Nonlinear adaptive learning control for unknown time‐varying parameters and unknown time‐varying delays

A new adaptive learning control approach is proposed for a class of first‐order nonlinear systems with two unknown time‐varying parameters and an unknown time‐varying delay. By reconstructing the system equation, all unknown time‐varying terms, including the time‐varying delay, are combined into an unknown periodic time‐varying vector, which is estimated by a periodic adaptive mechanism. By constructing a Lyapunov–Krasovskii‐like composite energy function (CEF), we prove the boundedness of all signals and the convergence of the tracking error. The results are extended to two classes of high‐order nonlinear systems with mixed parameters. Three simulation examples are provided to illustrate the effectiveness of the control algorithms proposed in this paper. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Discrete‐time adaptive control for nonlinear systems with periodic parameters: A lifting approach

In this paper we develop a general discrete‐time adaptive control approach suitable for nonlinear systems with periodic parametric uncertainties. The underlying idea of the new approach is to convert the periodic parameters into an augmented constant parametric vector by a lifting technique. The novelty of this approach is the establishment of a bridge between classical adaptive control problems and periodic adaptive control problems. As such, the well‐established discrete‐time adaptive control schemes can be easily applied to various control problems with periodic parameters, such as plants that do not meet the linear growth condition, plants that are nonlinear in parameters, plants with unknown control directions, plants in parametric‐strict‐feedback form, etc. Another major advantage of the new adaptive control is the ability to adaptively update all parameters in parallel, hence expedite the adaption speed. The effectiveness of the proposed approach is illustrated by simulation. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust adaptive fault‐tolerant tracking control for uncertain linear systems with time‐varying performance bounds

In this paper, the problem of robust adaptive fault‐tolerant tracking control with time‐varying performance bounds is investigated for a class of linear systems subject to parameter uncertainties, external disturbances and actuator failures. In order to ensure the norm of the tracking error less than the user‐defined time‐varying performance bounds, we propose a new control strategy which is predicated on the generalized restricted potential function. Compared with the existing result, a novel method which provides two design freedoms is developed to reduce the tracking error. According to the online estimation information provided by adaptive mechanism, a fault‐tolerant tracking control method guaranteeing time‐varying performance bounds is developed for robust tracking of reference model. It is shown that the closed‐loop signals are bounded and the tracking error within an a priori given, time‐varying performance bounds. A simulation result is provided to demonstrate the efficacy of the proposed fault‐tolerant tracking control method.     

Discrete‐time repetitive controller for time‐delay systems with disturbance observer

A novel discrete‐time repetitive controller design for time‐delay systems subject to a periodic reference and exogenous periodic disturbances is presented. The main idea behind the proposed approach is to take advantage of the plant delay in the controller design, and not to compensate for the effect of this delay. To facilitate this concept, we introduce an appropriate time‐delay and a compensator in a positive feedback connection with the plant, such that a generator for periodic signals is constructed. Then a proportional controller is used to stabilize the closed‐loop system. The tracking control capability is thus guaranteed according to the internal model principle (IMP). In addition, to attenuate external periodic disturbances, a disturbance observer (DO) is developed to simultaneously achieve reference tracking and disturbance rejection. The possible fractional delay due to the digital discretization is handled by using a fractional delay filter approximation. The proposed controller has a simple structure, in which only a proportional parameter and a low‐pass filter are required to be chosen. The closed‐loop stability conditions and a robustness analysis under model uncertainties are studied. Numerical simulations and practical experiments on a servo motor system are conducted to verify the feasibility and simplicity of the proposed controller. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Adaptive multivariable finite‐time continuous fault‐tolerant control of rigid spacecraft

The problem of fault‐tolerant attitude tracking control for rigid spacecraft in the presence of inertia uncertainties, actuator faults, and external disturbances is investigated in this paper. A novel adaptive finite‐time continuous fault‐tolerant control strategy is developed by combining the fast nonsingular terminal sliding mode surface and the adaptive multivariable super‐twisting algorithm, which improves the robustness while preserving high accuracy and finite‐time convergence. The main features of the control strategy are the double‐layer adaptive algorithm based on equivalent control, which ensures nonoverestimation of the control gain and the continuous controller, which maintains better property of chattering reduction. Finally, the efficiency of the proposed controller is illustrated by numerical simulations.     

Fixed‐time attitude tracking control for spacecraft based on adding power integrator technique

In this article, the fixed‐time attitude tracking problem for rigid spacecraft is investigated based on the adding‐a‐power‐integrator control technique. First, a fixed‐time attitude tracking controller is designed to guarantee fixed‐time convergence of tracking errors. Then, by considering the presence of random disturbance and actuator faults, an adaptive fault‐tolerant attitude tracking controller is designed to guarantee tracking errors converge to a residual set of zero in a fixed time. The complete bounds on settling time are derived independently of initial conditions. The simulation results illustrate the highly precise and robust attitude control performance obtained by using the proposed controllers.     

