Adaptive output feedback control of systems preceded by the Preisach-type hysteresis.

An adaptive output feedback controller is presented for a class of single-input-single-output (SISO) nonlinear systems preceded by an unknown hysteresis nonlinearity represented by the Preisach model. First, a novel model is developed to represent the hysteresis characteristic in order to handle the case where the hysteresis output is not directly measured. The model is motivated by the Preisach model but implemented by the neural networks (NN). Therefore, it is easily used for controller design. Then, a radius-basis-functional-neural-networks (RBF NN) adaptive controller based on the model estimation is presented by combining the high-gain state observer. The updated laws and control laws of the controller are derived from Lyapunov stability theorem, so that the ultimate boundedness of the closed-loop system is guaranteed. At last, an example is used to verify the effectiveness of the controller.     

Discrete-time neural network output feedback control of nonlinear discrete-time systems in non-strict form

An adaptive neural network (NN)-based output feedback controller is proposed to deliver a desired tracking performance for a class of discrete-time nonlinear systems, which are represented in non-strict feedback form. The NN backstepping approach is utilized to design the adaptive output feedback controller consisting of: (1) an NN observer to estimate the system states and (2) two NNs to generate the virtual and actual control inputs, respectively. The non-causal problem encountered during the control design is overcome by using a dynamic NN which is constructed through a feedforward NN with a novel weight tuning law. The separation principle is relaxed, persistency of excitation condition (PE) is not needed and certainty equivalence principle is not used. The uniformly ultimate boundedness (UUB) of the closed-loop tracking error, the state estimation errors and the NN weight estimates is demonstrated. Though the proposed work is applicable for second order nonlinear discrete-time systems expressed in non-strict feedback form, the proposed controller design can be easily extendable to an nth order nonlinear discrete-time system.     

Observer-based adaptive neural dynamic surface control for a class of non-strict-feedback stochastic nonlinear systems

The problem of adaptive output feedback stabilisation is addressed for a more general class of non-strict-feedback stochastic nonlinear systems in this paper. The neural network (NN) approximation and the variable separation technique are utilised to deal with the unknown subsystem functions with the whole states. Based on the design of a simple input-driven observer, an adaptive NN output feedback controller which contains only one parameter to be updated is developed for such systems by using the dynamic surface control method. The proposed control scheme ensures that all signals in the closed-loop systems are bounded in probability and the error signals remain semi-globally uniformly ultimately bounded in fourth moment (or mean square). Two simulation examples are given to illustrate the effectiveness of the proposed control design.     

Adaptive output feedback control of a class of non-linear systems using neural networks

This paper presents tools for the design of a neural network based adaptive output feedback controller for a class of partially or completely unknown non-linear multi-input multi-output systems without zero dynamics. Each of the outputs is assumed to have relative degree less or equal to 2. A neural network based adaptive observer is designed to estimate the derivatives of the outputs. Subsequently, the adaptive observer is integrated into a neural network based adaptive controller architecture. Conditions are derived which guarantee the ultimate boundedness of all the errors in the closed loop system. Stability analysis reveals simultaneous learning rules for both the adaptive neural network observer and adaptive neural network controller. The design approach is illustrated using a fourth order two-input two-output example, in which each output has relative degree two.     

Neural-network control of nonaffine nonlinear system with zero dynamics by state and output feedback

This paper focuses on adaptive control of nonaffine nonlinear systems with zero dynamics using multilayer neural networks. Through neural network approximation, state feedback control is firstly investigated for nonaffine single-input-single-output (SISO) systems. By using a high gain observer to reconstruct the system states, an extension is made to output feedback neural-network control of nonaffine systems, whose states and time derivatives of the output are unavailable. It is shown that output tracking errors converge to adjustable neighborhoods of the origin for both state feedback and output feedback control.     

