, a state observer is developed to estimate the unknown state variables and an extreme learning machine (ELM) is used to approximate the unknown functions. The output of the command filter replaces the virtual control signal'derivative, thereby circumventing the problem of ‘explosion of complexity’. Meanwhile, compensation signals are introduced to eliminate the filtering errors in a dynamic surface control (DSC). A Lyapunov–Krasovskii functional is designed to mitigate the unknown constant state time delay. During the controller design process, combining a prescribed performance control (PPC) with a command filter control, the tracking error can converge to a predetermined bound. Additionally, the effect of input saturation is eliminated with the aid of an auxiliary system. Finally, the effectiveness of such controller is further proved by taking an electromechanical system as an application object.

Robust adaptive prescribed performance control for nonlinear systems with arbitrary initial states

The initial state of nonlinear MIMO strict feedback systems is often unpredictable and random, and existing prescribed performance control (PPC) techniques can only guarantee system output constraints within a fixed initial value performance boundary. In this paper, an adaptive PPC method tailored for nonlinear systems was introduced, enabling the system stable tracking regardless of the arbitrary initial states. To guarantee that the tracking error consistently meets the prescribed performance boundary(PPB) envelope, we introduce a nonlinear mapping between the initial value of the prescribed performance functions(PPFs) and the system tracking errors, resulting in an asymmetric time-varying performance boundary. Building upon this foundation, an adaptive PPC scheme is proposed under the backstepping framework, integrated with a nonlinear disturbance observer (NDO). This method ensures that the tracking error remains within the desired PPB, regardless of external disturbances or system initial states. To prevent ‘complexity explosion’, a dynamic surface control (DSC) technology is employed to filter the virtual control signals of each subsystem. Furthermore, the ultimate uniform boundedness of the closed-loop signal has been demonstrated, and a practical flight vehicles roll control case was introduced to validate the efficacy of the proposed method.

A multilayer neural‐network‐based fault estimation and fault tolerant control scheme for uncertain system

AbstractThis work introduces a new actuator fault estimation approach coupled with a fault‐tolerant control (FTC) strategy for uncertain systems in an output feedback framework. The proposed method involves constructing a Multi‐Layer Neural Network (MLNN) observer‐based fault estimation unit to accurately predict system states and potential faults in the actuator channel. An online control allocation (CA) scheme is then developed, utilizing the derived estimates to actively reconfigure the virtual control signals among the healthy redundant actuators in the event of actuator malfunction. Furthermore, an adaptive neural network‐based output integral sliding mode control scheme is designed based on the virtual control. This integration enhances the overall system's robustness and significantly reduces the chattering effect. The stability analysis of the proposed fault estimations scheme is initially performed using MLNN structure, followed by a comprehensive closed‐loop stability analysis to establish the stability of the entire system. Finally, the effectiveness of the proposed method is validated on a nonlinear six‐degree‐of‐freedom model of multirotor unmanned aerial vehicle aircraft. Numerical simulations under different fault and failure scenarios validate the efficacy of the proposed method. The comparative analysis of the proposed scheme is conducted with the static output feedback control allocations and adaptive allocation strategy. This analysis focuses on evaluating performance using metrics such as root mean square error and mean square deviation, particularly in the presence of faults and failures. The results demonstrate the superior performance of the proposed scheme in fault/failure conditions.

Adaptive fixed-time neural consensus control for a class of uncertain nonlinear multi-agent systems with full state constraints

This paper is concerned with the fixed-time consensus control problem for non-strict feedback multi-agent systems with asymmetric output constraints and full state constraints. Considering the feasibility of controlling execution, a novel practical virtual control signal is developed utilizing both saturation function and hyperbolic tangent function to ensure that this signal can remain within the same restricted range as the corresponding state variable throughout entire operation process. In backstepping steps, the design of ideal virtual control signal also adopts a different form of piecewise function than before, introducing high-order polynomial functions to avoid singularity problems in the derivation process. In addition, function approximation ability of radial basis function neural networks technique is applied to estimate uncertainties derived from the system functions and controller design procedure. Moreover, universal barrier Lyapunov function approach is improved for constructing an adaptive constrained synchronization control scheme. By fixed-time stability theory, it is shown that the tracking errors of the MAS converge to an adjustable region around the origin in a fixed time and the state variables always obey their constraints. And the upper bound of the settling time is merely dependent on design parameters, which is not affected by the initial states of MAS. The effectiveness of the proposed control strategy is shown by a numerical simulation example at last. Two scenarios are provided to demonstrate the advantages of the control protocol proposed in this paper.