Adaptive finite‐time control for nonlinear teleoperation systems with asymmetric time‐varying delays

This paper addresses the adaptive finite‐time control problem of nonlinear teleoperation system in the presence of asymmetric time‐varying delays. To achieve the finite‐time position tracking, a novel adaptive finite‐time coordination algorithm based on subsystem decomposition is developed. By introducing a switching‐technique‐based error filtering into our design framework, the complete closed‐loop master (slave) teleoperation system is modeled as a special class of switched system, which is composed of two subsystems. To analyze such system, a finite‐time state‐independent input‐to‐output stability criterion is first developed for some normal switched nonlinear delayed systems. Then based on the classical Lyapunov–Krasovskii method, the stability of complete closed‐loop systems is obtained. It is shown that the proposed scheme can make the position errors converge into a deterministic domain in finite time when the robots continuously contact with human operator and/or the environment in the presence of asymmetric time‐varying delays. Finally, the simulation results are given to demonstrate the effectiveness. Copyright © 2015 John Wiley & Sons, Ltd.     

Discrete‐time low‐gain control of linear systems with input/output nonlinearities

Discrete‐time low‐gain control strategies are presented for tracking of constant reference signals for finite‐dimensional, discrete‐time, power‐stable, single‐input, single‐output, linear systems subject to a globally Lipschitz, non‐decreasing input nonlinearity and a locally Lipschitz, non‐decreasing, affinely sector‐bounded output nonlinearity (the conditions on the output nonlinearities may be relaxed if the input nonlinearity is bounded). Both non‐adaptive and adaptive gain sequences are considered. In particular, it is shown that applying error feedback using a discrete‐time ‘integral’ controller ensures asymptotic tracking of constant reference signals, provided that (a) the steady‐state gain of the linear part of the plant is positive, (b) the positive gain sequence is ultimately sufficiently small and (c) the reference value is feasible in a very natural sense. The classes of input and output nonlinearities under consideration contain standard nonlinearities important in control engineering such as saturation and deadzone. The discrete‐time results are applied in the development of sampled‐data low‐gain control strategies for finite‐dimensional, continuous‐ time, exponentially stable, linear systems with input and output nonlinearities. Copyright © 2001 John Wiley & Sons, Ltd.     

Adaptive finite‐time fault‐tolerant tracking control for a class of MIMO nonlinear systems with output constraints

In this work, we present a novel adaptive finite‐time fault‐tolerant control algorithm for a class of multi‐input multi‐output nonlinear systems with constraint requirement on the system output tracking error. Both parametric and nonparametric system uncertainties can be effectively dealt with by the proposed control scheme. The gain functions of the nonlinear systems under discussion, especially the control input gain function, can be not fully known and state‐dependent. Backstepping design with a tan‐type barrier Lyapunov function and a new structure of stabilizing function is presented. We show that under the proposed control scheme, finite‐time convergence of the output tracking error into a small set around zero is guaranteed, while the constraint requirement on the system output tracking error will not be violated during operation. An illustrative example on a robot manipulator model is presented in the end to further demonstrate the effectiveness of the proposed control scheme. Copyright © 2016 John Wiley & Sons, Ltd.     

Razumikhin–Nussbaum‐lemma‐based adaptive neural control for uncertain stochastic pure‐feedback nonlinear systems with time‐varying delays

This paper addresses the problem of adaptive neural control for a class of uncertain stochastic pure‐feedback nonlinear systems with time‐varying delays. Major technical difficulties for this class of systems lie in: (1) the unknown control direction embedded in the unknown control gain function; and (2) the unknown system functions with unknown time‐varying delays. Based on a novel combination of the Razumikhin–Nussbaum lemma, the backstepping technique and the NN parameterization, an adaptive neural control scheme, which contains only one adaptive parameter is presented for this class of systems. All closed‐loop signals are shown to be 4‐Moment semi‐globally uniformly ultimately bounded in a compact set, and the tracking error converges to a small neighborhood of the origin. Finally, two simulation examples are given to demonstrate the effectiveness of the proposed control schemes. Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive quantized tracking control for uncertain switched nonstrict‐feedback nonlinear systems with discrete and distributed time‐varying delays

