Observer design and output feedback stabilization for nonlinear multivariable systems with diffusion PDE-governed sensor dynamics

This paper addresses the problems of observer design and output feedback stabilization for a class of nonlinear multivariable systems, where the nonlinear system dynamics are described by ordinary differential equations (ODEs), and the sensor dynamics are governed by diffusion partial differential equations (PDEs). Based on the Luenberger observer theory, a Luenberger-type PDE-ODE cascaded observer is derived to estimate the state variables of the system. Then, an observer-based output feedback stabilizing controller is developed. The exponential stability of both the observer error system and closed-loop control system is proven via the Lyapunov direct method. Finally, numerical examples are provided to illustrate the effectiveness of the proposed design methods.     

Fuzzy observer-based command filtered tracking control for uncertain strict-feedback nonlinear systems with sensor faults and event-triggered technology

For the trajectory tracking problem of nth-order uncertain nonlinear systems with sensor faults, a fuzzy controller based on command filtered and event-triggered technology is designed to improve the tracking error of the system. Concurrently, a fault-tolerant control scheme is introduced to effectively solve the problem of sudden output sensor failure. Additionally, the proposed controller can also greatly avoid complexity explosion problem of derivations of virtual control laws, which makes the design of the controller simpler. Furthermore, an effective observer is designed to solve the problem of system state immeasurability. Therefore, the proposed control scheme makes the design of the controller more convenient and flexible. According to Lyapunov stability theory, it is proved that all closed-loop signals are uniformly and ultimately bounded. Finally, two simulation examples of second-order nonlinear system and single-link robot show the effectiveness of the proposed scheme.

     

Trajectory tracking control using velocity observer and disturbances observer for uncertain robot manipulators without tachometers

This paper deals with trajectory tracking control for rigid robot manipulators with model uncertainty and subject to external disturbances. The approach suggested herein does not require velocity measurement, because these robots are not equipped by tachometers for velocity measurement. For this purpose, two observers are proposed. The first is a velocity observer to estimate the missing velocity, and the second one is a disturbance observer to estimate the disturbance. Thereafter, these observers are integrated with the controller. Furthermore, semi-global asymptotic stability conditions of the composite controller consisting of a nonlinear controller, the velocity observer and the disturbance observer are established, and an estimate region of attraction is also given. This proof is based on Lyapunov theory. Finally, simulation results on two-links manipulator are provided to illustrate the effectiveness of the velocity observer based control using disturbance estimation (namely VOBCDE), when the Coulomb and viscous friction is considered as an external disturbance.     

Fuzzy adaptive output feedback control for robotic systems based on fuzzy adaptive observer

In this paper, a fuzzy adaptive output feedback control scheme based on fuzzy adaptive observer is proposed to control robotic systems with parameter uncertainties and external disturbances. It is supposed that only the joint positions of the robotic system can be measured, whereas the joint velocities are unknown and unmeasured. First, a fuzzy adaptive nonlinear observer is presented to estimate the joint velocities of robotic systems, and the observation errors are analyzed using strictly positive real approach and Lyapunov stability theory. Next, based on the observed joint velocities, a fuzzy adaptive output feedback controller is developed to guarantee stability of closed-loop system and achieve a certain tracking performance. Based on the Lyapunov stability theorem, it is proved that all the signals in closed-loop system are bounded. Finally, simulation examples on a two-link robotic manipulator are presented to show the efficiency of the proposed method.     

Adaptive fuzzy output-feedback control of uncertain SISO nonlinear systems

The output-feedback control problem of a class of uncertain SISO nonlinear systems is investigated based on an indirect adaptive fuzzy approach. Because the system states are not required to be available for measurement, an observer is designed to estimate the system states. Compared with the existing results in the observer design, the main advantages of the proposed adaptive fuzzy output-feedback control approach are as follows: (1) It does not require to assume that the sign of the control gain coefficient is known and Nussbaum-gain technique is utilized to control the nonlinear systems with both the unknown control direction and the unmeasured states; (2) The observer in this paper is designed for the states rather than the tracking errors, then it is convenient to compute; (3) The controller singularity problem is perfectly avoided. The stability of the closed-loop system is analyzed by using Lyapunov method. A simulation example is given to verify the feasibility of the proposed approach.     

Adaptive synchronization for uncertain complex dynamical network using fuzzy disturbance observer

This paper proposes a robust adaptive controller design method for synchronization of a complex dynamical network with uncertainty and disturbance. A fuzzy disturbance observer is used to estimate the overall disturbances without any prior knowledge about them. The proposed control method globally asymptotically synchronizes the network using adaptation laws obtained by using Lyapunov stability theory. The proposed method is applied to two chaotic systems and the results show the effectiveness of the approach.     