Anti-disturbance cooperative formation containment control for multiple autonomous underwater vehicles with collision-free and actuator saturation constraints

This article investigates the formation containment control (FCC) problem of multiple autonomous underwater vehicles system (MAUVS) in the simultaneous presence of disturbances, collision avoidance between autonomous underwater vehicles (AUVs) and actuator saturation constraints. Firstly, for the purpose of enhancing the resisting disturbance capability of the MAUVS, the extended state observers are designed to estimate the total disturbance comprised of internal uncertainties and external interferences in real time. In order to hinder the occurrence of complexity explosion during the backstepping design, tracking differentiators are adopted to provide estimates for the derivative of the virtual control signals. Furthermore, the auxiliary system is constructed for reducing the influence of the actuator saturation on the MAUVS. Potential functions are integrated into the designed FCC strategy, so that the collisions between AUVs can be effectively avoided while the MAUVS achieving formation containment. Afterwards, via resorting to Lyapunov stability theory, it is demonstrated that the formation tracking errors and containment errors are uniformly ultimately bounded. Lastly, the comparative simulation results are illustrated to validate the feasibility of the presented anti-disturbance FCC scheme with collision-free and anti-saturation.

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.

Adaptive RBF Neural Network Tracking Control of Stochastic Nonlinear Systems with Actuators and State Constraints

This paper investigates the adaptive neural network (NN) tracking control problem for stochastic nonlinear systems with multiple actuator constraints and full-state constraints. The issue of system full-state constraints is tackled by a generalized barrier Lyapunov function (GBLF), and the output constraints of the system are considered to be in the form of time-varying functions, which are more in line with the needs of real physical systems. The NN approximation technique is utilized to overcome the influence of the uncertainty term on controller design due to randomness. Based on the backstepping technique, a neural adaptive fixed-time tracking control strategy is designed. Under the designed control strategy, the tracking accuracy of the controlled system can reach the expectation in a fixed time. The multi-actuator constraints are converted into a generalized mathematical model to simplify the controller design process. Using the characteristics of the hyperbolic tangent function, a new function called practical virtual control signal is designed using the virtual control signal as the input. Due to the saturation constraint property of the hyperbolic tangent function, it is theoretically ensured that no state of the system exceeds the constraints through to the new form of the virtual controller. Using the adaptive controller constructed in this paper, the controlled system is semi-global fixed-time stabilized in probability (SGFSP). Finally, the effectiveness of the proposed control strategy is further verified by simulation examples.

Time‐optimal trajectory generation and observer‐based hierarchical sliding mode control for ballbots with system constraints

AbstractThis paper introduces a comprehensive motion planning–tracking–safety constraint scheme for a 3D ballbot system. A nonlinear control for the 3D ballbot system is designed based on three separate planes by utilizing extended state observer (ESO) to estimate coupling mechanisms. Three virtual control signals are generated from these distinct planes and can be used for formulating actual control signals. To overcome the complexity of nonlinear motion equations, flatness theory is used to construct the time‐optimal trajectory through an optimization problem, facilitating smooth movement of the ballbot, and obstacle avoidance based on RRT* waypoints. Furthermore, our work manipulates the hierarchical sliding mode controller (HSMC) as the nominal controller to ensure that the ballbot tracks to the optimal trajectory, unifying with the exponential control barrier function (ECBF) to address safety constraints in the body's deflection angle. Through extensive simulations and comparative analysis, the system demonstrates its effectiveness and safe operation in various working conditions.