Neural networks stabilization and disturbance attenuation for nonlinear switched impulsive systems

In this paper, we address the problem of neural networks (NNs) stabilization and disturbance rejection for a class of nonlinear switched impulsive systems. An adaptive NN feedback control scheme and an impulsive controller for output tracking error disturbance attenuation of nonlinear switched impulsive systems are given under all admissible switched strategy based on NN. The NN is used to compensate for the nonlinear uncertainties of switched impulsive systems, and the approximation error of NN is introduced to the adaptive law in order to improve the tracking attenuation quality of the switched impulsive systems. Impulsive controller is designed to attenuate effect of switching impulse. Under all admissible switching law, impulsive controller and adaptive NN feedback controller can guarantee asymptotic stability of tracking error and improve disturbance attenuation level of tracking error for the overall nonlinear switched impulsive system. Finally, a numerical example is given to demonstrate the effectiveness of the proposed control and stabilization methods.     

A suite of robust controllers for the manipulation of microscale objects.

A suite of novel robust controllers is introduced for the pickup operation of microscale objects in a microelectromechanical system (MEMS). In MEMS, adhesive, surface tension, friction, and van der Waals forces are dominant. Moreover, these forces are typically unknown. The proposed robust controller overcomes the unknown contact dynamics and ensures its performance in the presence of actuator constraints by assuming that the upper bounds on these forces are known. On the other hand, for the robust adaptive critic-based neural network (NN) controller, the unknown dynamic forces are estimated online. It consists of an action NN for compensating the unknown system dynamics and a critic NN for approximating a certain strategic utility function and tuning the action NN weights. By using the Lyapunov approach, the uniform ultimate boundedness of the closed-loop manipulation error is shown for all the controllers for the pickup task. To imitate a practical system, a few system states are considered to be unavailable due to the presence of measurement noise. An output feedback version of the adaptive NN controller is proposed by exploiting the separation principle through a high-gain observer design. The problem of measurement noise is also overcome by constructing a reference system. Simulation results are presented and compared to substantiate the theoretical conclusions.     

Adaptive output feedback control of nonlinear systems representedby input-output models

We consider a single-input-single-output nonlinear system which can be represented globally by an input-output model. The system is input-output linearizable by feedback and is required to satisfy a minimum phase condition. The nonlinearities are not required to satisfy any global growth condition. The model depends linearly on unknown parameters which belong to a known compact convex set. We design a semiglobal adaptive output feedback controller which ensures that the output of the system tracks any given reference signal which is bounded and has bounded derivatives up to the nth order, where n is the order of the system. The reference signal and its derivatives are assumed to belong to a known compact set. It is also assumed to be sufficiently rich to satisfy a persistence of excitation condition. The design process is simple. First we assume that the output and its derivatives are available for feedback and design the adaptive controller as a state feedback controller in appropriate coordinates. Then we saturate the controller outside a domain of interest and use a high-gain observer to estimate the derivatives of the output. We prove, via asymptotic analysis, that when the speed of the high-gain observer is sufficiently high, the adaptive output feedback controller recovers the performance achieved under the state feedback one     

Learning from NN output feedback control of nonlinear systems in Brunovsky canonical form

In this paper, we investigate the learning issue in the adaptive neural network (NN) output feedback control of nonlinear systems in Brunovsky canonical form with unknown affine term. With only output measurements, a high-gain observer (HGO) is employed to estimate the derivatives of the system output which may be associated with the generation of peaking phenomenon. The adverse effect of peaking on learning and its elimination strategies are analyzed. When the gain of HGO is chosen too high, it may cause the failure of learning from the unknown closed-loop system dynamics. Hence, the gain of HGO is not chosen too high to relieve peaking and guarantee the accuracy of the estimated system states. Then, learning from the unknown closed-loop system dynamics can be achieved. When repeating the same or similar control tasks, a neural learning controller is presented which can effectively recall and reuse the learned knowledge to guarantee the output tracking performance. Finally, simulation results demonstrate the effectiveness of the proposed scheme.     

