Adaptive neural novel prescribed performance control for non-affine pure-feedback systems with input saturation

An error constraint control problem is considered for pure-feedback systems with non-affine functions being possibly in-differentiable. A new constraint variable is used to construct virtual control that guarantees the tracking error within the transient and steady-state performance envelopment. The new error transformation avoids non-differentiable problems and complex deductions caused by traditional error constraint approaches. A locally semi-bounded and continuous condition for non-affine functions is employed to ensure the controllability and transform the closed-loop system into a pseudo-affine form. An auxiliary system with bounded compensation term is proposed for nonlinear systems with input saturation. On the basis of backstepping technique, an adaptive neural controller is designed to handle unknown terms and circumvent repeated differentiations of virtual controls. The boundedness and convergence of the closed-loop system are proved by Lyapunov theory. Asymptotic tracking is achieved without violating control input constraint and error constraint. Two examples are performed to verify the theoretical findings.     

Fuzzy adaptive high-gain-based observer backstepping control for SISO nonlinear systems with dynamical uncertainties

In this paper, a fuzzy adaptive output feedback control approach is developed for a class of SISO strict-feedback nonlinear systems with unmeasured states, unmodeled dynamics, and dynamical disturbances. In the backstepping recursive design, fuzzy logic systems are used to approximate the unknown nonlinear functions, a fuzzy adaptive high-gain observer is designed to estimate the unmeasured states; a dynamic signal is incorporated into the control scheme to dominate the dynamic uncertainties. Using the states estimates and combining the backstepping design technique, a fuzzy adaptive output feedback control is constructed recursively. It is proved that the proposed fuzzy adaptive output feedback control scheme can guarantee the all signals in the closed-loop system are semiglobally uniformly ultimately bounded (SUUB), and the observer and tracking error converges to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated via an example.     

Observer-based adaptive fuzzy finite-time prescribed performance tracking control for strict-feedback systems with input dead-zone and saturation

This paper considers the problems of finite-time prescribed performance tracking control for a class of strict-feedback nonlinear systems with input dead-zone and saturation simultaneously. The unknown nonlinear functions are approximated by fuzzy logic systems and the unmeasurable states are estimated by designing a fuzzy state observer. In addition, a non-affine smooth function is used to approximate the non-smooth input dead-zone and saturated nonlinearity, and it is varied to the affine form via the mean value theorem. An adaptive fuzzy output feedback controller is developed by backstepping control method and Nussbaum gain method. It guarantees that the tracking error falls within a pre-set boundary at finite time and all the signals of the closed-loop system are bounded. The simulation results illustrate the feasibility of the design scheme.

     

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.     

Observer-based adaptive fuzzy backstepping dynamic surface control design and stability analysis for MIMO stochastic nonlinear systems

In this paper, an adaptive fuzzy backstepping output feedback dynamic surface control (DSC) approach is developed for a class of multiinput and multioutput (MIMO) stochastic nonlinear systems with immeasurable states. Fuzzy logic systems are firstly utilized to approximate the unknown nonlinear functions, and then a fuzzy state observer is designed to estimate the immeasurable states. By combining adaptive backstepping technique and dynamic surface control (DSC) technique, an adaptive fuzzy output feedback backstepping DSC approach is developed. The proposed control method not only overcomes the problem of ??explosion of complexity?? inherent in the backstepping design methods, but also the problem of the immeasurable states. It is proved that all the signals of the closed-loop adaptive control stochastic system are semiglobally uniformly ultimately bounded (SUUB) in probability, and the observer errors and the output of the system converge to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approach.     

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.     

Robust adaptive dynamic surface control design for a flexible air-breathing hypersonic vehicle with input constraints and uncertainty

The flight control problem of a flexible air-breathing hypersonic vehicle is presented in the presence of input constraint and aerodynamic uncertainty. A control-oriented model, where aerodynamic uncertainty and the strong couplings between the engine and flight dynamics are included, is derived to reduce the complexity of controller design. The flexible dynamics are viewed as perturbations of the model. They are not taken into consideration at the level of control design, the influence of which is evaluated through simulation. The control-oriented model is decomposed into velocity subsystem and altitude subsystem, which are controlled separately. Then robust adaptive controller is developed for the velocity subsystem, while the controller which combines dynamic surface control and radial basis function neural network is designed for the altitude subsystem. The unknown nonlinear function is approximated by the radial basis function neural network. Minimal-learning parameter technique is utilized to estimate the maximum norm of ideal weight vectors instead of their elements to reduce the computational burden. To handle input constraints, additional systems are constructed to analyze their impact, and the states of the additional systems are employed at the level of control design and stability analysis. Besides, “explosion of terms” problem in the traditional backstepping control is circumvented using a first-order filter at each step. By means of Lyapunov stability theory, it is proved theoretically that the designed control law can assure that tracking error converges to an arbitrarily small neighborhood around zero. Simulations are performed to demonstrate the effectiveness of the presented control scheme in coping with input constraint and aerodynamic uncertainty.     