Multiple‐missile fixed‐time integrated guidance and control design with multi‐stage interconnected observers under impact angle and input saturation constraints

AbstractIn this paper, a novel three‐dimensional fixed‐time integrated guidance and control (IGC) scheme with multi‐stage interconnected observers is proposed for cooperative attacks using multiple missiles against a maneuvering target under impact angle and input saturation constraints. External disturbances, modeling errors, and aerodynamic parameter variations are considered as system uncertainties and a three‐channel fully coupled IGC model for multiple missiles is established. The IGC system is designed optimally based on fixed‐time stability theory, sliding mode control, and the backstepping technique. Three inter‐cascaded fixed‐time disturbance observers based on an improved super‐twisting algorithm are designed to estimate and compensate for system uncertainties. Second‐order command filters are used to constrain virtual control signals, and additional filtering error subsystems are introduced to compensate for the tracking errors of filters. System stability and uniformly ultimately fixed‐time boundedness of all states are proven using the Lyapunov stability theory. Finally, the limits of the acceleration components of the maneuvering target perpendicular to the line of sight direction are derived. The effectiveness of the designed IGC scheme and the ability of multi‐stage interconnected observers to sense disturbances with each other are verified through simulations.

Zero‐sum game for nonlinear multiagent systems with full‐state constraints

AbstractThis paper addresses the zero‐sum game problem for strict‐feedback nonlinear multiagent systems with full‐state constraints. Specifically, this paper focuses on the zero‐sum game scenario, wherein multiple agents aim to optimize the control strategies while considering the conflicting objectives of their opponents. To handle the full‐state constraints, a one‐to‐one nonlinear mapping technique is employed to convert the original strict‐feedback system into a more manageable pure‐feedback system without state constraints. In order to find a Nash equilibrium for virtual control signals and external disturbances, a simplified reinforcement learning algorithm is proposed, which tackles the challenges posed by solving the Hamilton–Jacobi–Isaacs equation. Unlike the existing optimal control strategies that deal with matching conditions, the optimal control strategy for strict‐feedback nonlinear systems needs to address the computational complexity issue arising from the repeated derivation of the virtual controller. To overcome the high‐order virtual controller problem, an approach based on the dynamic surface technique is introduced. By incorporating an approximation term of the high‐order virtual controller into the value function, the computational complexity challenge is effectively resolved. Based on the Lyapunov stability theorem, it is proved that all signals of the closed‐loop systems are semi‐global uniformly ultimately bounded and the tracking control performance can be guaranteed. Finally, simulation results are given to verify the effectiveness of the proposed control strategy.

Command filter-based adaptive neural tracking control of nonlinear systems with multiple actuator constraints and disturbances

In this paper, the adaptive practical finite-time tracking control problem for a class of strictly feedback nonlinear systems with multiple actuator constraints is investigated using backstepping techniques and practical finite-time stability theory. The effects of deadband and saturated nonlinear constraints on the controller design of nonlinear systems are addressed by the equivalent transformation method. The problem of complexity explosion due to the derivatives of virtual control signals is solved by using the virtual control signals as inputs to the command filters and using the outputs of the command filters to perform the corresponding control tasks. An adaptive neural network tracking backstepping control strategy based on the command filter technique and the backstepping design algorithm is proposed by approximating an unknown nonlinear function using a neural network. The control strategy ensures the boundedness of all variables in the closed-loop system, and the output tracking error fluctuates in a small region near the origin. Finally, simulations verify the effectiveness of the control strategy designed in this paper.

Double-loop frame-based adaptive neural sliding-mode control of single-input 3-DOF flexible-joint manipulator

Flexible-joint manipulators (FJMs) have been attracting much attention in recent decades. However, position control and vibration suppression of single-input (SI) multi-degrees-of-freedom (multi( ⩾ 3 )-DOF) FJM is still a high mountain to climb due to the characteristic that some states of such FJMs cannot be directly controlled by the SI. This paper aims to carry out this challenging research. We present a double-loop frame-based adaptive neural sliding-mode control method for an uncertain horizontal SI 3-DOF FJM, i.e. a two-link FJM with only one actuator at the first joint. Since only the actuator angle can be directly controlled, in the inner loop, we design a torque controller so that the actuator angle tracks a time-varying reference actuator angle, designed in real-time by the outer loop. In the outer loop, we consider the reference actuator angle as a virtual control signal and design it based on the dynamic coupling relationships, aiming to indirectly control the first link to its target position and suppress the vibration of both links. Furthermore, to enhance the transient system performance, we plan the input signal of the outer loop (i.e. the target angle) as a smooth reference-trajectory signal. The validity and superiority of this method are demonstrated in simulations.