This paper is concerned with an adaptive tracking problem for a more general class of switched nonstrict‐feedback nonlinear time‐delay systems in the presence of quantized input. The system structure in a nonstrict‐feedback form, the discrete and distributed time‐varying delays, the sector‐bounded quantized input, and arbitrary switching behavior are involved in the considered systems. In particular, to overcome the difficulties from the distributed time‐varying delays and the sector‐bounded quantized input, the mean‐value theorem for integrals and some special techniques are exploited respectively. Moreover, by combining the Lyapunov‐Razumikhin method, dynamic surface control technique, fuzzy logic systems approximation, and variable separation technique, a quadratic common Lyapunov function is easily built for all subsystems and a common adaptive quantized control scheme containing only 1 adaptive parameter is proposed. It is shown that the tracking error converges to an adjustable neighborhood of the origin whereas all signals of the closed‐loop systems are semiglobally uniformly ultimately bounded. Finally, 2 simulation examples are provided to verify the feasibility and effectiveness of the proposed design methodology.     

Adaptive disturbance observer‐based finite‐time continuous fault‐tolerant control for reentry RLV

The control effectors of reusable launch vehicle (RLV) can produce significant perturbations and faults in reentry phase. Such a challenge imposes tight requirements to enhance the robustness of vehicle autopilot. Focusing on this problem, a novel finite‐time fault‐tolerant control strategy is proposed for reentry RLV in this paper. The key of this strategy is to design an adaptive‐gain multivariable finite‐time disturbance observer (FDO) to estimate the synthetical perturbation with unknown bounds, which is composed of model uncertainty, external disturbance, and actuator fault considered as the partial loss of actuator effectiveness in this work. Then, combined with the finite‐time high‐order observer and differentiator, a continuous homogeneous second‐order sliding mode controller based on the terminal sliding mode and super‐twisting algorithm is designed to achieve a fast and accurate RLV attitude tracking with chattering attenuation. The main features of the integrated control strategy are that the adaptation algorithm of FDO can achieve non‐overestimating values of the observer gains and the second‐order super‐twisting sliding mode approach can obtain a more elegant solution in finite time. Finally, simulation results of classical RLV (X‐33) are provided to verify the effectiveness and robustness of the proposed fault‐tolerant controller in tracking the guidance commands. Copyright © 2017 John Wiley & Sons, Ltd.     

Straight‐Line Tracking Control of an Agricultural Vehicle with Finite‐Time Control Technique

For the agricultural vehicle straight‐line tracking system, three control algorithms based upon the finite‐time control technique have been proposed to force the vehicle to track a straight line. Without considering the lumped disturbance, a backstepping‐like finite‐time state‐feedback controller is first developed. On this basis, an adaptive state‐feedback controller in conjunction with integral sliding mode is further developed in the presence of the lumped disturbance. Finally, a sliding mode disturbance observer is given to estimate the lumped disturbance, and the composite control scheme is presented. Under the composite controller, the lumped disturbance can be compensated and thus the disturbance rejection property has been significantly improved. Simulation results verify the proposed control algorithms.     

Robust adaptive fixed‐time tracking control of 6‐DOF spacecraft fly‐around mission for noncooperative target

The fixed‐time relative position tracking and attitude synchronization control problem of a spacecraft fly‐around mission for a noncooperative target in the presence of parameter uncertainties and external disturbances is investigated. Firstly, a novel and coupled relative position and attitude motion model for a noncooperative fly‐around mission is established. Subsequently, a novel nonsingular fast terminal sliding mode (NFTSM) surface is developed, and the explicit estimation of the convergence time independent of initial states is provided. Fair and systematic comparisons among several typical terminal sliding modes show that the designed NFTSM has faster convergence performance than the fast terminal sliding mode. Then, a robust integrated adaptive fixed‐time NFTSM control law with no precise knowledge of the mass and inertia matrix and disturbances by combining the nonsingular terminal sliding mode technique with an adaptive methodology is proposed, which can eliminate the chattering phenomenon and guarantee that the relative position and attitude tracking errors can converge into the small regions containing the origin in fixed time. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed control schemes.     

Monotonic convergence and robustness of higher‐order gain‐adaptive iterative learning control

For a class of repetitive linear discrete time‐invariant systems with higher relative degree, a higher‐order gain‐adaptive iterative learning control (HOGAILC) is developed while minimizing the energy increment of two adjacent tracking errors with the argument being the iteration‐time‐variable learning‐gain vector (ITVLGV). By taking advantage of rows/columns exchanging transformation of matrix, the ITVLGV is achieved in an explicit form which is dependent upon the system Markov parameters and adaptive to the iterationwise tracking‐error vector. Algebraic derivation demonstrates that the HOGAILC is strictly monotonously convergent. On the basis of the adaptive mode, a damping quasi‐HOGAILC strategy is exploited while the uncertainties of the system Markov parameters exist. Rigorous analysis delivers that the damping quasi‐scheme is strictly monotonically convergent and thus the HOGAILC mechanism is robust to a wider range of uncertainty of system parameters and the damping factor may relax the uncertainty range. Numerical simulations are made to illustrate the validity and the effectiveness.     

