Low-complexity robust tracking of high-order nonlinear systems with application to underactuated mechanical dynamics

This paper presents a low-complexity design approach with predefined transient and steady-state tracking performance for global practical tracking of uncertain high-order nonlinear systems. It is assumed that all nonlinearities and their bounding functions are unknown and the reference signal is time varying. A simple output tracking scheme consisting of nonlinearly transformed errors and positive design parameters is presented in the presence of virtual and actual control variables with high powers where the error transformation technique using time-varying performance functions is employed. Contrary to the existing results using known nonlinear bounding functions of model nonlinearities, the proposed tracking scheme can be implemented without using nonlinear bounding functions (i.e., the feedback domination design), any adaptive and function approximation techniques for estimating unknown nonlinearities. It is shown that the tracking performance of the proposed control system is ensured within preassigned bounds, regardless of high-power virtual and actual control variables. The motion tracking problem of an underactuated unstable mechanical system with unknown model parameters and nonlinearities is considered as a practical application, and simulation results are provided to show the effectiveness of the proposed theoretical result.     

A low-complexity tracker design for uncertain nonholonomic wheeled mobile robots with time-varying input delay at nonlinear dynamic level

A low-complexity design problem of tracking scheme for uncertain nonholonomic mobile robots is investigated in the presence of unknown time-varying input delay. It is assumed that nonlinearities and parameters of robots and their bounds are unknown. Based on a nonlinear error transformation, a tracking control scheme ensuring preassigned bounds of overshoot, convergence rate, and steady-state values of a tracking error is firstly presented in the absence of input delay, without using any adaptive and function approximation mechanism to estimate unknown nonlinearities and model parameters and computing repeated time derivatives of certain signals. Then, we develop a low-complexity tracking scheme to deal with unknown time-varying input delay of mobile robots where some auxiliary signals and design conditions are derived for the design and stability analysis of the proposed tracking scheme. The boundedness of all signals in the closed-loop system and the guarantee of tracking performance with preassigned bounds are established through Lyapunov stability analysis. The validity of the proposed theoretical result is shown by a simulation example.     

Adaptive fault compensation control for a class of nonlinear systems with unknown time-varying delayed faults

An adaptive approximation design for the fault compensation (FC) control is addressed for a class of nonlinear systems with unknown multiple time-delayed nonlinear faults. The magnitude and occurrence time of the multiple faults with unknown time-varying delays are unknown. The function approximation technique using neural networks is employed to adaptively approximate the unknown nonlinear effects and changes in model dynamics due to the time-delayed faults. We design an adaptive memoryless FC control system with a prescribed performance bound to compensate the faults and to guarantee the transient performance of the tracking error from unexpected changes of system dynamics. The adaptive laws for neural networks and the bound of residual approximation errors are derived using the Lyapunov stability theorem, which are used for proving that the tracking error is preserved within the prescribed performance bound regardless of unknown multiple time-delayed nonlinear faults. Simulation examples are presented for illustrating the effectiveness of the proposed control methodology     

Actuator fault diagnosis for uncertain T–S fuzzy systems with local nonlinear models

This article investigates the problem of fault diagnosis (FD) for a class of nonlinear state-feedback control systems subject to parameter uncertainties. The considered nonlinear systems are described by T–S fuzzy models with local nonlinear parts and uncertain grades of membership. First, a general actuator fault model is proposed, which considers bias faults and gain faults. Then, a switching technique is introduced to address the unknown membership functions, external disturbances, faults, and their coupling. Furthermore, an adaptive FD observer design method combined with the switching technique is proposed to estimate the occurred actuator fault. It is noted that the obtained fault errors converge exponentially to zero. Finally, a numerical example of NSV reentry dynamic model is given to confirm the effectiveness of the new results.     

BLS-based formation control for nonlinear multi-agent systems with actuator fault and input saturation

This paper studies the formation control of a nonlinear multi-agent system based on a broad learning system under actuator fault and input saturation. Firstly, the multi-agent tracking error is proposed based on graph theory. Besides, fault tolerance should be considered when actuator fault exists. Meanwhile, the broad learning system is put forward to approximate the unknown nonlinear function in the multi-agent system. Then, an input saturation auxiliary system is introduced to reduce the adverse effects of input saturation constraints. At the same time, the disturbance observer technology is used to estimate the actuator failure as a lumped uncertainty. At last, dynamic surface control is introduced to realize formation control with actuator fault and input saturation. Obviously, it is difficult to design a controller with unknown nonlinear function, input saturation, and actuator fault existing in the multi-agent system. The Lyapunov method can prove the stability of the formation control. The simulation results verify the effectiveness of the controller.