Adaptive fuzzy output feedback control of uncertain nonlinear systems with nonsymmetric dead-zone input

In this paper, we present an adaptive control scheme for a class of uncertain nonlinear system with unknown nonsymmetric dead-zone nonlinearity. It is assumed that the system states are unmeasurable. Therefore, an observer is designed to estimate those unmeasured states. The controller is designed by using the backstepping control design procedure. The proposed adaptive scheme requires only the information that the dead-zone slopes are bounded. The new control scheme ensures bounded-error trajectory tracking and the boundedness of all the signals in the closed-loop. The feasibility is investigated by an illustrative simulation example.     

Direct adaptive neural control of chaos in the permanent magnet synchronous motor

In this paper, a direct adaptive neural speed tracking control is addressed for the chaotic permanent magnet synchronous motor (PMSM) drive systems via backstepping. Neural networks are directly used to approximate unknown and desired control signals and a novel direct adaptive tracking controller is constructed via backstepping. The proposed adaptive neural controllers guarantee that the tracking error converges to a small neighborhood of the origin. Compared with the conventional backstepping method, the designed neural controller??s structure is very simple. Simulation results show that the proposed control scheme can suppress the chaos of PMSM and guarantees the perfect tracking performance even with the existence of unknown parameters.     

Backstepping control for the optoelectronic stabilized platform based on adaptive fuzzy logic system and nonlinear disturbance observer

A composite controller based on a backstepping controller with an adaptive fuzzy logic system and a nonlinear disturbance observer is proposed in this paper to address the disturbance and uncertainty issues in the control of the optoelectronic stabilized platform. The matched and unmatched disturbances and system uncertainty are included in the stabilized platform model. The system's uncertainty and disturbance are approximated and estimated using an adaptive fuzzy logic system and a nonlinear disturbance observer. Moreover, the backstepping control algorithm is utilized to control the system. The simulations are performed in four states to confirm the viability of the proposed control technique. The proportional integral controller, proportional integral-disturbance observer controller, and fuzzy backstepping controller are contrasted with the proposed controller. It has been noted that the proposed controller's instantaneous disturbance's highest value is 5.1°/s. The maximal value of the coupling output for the two gimbals utilizing the proposed controller, however, is 0.0008°/s and 0.0018°/s, respectively. The findings presented here demonstrate that the backstepping controller, which is based on an adaptive fuzzy logic system and a nonlinear disturbance observer, is capable of precise tracking and dynamic tracking of a stabilized platform under disturbance and uncertainty.

     

Reduced-order observer-based backstepping tracking control for a class of stochastic nonlinear systems

In this paper, an output feedback tracking control scheme is put forwarded for a class of stochastic nonlinear systems, whose dynamics involve not only unknown parameters but also unmeasured states multiplied by output nonlinearities. A type of reduced-order observer is first developed. By adding some output related items in the observer, the estimation error realize global asymptotic convergence under disturbance free condition, and global bounded convergence when considering disturbance. Besides, the dimension of the closed-loop system is reduced, and the update law of this observer gain is beneficial for steady tracking. After the observer was established, the controller is constructed by employing the adaptive backstepping approach, and a smooth nonsingular robust item is proposed to handle the influence of stochastic disturbance. All the signals in the closed system is proved to be globally bounded in probability. Moreover the output tracking error converges to an arbitrary small neighborhood of the origin by proper choosing of the design parameters. The simulation results based on current control scheme and the comparison with the previous method illustrate that the proposed output feedback scheme realizes good tracking performance and strong ability on stochastic disturbance attenuation.     

Observer-based adaptive fuzzy backstepping control of MIMO stochastic nonlinear strict-feedback systems

In this paper, an adaptive fuzzy output feedback control approach is proposed for a class of multiinput and multioutput (MIMO) uncertain stochastic nonlinear strict-feedback systems 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. Utilizing the designed the fuzzy state observer and by combining the adaptive backstepping control design, an adaptive fuzzy output feedback control approach is developed. It is proved that the proposed control approach can guarantee that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded (SUUB) in probability, and the observer errors and the output of the system converge to a small neighborhood of the origin by appropriate choice of the design parameters. A simulation example is provided to show the effectiveness of the proposed approach.     