Nonsingular predefined‐time dynamic surface control of a flexible‐joint space robot with actuator constraints

AbstractTo achieve predefined‐time trajectory tracking control of a flexible‐joint space robot(FJSR) with actuator constraints, a nonsingular predefined‐time dynamic surface control scheme is developed. The input saturation caused by actuator constraints is addressed via the designed predefined‐time anti‐saturation compensator. On this basis, two different control laws are designed for such high‐order nonlinear systems by utilizing the backstepping technique, and a novel nonlinear filter is constructed to filter the virtual control signals, thus avoiding the “differential expansion” phenomenon. Moreover, a singularity‐free auxiliary function is designed to solve the singularity issue generated by the derivative of fractional power terms in the predefined‐time control algorithm framework. The closed‐loop system is proven to be semi‐globally predefined‐timely uniformly ultimately bounded (SGPTUUB) via constructing the suitable Lyapunov function. The difference and effectiveness of the two designed control laws are illustrated by the conducted simulations. Both of them allow the FJSR system to track the desired trajectory in a reasonably predefined time.

A Concurrent Event-Triggered Approach for Fuzzy Adaptive Control of Nonlinear Strict-Feedback Systems.

If a control input signal constructed by backstepping is used to generate an event-triggered control signal, then not only the real control input is discontinuous, but all the virtual control signals that make up the control signal are also discontinuous and have the same triggering instants with the control input. This fact makes the control design and stability analysis more difficult and complex via backstepping. This article focuses on this problem and works at coming up a new backstepping design procedure of event-triggered fuzzy adaptive control for nonlinear strict feedback systems. A concurrent event-triggered mechanism is proposed to ensure that the real control input and the virtual control signals have the same triggering instants. Then, a systemic backstepping design procedure is developed to construct event-triggered fuzzy adaptive controller. The Lyapunov technique for nonlinear impulsive system is employed to provide the closed-loop stability analysis. It is shown that the derived event-triggered fuzzy adaptive controller ensures that the closed-loop system output well follows the desired tracking trajectory and the other closed-loop signals remain bounded. Eventually, two examples are provided to further verify the applicability and reliability of the presented control scheme.

Event-Triggered Adaptive Control of Uncertain Strict-Feedback Nonlinear Systems Using Fully Actuated System Approach.

In most existing results, event-triggered controllers are designed based on the backstepping design approach for uncertain strict-feedback nonlinear systems (SFNSs). However, the transmitted signals in the event-triggered scheme (ETS) are discontinuous, which makes the repetitive differentiation of virtual control signals undefined. To overcome this deficiency, this article designs an event-triggered adaptive controller for uncertain SFNSs based on the fully actuated system (FAS) approach. Since the system states and the adaptive parameters are only updated at each triggering instant, the original dynamics cannot be completely removed by using the FAS approach, leading to that the asymptotic stability of the control system is difficult to be guaranteed. To handle such a problem, an ETS with the adaptive parameters is constructed based on Lyapunov method to compensate the effect of triggering. As a result, the asymptotic stability of the system can be guaranteed in the presence of nonlinearities without the global Lipschitz condition, and Zeno behavior can be avoided by using the contradiction method. Furthermore, a positive lower bound for interevent intervals can be got by adding a constant into the ETS, which ensures that the system is practically stabilizable under the bounded nonlinearities. Finally, two simulation examples are presented to demonstrate the superiority and effectiveness of the proposed approach.

Fast finite‐time adaptive backstepping containment control for high‐order stochastic nonlinear multi‐agent systems

SummaryIn this paper, the fast finite‐time backstepping containment control strategy is considered for high‐order stochastic multi‐agent systems. The addition of the finite‐time command filter avoids calculating explosion which occurs in the differential process of virtual control signals for the high‐order system on the traditional backstepping and makes convergence speed of control system faster. The influence of filtering errors generated by filter for control systems is eliminated by establishing error compensation systems. The fuzzy logic systems approximate unknown dynamics of systems. It proves the closed‐loop systems are practically fast finite‐time stable in mean square. The given simulation results show the effectiveness of the proposed control strategy.