Adaptive Fault‐Tolerant Attitude Tracking Control of Rigid Spacecraft on Lie Group with Fixed‐Time Convergence

This paper investigates the fixed‐time attitude tracking problem for rigid spacecraft in the presence of inertial uncertainties, external disturbances, actuator faults, and input saturation constraints. The logarithm map is first utilized to transform the tracking problem on SO(3) into the stabilization one on its associated Lie algebra ( ). A novel nonsingular fixed‐time‐based sliding mode is designed, which not only avoids the singularity but also guarantees that the convergence time of tracking errors along the sliding surface is independent of the state value. Then, an adaptive fault‐tolerant control law is constructed, in which an online adaptive law is incorporated to estimate the upper boundary of the lumped uncertainties. The combined control scheme enforces the system state to reach a neighborhood of the sliding surface in the sense of the fixed‐time concept. The key feature of the resulting control scheme is that it can accommodate actuator failures under limited control torque without the knowledge of fault information. Numerical simulations are finally performed to demonstrate the effectiveness of the proposed fixed‐time controllers.     

Adaptive fault‐tolerant time‐varying formation tracking for multiagent systems with multiple leaders

In this paper, an adaptive fault‐tolerant time‐varying formation control problem for nonlinear multiagent systems with multiple leaders is studied against actuator faults and state‐dependent uncertainties. Simultaneously, the followers form a predefined formation while tracking reference signal determined by the convex combination of the multiple leaders. Based on the neighboring relative information, an adaptive fault‐tolerant formation time‐varying control protocol is constructed to compensate for the influences of actuator faults and model uncertainties. In addition, the updating laws can be adjusted online through the adaptive mechanism, and the proposed control protocol can guarantee that all the signals in the closed‐loop systems are bounded. Lyapunov‐like functions are addressed to prove the stability of multiagent systems. Finally, two examples are provided to demonstrate the effectiveness of the theoretical results.     

Robust Adaptive Fractional‐Order Terminal Sliding Mode Control for Lower‐Limb Exoskeleton

This paper introduces a robust adaptive fractional‐order non‐singular fast terminal sliding mode control (RFO‐TSM) for a lower‐limb exoskeleton system subject to unknown external disturbances and uncertainties. The referred RFO‐TSM is developed in consideration of the advantages of fractional‐order and non‐singular fast terminal sliding mode control (FONTSM): fractional‐order is used to obtain good tracking performance, while the non‐singular fast TSM is employed to achieve fast finite‐time convergence, non‐singularity and reducing chattering phenomenon in control input. In particular, an adaptive scheme is formulated with FONTSM to deal with uncertain dynamics of exoskeleton under unknown external disturbances, which makes the system robust. Moreover, an asymptotical stability analysis of the closed‐loop system is validated by Lyapunov proposition, which guarantees the sliding condition. Lastly, the efficacy of the proposed method is verified through numerical simulations in comparison with advanced and classical methods.     

The Framework for Linear Periodic Time‐Delay Systems Based on Semi‐Discretization: Stability Analysis and Control

Stability analysis and control for linear periodic time‐delay systems are investigated in this paper. In this framework, a semi‐discretization method is used to develop a mapping of the system response in a finite‐dimensional state space. With the mapping, the stability region and stability boundary can be identified by comparing the maximum absolute value of its eigenvalues to 1. More importantly, an efficient stability criterion is presented for periodic neutral systems. In addition, minimization of the maximum absolute value of the mapping's eigenvalues leads to optimal control gains. The tracking control problem is also discussed. Two numerical examples are given to illustrate the effectiveness of the proposed method.     

Finite‐Time Fault‐Tolerant Control for a Class of Non‐Affine Nonlinear System Using Sliding Mode Disturbance Observer

This study investigates a finite‐time fault‐tolerant control scheme for a class of non‐affine nonlinear system with actuator faults and unknown disturbances. A global approximation method is applied to non‐affine nonlinear system to convert it into an affine‐like expression with accuracy. An adaptive terminal sliding mode disturbance observer is proposed to estimate unknown compound disturbances in finite time, including external disturbances and system uncertainties, which enhances system robustness. Controllers based on finite‐time Lyapunov theory are designed to force tracking errors to zero in finite time. Simulation results demonstrate the effectiveness of proposed method.