     

Robust adaptive nonlinear control for uncertain control-affine systems and its applications

This paper addresses the robust tracking control problem for a class of uncertain nonlinear systems with time-varying parameters, perturbed by external disturbances. The unknown time-varying parameters and disturbances are neither required to be periodic nor to have known bounds. Depending on the characteristics of disturbance signals, two adaptive-based control algorithms are developed. First, an adaptive H _∞ control is designed that achieves: (i) an H _∞ tracking performance when the external disturbances are L ₂ signals, and (ii) the convergence of tracking error to zero if the disturbances are bounded and L ₂ signals. Then a novel adaptive control algorithm is proposed, only with the assumption of boundedness of disturbances, to drive the tracking error to zero. The designed tracking controllers are then used for controlling a cart-pendulum system, as an underactuated mechanical system, and chaos synchronization of uncertain Genesio–Tesi chaotic system. Numerical simulations are also given to demonstrate the effectiveness of the proposed control schemes.     

Resilient anti-disturbance dynamic surface control of uncertain strict-feedback systems subject to partial loss of actuator effectiveness

This paper is concerned with the tracking control of a class of uncertain strict-feedback systems subject to partial loss of actuator effectiveness, in addition to uncertain model dynamics and unknown disturbances. A resilient anti-disturbance dynamic surface control method is proposed to achieve stable tracking regardless of partial actuator faults. First, data-driven adaptive extended state observers are designed based on memory-based identifiers, such that the uncertain model dynamics, external disturbances and the unknown input gains due to actuator faults can be estimated. Next, a resilient anti-disturbance dynamic surface controller is developed based on recovered information from the data-driven adaptive extended state observers. After that, it is proven that the cascade system formed by the observer and controller is input-to-state stable. Finally, comparative studies are performed to validate the efficacy of the resilient anti-disturbance dynamic surface control method for nonlinear strict-feedback systems subject to partial loss of actuator effectiveness.

     

Adaptive tracking control for a class of nonlinear non-strict-feedback systems

This paper focuses on the adaptive tracking control problem for a class of nonlinear non-strict-feedback systems. By introducing a compact set, the restrictive assumption that the lower bounds of the control gain functions must be positive constants is canceled in the proposed method, and the compact set is proved to be invariant set eventually. The functions in non-strict-feedback system are no longer required to be differentiable, and the neural networks are constructively used to deal with the unknown system functions, which contain the whole state variables of the non-strict-feedback system. Furthermore, it is rigorously proved that all the closed-loop signals are bounded and the tracking error converges to a small residual set asymptotically. Finally, simulation examples are provided to demonstrate the effectiveness of the designed method.     

Robust synchronization of uncertain fractional-order chaotic systems with time-varying delay

This paper presents a new technique using a recurrent non-singleton type-2 sequential fuzzy neural network (RNT2SFNN) for synchronization of the fractional-order chaotic systems with time-varying delay and uncertain dynamics. The consequent parameters of the proposed RNT2SFNN are learned based on the Lyapunov–Krasovskii stability analysis. The proposed control method is used to synchronize two non-identical and identical fractional-order chaotic systems, with time-varying delay. Also, to demonstrate the performance of the proposed control method, in the other practical applications, the proposed controller is applied to synchronize the master–slave bilateral teleoperation problem with time-varying delay. Simulation results show that the proposed control scenario results in good performance in the presence of external disturbance, unknown functions in the dynamics of the system and also time-varying delay in the control signal and the dynamics of system. Finally, the effectiveness of proposed RNT2SFNN is verified by a nonlinear identification problem and its performance is compared with other well-known neural networks.     

Fault-tolerant sliding mode attitude control for flexible spacecraft under loss of actuator effectiveness

In this paper, a novel fault-tolerant attitude control synthesis is carried out for a flexible spacecraft subject to actuator faults and uncertain inertia parameters. Based on the sliding mode control, a fault-tolerant control law for the attitude stabilization is first derived to protect against the partial loss of actuator effectiveness. Then the result is extended to address the problem that the actual output of the actuators is constrained. It is shown that the presented controller can accommodate the actuator faults, even while rejecting external disturbances. Moreover, the developed control law can rigorously enforce actuator-magnitude constraints. An additional advantage of the proposed fault-tolerant control strategy is that the control design does not require a fault detection and isolation mechanism to detect, separate, and identify the actuator faults on-line; the knowledge of certain bounds on the effectiveness factors of the actuator is not used via the adaptive estimate method. The associated stability proof is constructive and accomplished by the development of the Lyapunov function candidate, which shows that the attitude orientation and angular velocity will globally asymptotically converge to zero. Numerical simulation results are also presented which not only highlight the ensured closed-loop performance benefits from the control law derived here, but also illustrate its superior fault tolerance and robustness in the face of external disturbances when compared with the conventional approaches for spacecraft attitude stabilization control.     

