Adaptive learning control of linear systems by output error feedback

This paper addresses the problem of designing an output error feedback tracking control for single-input, single-output uncertain linear systems when the reference output signal is smooth and periodic with known period T. The considered systems are required to be observable, minimum phase, with known relative degree and known high frequency gain sign. By developing in Fourier series expansion a suitable unknown periodic input reference signal, an output error feedback adaptive learning control is designed which ‘learns’ the input reference signal by identifying its Fourier coefficients: bounded closed-loop signals and global exponential tracking of both the input and the output reference signals are obtained when the Fourier series expansion is finite, while global exponential convergence of the input and output tracking errors into arbitrarily small residual sets is achieved otherwise. The structure of the proposed controller depends only on the relative degree, the reference signal period, the high frequency gain sign and the number of estimated Fourier coefficients.     

Robust adaptive state-feedback tracking for nonlinear systems

For a class of singie-input/single-output uncertain nonlinear systems, affected both by uncertain time-varying parameters (with known bounds) and unknown time-varying bounded disturbances, a new robust adaptive state-feedback control algorithm is presented. It guarantees: boundedness of all signals and arbitrary disturbance attenuation when both disturbances and time-varying parameters are present, and asymptotic tracking with arbitrary transient performance when no disturbance is acting on the system and parameters are constant. The adaptation may be switched off, still guaranteeing bounded signals and disturbance attenuation     

Adaptive Learning Control of Nonlinear Systems by Output Error Feedback

This paper addresses the problem of designing an output error feedback control for single-input, single-output nonlinear systems with uncertain, smooth, output-dependent nonlinearities whose local Lipschitz constants are known. The considered systems are required to be observable, minimum phase with known relative degree and known high frequency gain sign: linear systems are included. The reference output signal is assumed to be smooth and periodic with known period. By developing in Fourier series expansion a suitable periodic input reference signal, an output error feedback adaptive learning control is designed which ldquolearnsrdquo the input reference signal by identifying its Fourier coefficients: bounded closed loop signals and exponential tracking of both input and output reference signals are obtained when the Fourier series expansion is finite, while arbitrary small tracking errors are exponentially achieved otherwise. The resulting control is not model based, is independent of the system order and depends only on the relative degree, the reference signal period and the high frequency gain sign.     

控制方向未知的时变非线性系统鲁棒控制

针对一类具有未知时变控制方向、不确定时变参数以及未知时变有界干扰的严反馈非线性系统,给出一种带有死区修正算法的鲁棒控制方法.在控制系数符号未知的情况下,通过在反步法中引入Nussbaum增益和死区修正技术,得到一种修正的鲁棒反步设计方法.该方法不需要未知时变控制系数的上下界先验知识以及不确定参数和外界干扰的上界信息.算法保证了闭环系统所有信号的有界性,同时使得跟踪误差收敛于零的任意小邻域内.     

Robust tracking control design for uncertain robotic systems with persistent bounded disturbances

In this study, a robust nonlinear L_∞‐gain tracking control design for uncertain robotic systems is proposed under persistent bounded disturbances. The design objective is that the peak of the tracking error in time domain must be as small as possible under persistent bounded disturbances. Since the nonlinear L_∞ ‐gain optimal tracking control cannot be solved directly, the nonlinear L_∞ ‐gain optimal tracking problem is transformed into a nonlinear L_∞ ‐gain tracking problem by given a prescribed disturbance attenuation level for the L_∞ ‐gain tracking performance. To guarantee that the L_∞ ‐gain tracking performance can be achieved for the uncertain robotic systems, a sliding‐mode scheme is introduced to eliminate the effect of the parameter uncertainties. By virtue of the skew‐symmetric property of the robotic systems, sufficient conditions are developed for solving the robust L_∞ ‐gain tracking control problems in terms of an algebraic equation instead of a differential equation. The proposed method is simple and the algebraic equation can be solved analytically. Therefore, the proposed robust L_∞ ‐gain tracking control scheme is suitable for practical control design of uncertain robotic systems. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Practical output regulation for bounded linear infinite-dimensional state space systems

We develop the mathematical foundations of practical state space output regulation for bounded infinite-dimensional linear systems. By practical output regulation we mean asymptotic tracking of references and rejection of disturbances with a given accuracy. Our main results are general upper bounds for the norms perturbations to the parameters of the exosystem, the plant and a controller which achieves exact output regulation. These bounds depend explicitly on the desired tracking accuracy ε>0. In this paper, all perturbations are assumed to be bounded, additive and linear. Our results apply for both feedforward and error feedback controllers, and for arbitrary bounded uniformly continuous reference/disturbance signals.     