Novel reaching law based predictive sliding mode control for lateral motion control of in‐wheel motor drive electric vehicle with delay estimation

AbstractThe lateral motion control of an in‐wheel motor drive electric vehicle (IWMD‐EV) necessitates an accurate measurement of the vehicle states. However, these measured states are always affected by delays due to sensor measurements, communication latencies, and computation time, which results in the degradation of the controller performance. Motivated by this issue, a novel reaching law based predictive sliding mode control (NRL‐PSMC) is proposed to maintain the lateral motion control of the IWMD‐EV subjected to unknown time delay. Initially, a PSMC framework is built, in which a predictor integrating with the sliding mode control is designed to eliminate the effect of time delay and generate the virtual control signals. Further, to alleviate the chattering phenomenon, a novel‐reaching law is developed, enabling the vehicle to track the desired states effectively. Subsequently, a dynamic control allocation technique is presented to optimally allocate the virtual control input to the actual control input. The accurate estimation of the aforementioned unknown delay is realized through a delay estimator. Finally, simulation and hardware‐in‐the‐loop experiments are performed for three specific driving manoeuvres, and the results demonstrate the effectiveness of the proposed controller design.

Distributed Formation Control with Obstacle and Collision Avoidance for Hypersonic Gliding Vehicles Subject to Multiple Constraints

Multiple hypersonic gliding vehicles’ (HGVs’) formation control problems with obstacle and collision avoidance are investigated in this paper, which is addressed in the stage of entry gliding. The originality of this paper stems from the formation control algorithm where constraints of dynamic pressure, heating rate, total aerodynamic load, control inputs, collision avoidance, obstacle avoidance, and the terminal states are considered simultaneously. The algorithm implements a control framework designed to be of two terms: distributed virtual controller and actual control input solver. The distributed virtual controller is based on distributed model predictive control with synchronous update strategy, where the virtual control signals are derived by the optimization simultaneously at each time step for each HGV under directed communication topology. Subsequently, according to the virtual control signals obtained, a coupled nonlinear equation set is solved to get actual control signals: each HGV’s bank angle together with the angle of attack. The actual control input solver adopts a feasible solution process to calculate the actual control signals while dealing with constraints. Finally, extensive numerical simulations are implemented to unveil the proposed algorithm’s performance and superiority.

Adaptive fuzzy neural network finite‐time command filtered control of n‐link robotic systems with actuator saturation

AbstractThe finite time tracking control of n‐link robotic system is studied for model uncertainties and actuator saturation. Firstly, a smooth function and adaptive fuzzy neural network online learning algorithm are designed to address the actuator saturation and dynamic model uncertainties. Secondly, a new finite‐time command filtered technique is proposed to filter the virtual control signal. The improved error compensation signal can reduce the impact of filtering errors, and the tracking errors of system quickly converge to a smaller compact set within finite time. Finally, adaptive fuzzy neural network finite‐time command filtered control achieves finite‐time stability through Lyapunov stability criterion. Simulation results verify the effectiveness of the proposed control.

Event-Triggered Adaptive Control for a Class of Nonlinear Systems With Mismatched Uncertainties via Intermittent and Faulty Output Feedback

Due to the difficulty in handling the issue of non-differentiable virtual control signals, there is still no available result considering output-triggering and sensor faults simultaneously for nonlinear systems subject to mismatched parametric uncertainties via backstepping design, even though the underlying problem is practically important and frequently encountered. In this paper, to deal with this challenging problem, several crucial design ideas are proposed in developing the control scheme. Firstly, to generate the continuous substitutes for the states, which are necessary in differentiating the virtual control signals in the backstepping design, we construct a state observer driven by intermittent and faulty output arising from output-triggering and sensor faults. Secondly, to ensure the existence of the first derivative of the virtual control signal, we use the estimated output signal to design the virtual control signals. Thirdly, to avoid the repeated differentiations of virtual control signals in backstepping design, we employ the idea of dynamic filtering technique. It is shown that all signals in the resulting closed-loop system are semi-globally uniformly ultimately bounded. Simulation examples are given to demonstrate the effectiveness of the proposed control strategy.