An output-feedback adaptive actuator failure compensation controller for systems with unknown state delays

This paper presents an output-feedback adaptive controller for a class of linear systems with unknown time-varying state delay and in the presence of actuator failures. We consider a common type of actuator failure in which some unknown system inputs may be stuck at some unknown fixed values and at unknown time instants. The adaptive controller is designed based on SPR–Lyapunov approach for relative degree one and two cases. Closed-loop system stability and asymptotic output tracking are proved using suitable Lyapunov–Krasovskii functional for each case. Simulation results are provided to demonstrate the effectiveness of the proposed results.     

Robust adaptive synchronization for a class of chaotic systems with actuator failures and nonlinear uncertainty

This paper is concerned with the robust adaptive synchronization problem for a class of chaotic systems with actuator failures and unknown nonlinear uncertainty. Combining adaptive method and linear matrix inequality (LMI) technique, a novel type of robust adaptive reliable synchronization controller is proposed, which can eliminate the effect of actuator fault and nonlinear uncertainty on systems. After solving a set of LMIs, synchronization error between the master chaotic and slave chaotic systems can converge asymptotically to zero. Finally, illustrate examples about chaotic Chua’s circuit system and Lorenz systems are provided to demonstrate the effectiveness and applicability of the proposed design method.     

Adaptive fixed-time control for nonlinear systems against time-varying actuator faults

Nonlinear Dynamics - The adaptive fixed-time control problem for nonlinear systems with time-varying actuator faults is investigated in this paper. A novel adaptive fixed-time controller is...     

Rich dynamics caused by delay in a nonchaotic Rulkov map

This paper proposes a new nonlinear control scheme incorporating a state observer, a fuzzy neural network (FNN) and a new Nussbaum function for strict-feedback nonlinear systems by considering several challenges. These challenges are external disturbances, uncertain dynamics, unmeasured states, constrained input, unknown control direction, singularity issue, and actuator’s faults of different types. The scheme uses approximations of the unknown system’s dynamics provided by the FNN, the system’s states variables estimation provided by a model-free high-gain observer, and the control direction provided by the Nussbaum function. Compared to existing schemes, in addition to the fact that the new scheme can tackle simultaneously all the aforementioned challenges with better tracking performances, it also cancels the assumption about the positive definiteness of the control gain function found in many works. Thus, the scheme suites for more applications as it can be applied in cases where the control gain can be either semi-negative/negative-definite, semi-positive/positive-definite. Furthermore, the knowledge of the bounds for uncertain dynamics, actuation faults, FNN approximation errors and external disturbances is not required as it is for many other schemes. The effectiveness of the scheme is illustrated by its successful application to three examples, which are the pitch angle control for a Boeing 747-100/200 represented by the ultimate approximate nonlinear longitudinal model over up-and-away flight regime, the trajectory tracking control of a one-link manipulator actuated by a brush DC (BDC) motor, and the position tracking control for an inverted pendulum.     

Finite-time tracking control for a class of high-order nonlinear systems and its applications

This study investigates the problem of finite-time tracking control for a class of high-order nonlinear systems. Due to the existence of uncertain time-varying control coefficient and unknown nonlinear perturbations in the nonlinear dynamics, the existing finite-time control results cannot solve the finite-time tracking problem for this kind of nonlinear systems. Based on the technique of adding a power integrator a variable structure control method is proposed. Under the proposed control law, it is shown that the reference signal can be tracked in a finite time. As an application of the proposed theoretic results, the problem of finite-time attitude tracking control for the roll channel of bank-to-turn missile is solved. Simulation results are given to demonstrate the effectiveness of the proposed method.     