Adaptive output feedback control of uncertain nonlinear chaotic systems based on dynamic surface control technique

In this paper, an adaptive output feedback control algorithm based on the dynamic surface control (DSC) is proposed for a class of uncertain chaotic systems. Because the system states are assumed to be unavailable, an observer is designed to estimate those unavailable states. The main advantage of this algorithm can overcome the problem of “explosion of complexity” inherent in the backstepping design. Thus, the proposed control approach is simpler than the traditional backstepping control for the uncertain chaotic systems. The stability analysis shows that the system is stable in the sense that all signals in the closed-loop system are uniformly ultimately bounded (UUB) and the system output can track the reference signal to a bounded compact set. Finally, an example is provided to illustrate the effectiveness of the proposed control system.     

基于反演高阶滑模的飞行器最优末制导律

针对传统最优末制导律鲁棒性能较弱,且对参数摄动及外扰敏感的不足,而滑模控制对扰动具有较强鲁棒性的优点,提出一种新的基于反演准连续高阶滑模的最优末制导律,其中反演控制能够有效保证系统全局稳定性,而准连续高阶滑模控制则用于消除扰动影响。为了去除抖振效果,引入自适应超螺旋算法在线更新控制参数以消除符号函数导致的高频抖振影响。仿真结果表明:飞行器在该末制导律导引下,弹目视线角速率快速收敛,从而保证飞行器有很高的命中精度;鲁棒性较强;能够较好的满足约束条件要求。     

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.     

Adaptive fuzzy backstepping output feedback control for a class of MIMO time-delay nonlinear systems based on high-gain observer

In this paper, an adaptive fuzzy backstepping output feedback control approach is developed for a class of multiinput and multioutput (MIMO) nonlinear systems with time delays and immeasurable states. Fuzzy logic systems are employed to approximate the unknown nonlinear functions, and an adaptive fuzzy high-gain observer is developed to estimate the unmeasured states. Using the designed high-gain observer, and combining the fuzzy adaptive control theory with the backstepping approach, an adaptive fuzzy output feedback control is constructed recursively. It is proved that all the signals of the closed-loop adaptive control system are semiglobally uniformly ultimately bounded (SUUB) and the tracking error converges to a small neighborhood of the origin.     

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.     

Fuzzy adaptive dynamic surface control for a single-link flexible-joint robot

In this paper, a fuzzy adaptive controller is proposed for a single-link flexible-joint robot. Fuzzy logic systems are used to approximate unknown nonlinearities, and then a fuzzy state observer is designed to estimate the immeasurable states. By combining the adaptive backstepping design with dynamic surface control (DSC) technique, a fuzzy adaptive output-feedback backstepping control approach is developed. It is proved that all the signals of the resulting closed-loop system are semiglobally uniformly ultimately bounded (SGUUB), and both the observer and tracking errors converge to a small neighborhood of the origin by appropriate choosing the design parameters. The simulation results are provided to demonstrate the effectiveness of the proposed controller. Two key advantages of our scheme are that (i)?the proposed control method does not require that the link velocity and actuator velocity of single-link flexible-joint robot be measured directly, and (ii)?the problem of ??explosion of complexity?? is avoided.     

Real-time robust adaptive control of robots subjected to actuator voltage constraint

This paper is concerned with the problem of design and implementation of a robust adaptive control strategy for electrically driven robots while considering to the constraints on the actuator voltage input. The proposed approach provides a flexible design framework and stable to deal with robustness compared with many other adaptive controllers, such as halting/slowing adaption techniques and adaptively adjusting command signal, which are proposed for robotic applications. The control design procedure is based on a new form of universal approximation theory and using Stone–Weierstrass theorem, to avoid saturation besides being robust against both structured and unstructured uncertainties associated with external disturbances and actuated manipulator dynamics. Moreover, the proposed approach eliminates problems arising from classic adaptive feedforward control scheme. The analytical studies as well as experimental results produced using MATLAB/SIMULINK external mode control on a two degree of freedom electrically driven robot demonstrate high performance of the proposed control schemes.     

System modeling and tracking control of mobile manipulator subjected to dynamic interaction and uncertainty

Trajectory tracking of a mobile manipulator is a challenging research because of its complex nonlinearity and dynamics. This paper presents an adaptive control strategy for trajectory tracking of a mobile manipulator system that consists of a wheeled platform and a modular manipulator. When a robot system moves in the presence of sliding, it is difficult to accurately track its trajectory by applying the backstepping approach, even if we employ a non-ideal kinematic model. To address this problem, we propose using a combination of adaptive fuzzy control and backstepping approach based on a dynamic model. The proposed control scheme considers the dynamic interaction between the platform and manipulator. To accurately track the trajectory, we propose a fuzzy compensator in order to compensate for modeling uncertainties such as friction and external disturbances. Moreover, to reduce approximation errors and ensure system stability, we include a robust term to the adaptive control law. Simulation results obtained by comparing several cases reveal the presence of the dynamic interaction and confirm the robustness of the designed controller. Finally, we demonstrate the effectiveness and merits of the proposed control strategy to counteract the modeling uncertainties and accurately track the trajectory.