Adaptive tracking control of wheeled mobile robots with unknown longitudinal and lateral slipping parameters

An adaptive control approach is proposed for trajectory tracking of wheeled mobile robot (WMR) with unknown longitudinal and lateral slipping. A kinematic model of tracked WMR is established in this paper, in which both longitudinal and lateral slipping are considered and processed as three time-varying parameters. Sliding mode observer is then introduced to real time estimate the slip parameters online. A stable tracking control law for this robot system is proposed by backstepping method, and the asymptotic stability is guaranteed by Lyapunov theory. Meanwhile, the controller gains are determined online by poles placement method. Simulation results show the effectiveness and robustness of the proposed method.     

A criterion of robustness intelligent nonlinear control for multiple time-delay systems based on fuzzy Lyapunov methods

A control system with state feedback controllers, in which the fuzzy Lyapunov approach is developed for the stability criterion, is studied. The proposed intelligent design provides a systematic and effective framework for the control systems. The global nonlinear controller is constructed based on T–S (Takagi–Sugeno) fuzzy controller design techniques, blending all such local state feedback controllers. Based on this design, the stability conditions of a multiple time-delay system are derived in terms of the fuzzy Lyapunov theory. The effectiveness and the feasibility of the proposed controller design method are demonstrated through numerical simulations.     

惯性平台稳定回路基于Backstepping的动态滑模控制(英文)

针对带不匹配不确定非线性干扰的惯性平台稳定回路跟踪控制问题,提出了基于backstepping的动态滑模控制方法。首先,建立了惯性平台稳定回路的等价模型,该模型由一个线性模型加上一个不确定的非线性函数组成。然后,基于backstepping方法设计了带渐近稳定滑模面的动态滑模控制器,解决了模型不匹配的问题,并提高了系统的鲁棒性。进而应用Lyapunov稳定性理论证明了所设计的控制器不仅能保证闭环系统的稳定性,而且可以通过选择适当的控制器参数来调整跟踪误差的收敛率。最后,仿真结果表明,基于backstepping的动态滑模控制方法与PID控制方法相比,提高了系统的跟踪精度,增强了鲁棒性。     

Decentralized adaptive neural network control for mechanical systems with dead-zone input

We propose a decentralized adaptive robust controller for trajectory tracking of mechanical systems with dead-zone input in this paper. The considered mechanical systems are with high-order interconnections and unknown non-symmetric nonlinear input. In each local controller, the neural network control is introduced to estimate the uncertainties and disturbances, meanwhile the siding mode control and adaptive technical are designed to compensate for the approximation errors. A nonlinear function is chosen to deal with the interconnections. Following, the stability and robustness are verified by using Lyapunov stability theorem. Finally, simulations are provided to support the theoretical 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.

     

Analysis and control of a hyperchaotic system with only one nonlinear term

In order to promote the development of chaos in nonlinear systems, and explore more convenient controllers for the engineering application, a four-dimensional nonlinear dynamic system with only one nonlinear term was constructed and its complex dynamic characteristics were analyzed, including the phase trajectory map, Lyapunov exponents, and so on. Furthermore, the recursive backstepping method was proposed to design a different controller; the hyperchaotic system was controlled to an equilibrium point and a periodic orbit. Theoretical analysis is in agreement with simulation results. The results show that the recursive backstepping control method can wipe off chaos, and make the hyperchaotic system achieve stable states. The control process is a smooth transition, and the transition time is short.     

Nonlinear adaptive task space control for a 2-DOF redundantly actuated parallel manipulator

A nonlinear adaptive (NA) controller in the task space is developed for the trajectory tracking of a 2-DOF redundantly actuated parallel manipulator. The dynamic model with nonlinear friction is established in the task space for the parallel manipulator, and the linear parameterization expression of the dynamic model is formulated. Based on the dynamic model, a new control law including adaptive dynamics compensation, adaptive friction compensation and error elimination items is designed. After defining a quadratic performance index, the parameter update law is derived with the gradient descent algorithm. The stability of the parallel manipulator system is proved by the Lyapunov theorem, and the convergence of the tracking error and the error rate is proved by the Barbalat’s lemma. The NA controller is implemented in the trajectory tracking experiments of an actual 2-DOF redundantly actuated parallel manipulator, and the experiment results are compared with the APD controller.     

Observer-based adaptive robust control of nonlinear nonaffine systems with unknown gain sign

In this paper, a direct adaptive robust controller for a class of SISO nonaffine nonlinear systems is presented. The existence of an ideal controller is proved based on the Implicit Function Theorem. Since the Implicit Function Theorem only guarantees the existence of the controller and does not provide a way to construct it, a neural network is employed to approximate the unknown ideal controller. In addition, an observer is designed to estimate the system states because all the states may not be available for measurements. In this method, a priori knowledge about the sign of control gain is not required and, in order to cope with unknown control direction, the Nussbaum-type technique is used. Moreover, only one adaptive parameter is needed to be updated and also a robust term is used in the control signal to reduce the effect of external disturbances and approximation errors. Furthermore, the stability analysis for the closed-loop system is presented based on the Lyapunov stability method. Theoretical results are illustrated through a simulation example. These simulations show the effectiveness of the proposed method.     