Output Feedback Control of a Quadrotor UAV Using Neural Networks

In this paper, a new nonlinear controller for a quadrotor unmanned aerial vehicle (UAV) is proposed using neural networks (NNs) and output feedback. The assumption on the availability of UAV dynamics is not always practical, especially in an outdoor environment. Therefore, in this work, an NN is introduced to learn the complete dynamics of the UAV online, including uncertain nonlinear terms like aerodynamic friction and blade flapping. Although a quadrotor UAV is underactuated, a novel NN virtual control input scheme is proposed which allows all six degrees of freedom (DOF) of the UAV to be controlled using only four control inputs. Furthermore, an NN observer is introduced to estimate the translational and angular velocities of the UAV, and an output feedback control law is developed in which only the position and the attitude of the UAV are considered measurable. It is shown using Lyapunov theory that the position, orientation, and velocity tracking errors, the virtual control and observer estimation errors, and the NN weight estimation errors for each NN are all semiglobally uniformly ultimately bounded (SGUUB) in the presence of bounded disturbances and NN functional reconstruction errors while simultaneously relaxing the separation principle. The effectiveness of proposed output feedback control scheme is then demonstrated in the presence of unknown nonlinear dynamics and disturbances, and simulation results are included to demonstrate the theoretical conjecture.      

一般严格反馈型非线性系统的自适应控制

研究一般严格反馈型非线性系统的控制问题．假设系统的对象模型、状态均未知,只有输出是可测的．应用自适应模糊神经推断系统辨识对象模型,状态观测器设计为Luenberger型,控制器由反步控制、变结构控制和3层神经网络直接控制综合而成．理论分析和仿真研究都说明此方案能够有效地控制只有输出可测的一般严格反馈型非线性系统．     

Reinforcement learning-based output feedback control of nonlinear systems with input constraints.

A novel neural network (NN)-based output feedback controller with magnitude constraints is designed to deliver a desired tracking performance for a class of multi-input and multi-output (MIMO) strict feedback nonlinear discrete-time systems. Reinforcement learning is proposed for the output feedback controller, which uses three NNs: 1) an NN observer to estimate the system states with the input-output data, 2) a critic NN to approximate certain strategic utility function, and 3) an action NN to minimize both the strategic utility function and the unknown dynamics estimation errors. Using the Lyapunov approach, the uniformly ultimate boundedness (UUB) of the state estimation errors, the tracking errors and weight estimates is shown.     

Adaptive observer and nonlinear control strategy for chemical reactors via neural networks

An adaptive observer and nonlinear feedback control strategy with constraints on control action are developed by using a supervised learning rule of a neural network and the theory of functional-link networks. The convergence of the adaptive observer and the stability of the control system are proven. They are applied to the control of an exothermic stirred-tank reactor. It is shown that an adaptive observer for concentration can be constructed for a reaction system when only temperature measurements are available on line. An adaptive observer is used to identify the pre-exponential Arrhenius constant and to provide on line estimation of the unmeasured reactant concentration for a nonlinear state-feedback controller. Simulations show that the combined observer/controller provides satisfactory closed-loop behaviour, fast responses and strong robustness. Estimated and actual concentration are in good agreement. A nonlinear feedback controller can provide effective feedback control over a wide range of operating conditions.     

Adaptive Output Feedback Control of Flexible-Joint Robots Using Neural Networks: Dynamic Surface Design Approach

In this paper, we propose a new robust output feedback control approach for flexible-joint electrically driven (FJED) robots via the observer dynamic surface design technique. The proposed method only requires position measurements of the FJED robots. To estimate the link and actuator velocity information of the FJED robots with model uncertainties, we develop an adaptive observer using self-recurrent wavelet neural networks (SRWNNs). The SRWNNs are used to approximate model uncertainties in both robot (link) dynamics and actuator dynamics, and all their weights are trained online. Based on the designed observer, the link position tracking controller using the estimated states is induced from the dynamic surface design procedure. Therefore, the proposed controller can be designed more simply than the observer backstepping controller. From the Lyapunov stability analysis, it is shown that all signals in a closed-loop adaptive system are uniformly ultimately bounded. Finally, the simulation results on a three-link FJED robot are presented to validate the good position tracking performance and robustness of the proposed control system against payload uncertainties and external disturbances.     