Prescribed performance adaptive fuzzy output-feedback control of uncertain nonlinear systems with unmodeled dynamics

In this paper, an adaptive fuzzy output-feedback control approach is proposed for a class of uncertain nonlinear systems with unknown nonlinear functions, unmodeled dynamics, and without the measurements of the states. The fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy state observer is designed for estimating the unmeasured states. To solve the problem of unmodeled dynamics, the dynamical signal combined with changing supply function is incorporated into the backstepping recursive design technique. Under the framework of the backstepping control design technique and incorporated by the predefined performance technique, a new robust adaptive fuzzy output feedback control scheme is constructed. It is shown that all the signals of the resulting closed-loop system are bounded, and the system output remains an adjustable neighborhood of the origin with the prescribed performance bounds. A simulation example and comparison with the previous control methods are provided to show the effectiveness of the proposed control approach.     

Event-triggered robust adaptive control for uncertain nonlinear systems preceded by actuator dead-zone

It is both theoretically and practically important to investigate the problem of event-triggered adaptive tracking control for a class of uncertain nonlinear systems subject to actuator dead-zone, which aims at reducing communication rate and compensating actuator nonlinearity simultaneously. In this paper, to handle such a problem, an event-trigger based adaptive compensation scheme is proposed for the system preceded by actuator dead-zone. The challenges of this work can be roughly classified into two categories: how to compensate the nonsmooth dead-zone nonlinearity and how to eliminate the quantization signal effects caused by event-triggered strategy. To resolve the first challenge, a new decomposition of dead-zone mathematical model is employed so that dead-zone nonlinearity can be successively compensated by using robust approach. In addition, an adaptive controller and its triggering event are co-designed based on the relative threshold strategy, such that an asymptotic tracking performance can be ensured. The proposed scheme is proved to guarantee the globally bounded of all closed-loop signals and the asymptotic convergence performance of tracking error toward zero. The simulation results illustrate the effectiveness of our proposed control scheme.     

Fuzzy-approximation-based adaptive control of the chaotic permanent magnet synchronous motor

This paper focus on the problem of position tracking control for the chaotic permanent magnet synchronous motor drive system with parameter uncertainties. Fuzzy logic systems are used to approximate the nonlinearities and the adaptive backstepping technique is employed to construct controllers. The proposed adaptive fuzzy controllers guarantee that the tracking error converges to a small neighborhood of the origin. Compared with the conventional backstepping, the designed fuzzy controllers?? structure is very simple. Simulation results show that the proposed control scheme can suppress chaos of PMSM and guarantee the perfect tracking performance even under the unknown parameters.     

Adaptive fuzzy backstepping output feedback control of nonlinear uncertain time-delay systems based on high-gain filters

In this paper, an adaptive fuzzy output feedback control approach is developed for a class of SISO uncertain nonlinear strict-feedback systems. The considered nonlinear systems contain unknown nonlinear functions, unknown time-varying delays and unmeasured states. The fuzzy logic systems are first used to approximate the unknown nonlinear functions, and then a high-gain filter is designed to estimate the unmeasured states. Combining the backstepping recursive design technique and adaptive fuzzy control design, an adaptive fuzzy output feedback backstepping control method is developed. It is proved that the proposed adaptive fuzzy control approach can guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and both the observer error and tracking error converge to a small neighborhood of the origin. Two key advantages of our scheme are that (i) the high-gain filter is designed to estimate unmeasured states of time-delay nonlinear system, and (ii) the virtual control gains are functions. A simulation is included to illustrate the effectiveness of the proposed approach.     

Low-complexity differentiator-based decentralized fault-tolerant control of uncertain large-scale nonlinear systems with unknown dead zone

This paper investigates a low-complexity robust decentralized fault-tolerant prescribed performance control scheme for uncertain larger-scale nonlinear systems with consideration of the unknown nonlinearity, actuator failures, dead-zone input, and external disturbance. Firstly, a new simple finite-time-convergent differentiator is developed to obtain the unmeasurable state variables with arbitrary accuracy. Then, a time-varying sliding manifold involving the output tracking error and its high-order derivatives is constructed to tackle the high-order dynamics of subsystems. Sequentially, a robust decentralized fault-tolerant control scheme is proposed for each sliding manifold with prescribed convergence rate. The prominent advantage of the proposed fault-tolerant control scheme is that any specialized approximation technique, disturbance observer, and recursive procedure of backstepping technique are avoided, which dramatically alleviates the complexity of controller design. Finally, two groups of illustrative examples are employed to demonstrate the effectiveness of the low-complexity decentralized fault-tolerant control scheme under the developed finite-time-convergent differentiator.