Event-triggered finite-time resilient control for switched systems: an observer-based approach and its applications to a boost converter circuit system model

Under an event-triggered communication scheme (ETCS), this note focuses on the observer-based finite-time resilient control problem for a class of switched systems. Different from the existing finite-time problems, not only the problem of finite-time boundedness (FTBs) but also the problem of input-output finite-time stability (IO-FTSy) are considered in this paper. To effectively use the network resources, an ETCS is formulated for switched systems. Considering that not all the states could be measured, thus an event-triggered observer is constructed, and then, an observer-based resilient controller is devised, which robustly stabilizes the given systems in the meaning of finite-time control. Based on time-delay method and Lyapunov functional approach, interesting results are derived to verify the properties of the FTBs and the IO-FTSy of the event-triggered (ET) closed-loop error switched systems. All the matrix inequalities can be converted to linear matrix inequalities (LMIs) so as to simultaneously obtain the controller gain and observer gain. Finally, the applicability of the proposed control scheme is verified via a boost converter circuit system.     

A new adaptive fuzzy sliding mode observer for a class of MIMO nonlinear systems

In this paper, a new adaptive fuzzy sliding mode (AFSM) observer is proposed which can be used for a class of MIMO nonlinear systems. In the proposed algorithm, the zero-input dynamics of the plant could be unknown. In this method, a fuzzy system is designed to estimate the nonlinear behavior of the observer. The output of fuzzy rules are tuned adaptively, based on the observer error. The output connection matrix is used to combine the observer errors of individual subsystems. A robust term, which is designed based on the sliding mode theory, is added to the observer to compensate the fuzzy estimation error. The estimation error bound is adjusted by an adaptive law. The main advantage of the proposed observer is that, unlike many of the previous works, the measured outputs is not limited to the first entries of a canonical-form state vector. The proposed observer estimates the closed-loop state tracking error asymptotically, provided that the output gain matrix includes Hurwitz coefficients. The chattering is eliminated by using boundary layers around the sliding surfaces and the observer convergence is proved using a Lyapunov-based approach. The proposed method is applied on a real multilink robot manipulator. The performance of the observer shows its effectiveness in the real world.     

Output feedback controller for hysteretic time-delayed MIMO nonlinear systems

In this paper, an H ^?? output feedback controller is developed for a class of time-delayed MIMO nonlinear systems, containing backlash as an input nonlinearity. Particularly, a state observer is proposed to estimate unmeasurable states. The control law can be divided into two elements: An adaptive interval type-2 fuzzy part which approximates the uncertain model. The second part is an H ^??-based controller, which attenuates the effects of external disturbances and approximation errors to a prescribed level. Furthermore, the Lyapunov theorem is used to prove stability of proposed controller and its robustness to external disturbance, hysteresis input nonlinearity, and time varying time-delay. As an example, the designed controller is applied to address the tracking problem of 2-DOF robotic manipulator. Simulation results not only verify the robust properties but also in comparison with an existing method reveal the ability of the proposed controller to exclude the effects of unknown time varying time-delays and hysteresis input nonlinearity.     

猎雷声纳基阵姿态稳定系统自适应反步法控制

针对带非线性摩擦力矩和负载扰动的高精度猎雷声纳基阵姿态稳定系统,提出了一种基于神经网络的自适应反步法控制方法。其中神经网络用于估计未知非线性摩擦力矩,进而设计反步法控制器和参数自适应律来对神经网络估计误差和负载扰动进行补偿。最后应用Lyapunov方法证明了所提出的自适应控制器能保证闭环系统的稳定性,并且可以通过选择适当的控制器参数来调整收敛率。仿真结果表明,基于神经网络的自适应反步法控制方法与PID控制相比,系统的动、静态性能指标及鲁棒性得到了全面的改善,与双闭环PID控制相比,跟踪精度提高了3倍多。     

Adaptive interval type-2 fuzzy sliding mode control for unknown chaotic system

In this paper, a novel adaptive interval type-2 fuzzy sliding mode control (AIT2FSMC) methodology is proposed based on the integration of sliding mode control and adaptive interval type-2 fuzzy control for chaotic system. The AIT2FSMC system is comprised of a fuzzy control design and a hitting control design. In the fuzzy control design, an interval type-2 fuzzy controller is designed to mimic a feedback linearization (FL) control law. In the hitting control design, a hitting controller is designed to compensate the approximation error between the FL control law and the interval type-2 fuzzy controller. The parameters of the interval type-2 fuzzy controller, as well as the uncertainty bound of the approximation error, are tuned adaptively. The adaptive laws are derived in the sense of Lyapunov stability theorem, thus the stability of the system can be guaranteed. The proposed control system compared to adaptive fuzzy sliding mode control (AFSMC). Simulation results show that the proposed control systems can achieve favorable performance and robust with respect to system uncertainties and external disturbances.