Output Feedback Adaptive Neural Control Without Seeking SPR Condition

For output‐feedback adaptive control of affine nonlinear systems based on feedback linearization and function approximation, the observation error dynamics usually should be augmented by a low‐pass filter to satisfy a strictly positive real (SPR) condition so that output feedback can be realized. Yet, this manipulation results in filtering basis functions of approximators, which makes the order of the controller dynamics very large. This paper presents a novel output‐feedback adaptive neural control (ANC) scheme to avoid seeking the SPR condition. A saturated output‐feedback control law is introduced based on a state‐feedback indirect ANC structure. An adaptive neural network (NN) observer is applied to estimate immeasurable system state variables. The output estimation error rather than the basis functions is filtered and the filter output is employed to update NNs. Under given initial conditions and sufficient control parameter constraints, it is proved that the closed‐loop system is uniformly ultimately bounded stable in the sense that both the state estimation errors and the tracking errors converge to small neighborhoods of zero. An illustrative example is provided to demonstrate the effectiveness of this approach.     

压电陶瓷驱动平台自适应输出反馈控制

压电陶瓷驱动平台的精度和动态特性主要取决于所设计的控制器是否可以有效地补偿压电陶瓷固有的迟滞特性. 针对这一问题, 提出了一种基于神经网络 (Neural network, NN)的自适应输出反馈控制策略. 为了避免压电陶瓷速度测量噪声的影响, 采用高增益观测器对压电陶瓷平台的速度状态进行估计; 为了克服压电陶瓷的迟滞非线性特征, 采用神经网络动态补偿策略; 针对神经网络逼近误差和观测器估计误差, 控制器设计中增加了鲁棒控制项. 最后应用Lyapunov 稳定性理论证明了所提出的控制器的收敛性问题. 仿真实验表明了所提控制方法的有效性.     

Adaptive observers for unknown general nonlinear systems

Several neural network (NN) models have been applied successfully for modeling complex nonlinear dynamical systems. However, the stable adaptive state estimation of an unknown general nonlinear system from its input and output measurements is an unresolved problem. This paper addresses the nonlinear adaptive observer design for unknown general nonlinear systems. Only mild assumptions on the system are imposed: output equation is at least C(1) and existence and uniqueness of solution for the state equation. The proposed observer uses linearly parameterized neural networks (LPNNs) whose weights are adaptively adjusted, and Lyapunov theory is used in order to guarantee stability for state estimation and NN weight errors. No strictly positive real (SPR) assumption on the output error equation is required for the construction of the proposed observer.     

Design of an amplitude-bounded output feedback adaptive neural control with guaranteed componentwise performance

This paper proposes a methodology for the design of a mixed output feedback linear and adaptive neural controller that guarantees componentwise boundedness of the tracking error within an a priori specified compact polyhedron for an uncertain nonlinear system. The approach is based on the design of a robust invariant ellipsoidal set where the adaptive neural network (NN) control is modeled as an amplitude-bounded signal. A linear error observer is employed to recover the unmeasured states, and a linear gain controller is used to enforce the containment of the ellipsoidal set within the performance polyhedron. The analysis and design of the observer and linear controller is set up as an LMI problem. The linear observer/controller scheme is then augmented with a general adaptive NN element having the purpose of approximating and compensating for the unknown nonlinearities thus providing performance improvement. The only requirement for the adaptive control signals is that their amplitudes must be confined within pre-specified limits. For this purpose, a novel mechanism called adaptive control redistribution is introduced to manage the adaptive NN control confinement during the online operation. A numerical example is used to illustrate the design methodology.     

Neural network-based adaptive controller design of roboticmanipulators with an observer

A neural network (NN)-based adaptive controller with an observer is proposed for the trajectory tracking of robotic manipulators with unknown dynamics nonlinearities. It is assumed that the robotic manipulator has only joint angle position measurements. A linear observer is used to estimate the robot joint angle velocity, while NNs are employed to further improve the control performance of the controlled system through approximating the modified robot dynamics function. The adaptive controller for robots with an observer can guarantee the uniform ultimate bounds of the tracking errors and the observer errors as well as the bounds of the NN weights. For performance comparisons, the conventional adaptive algorithm with an observer using linearity in parameters of the robot dynamics is also developed in the same control framework as the NN approach for online approximating unknown nonlinearities of the robot dynamics. Main theoretical results for designing such an observer-based adaptive controller with the NN approach using multilayer NNs with sigmoidal activation functions, as well as with the conventional adaptive approach using linearity in parameters of the robot dynamics are given. The performance comparisons between the NN approach and the conventional adaptation approach with an observer is carried out to show the advantages of the proposed control approaches through simulation studies