控制方向未知的全状态约束非线性系统的鲁棒自适应跟踪控制

针对一类控制方向未知的含有时变不确定参数和未知时变有界扰动的全状态约束非线性系统,本文提出了一种基于障碍Lyapunov函数的反步自适应控制方法.障碍Lyapunov函数保证了系统状态在运行过程中始终保持在约束区间内;Nussbaum型函数的引入解决了系统控制方向未知的问题;光滑投影算法确保了不确定时变参数的有界性.障碍Lyapunov函数、Nussbaum型函数及光滑投影算法与反步自适应方法的有效结合首次解决了控制方向未知的全状态约束非线性系统的跟踪控制问题.所设计的自适应鲁棒控制器能在满足状态约束的前提下确保闭环系统的所有信号有界.通过恰当地选取设计参数,系统的跟踪误差将收敛于0的任意小的邻域内.仿真结果表明了控制方案的可行性.     

Output feedback adaptive DSC for nonlinear systems with guaranteed L-infinity tracking performance

In this paper, the problem of output tracking for a class of uncertain nonlinear systems is considered. First, neural networks are employed to cope with uncertain nonlinear functions, based on which state estimation is constructed. Then, an output feedback control system is designed by using dynamic surface control (DSC). To guarantee the L-infinity tracking performance, an initialization technique is presented. The main feature of the scheme is that explosion of complex- ity problem in backstepping control is avoided, and there is no need to update the unknown parameters including control gains as well as neural networks weights, the adaptive law with one update parameter is necessary only at the first design step. It is proved that all signals of the closed-loop system are semiglobally uniformly ultimately bounded and the L-infinity performance of system tracking error can be guaranteed. Simulation results demonstrate the effectiveness of the proposed scheme.     

带有干扰的时变系统的变结构鲁棒控制

对含有未知时变参数和外界干扰的单输入单输出线性时变系统,给出了一种变结构鲁棒输出跟踪控制器.系统参数不限定为慢时变或者结构已知的,只要求光滑有界且所需高阶导数有界.通过引入辅助信号和带有记忆功能的正规化信号,以及适当选择控制器参数,该变结构控制器能保证闭环系统所有信号的有界性,跟踪误差能被调整到任意小的范围内.     

Active fault tolerant control for nonlinear systems with simultaneous actuator and sensor faults

The goal of this paper is to describe a novel fault tolerant tracking control (FTTC) strategy based on robust fault estimation and compensation of simultaneous actuator and sensor faults. Within the framework of fault tolerant control (FTC) the challenge is to develop an FTTC design strategy for nonlinear systems to tolerate simultaneous actuator and sensor faults that have bounded first time derivatives. The main contribution of this paper is the proposal of a new architecture based on a combination of actuator and sensor Takagi-Sugeno (T-S) proportional state estimators augmented with proportional and integral feedback (PPI) fault estimators together with a T-S dynamic output feedback control (TSDOFC) capable of time-varying reference tracking. Within this architecture the design freedom for each of the T-S estimators and the control system are available separately with an important consequence on robust L ₂ norm fault estimation and robust L ₂ norm closed-loop tracking performance. The FTTC strategy is illustrated using a nonlinear inverted pendulum example with time-varying tracking of a moving linear position reference.     

Robust consensus tracking of double‐integrator dynamics by bounded distributed control

This paper studies the robust consensus tracking problem of multiple second‐order systems with additive disturbances and a direct communication topology. We design a continuous, bounded and distributed controller that is composed of a tracker and an uncertainty and disturbance estimator. The tracker makes the nominal closed‐loop system globally asymptotically stable, while the output of uncertainty and disturbance estimator attenuates the effect of disturbances. We show that if the disturbances converge to constants, the tracking error converges asymptotically to zero, whereas for other types of disturbances, the obtained error system is small‐signal L_∞ stable. Some inequalities are developed to show the relationship between the ultimate bounds of tracking errors and the design parameters. Finally, simulation results for four cases are presented to demonstrate the performance of the controller. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust adaptive learning control for nonlinear systems with extended matching unstructured uncertainties

The exponential output tracking problem for a class of single‐input, single‐output uncertain nonlinear systems, including systems with extended matching unstructured uncertainties and without a well‐defined global relative degree, is addressed. Conditions on the uncertain system dynamics are derived, which allow us to design a state‐feedback learning control achieving semi‐global exponential output tracking of sufficiently smooth and periodic reference signals of known period, while guaranteeing ??₂ and ??_∞ transient performances during the learning phase. The application of the proposed learning approach to the position tracking control problem for uncertain permanent magnet step motors with non‐sinusoidal flux distribution and uncertain position‐dependent load torque allows us to provide a solution to a yet unsolved problem. Copyright © 2011 John Wiley & Sons, Ltd.     

Adaptive output feedback tracking controller for a class of uncertain strict feedback nonlinear systems in the absence of state measurements

In this article, design of an adaptive control scheme for a class of uncertain single-input single-output systems in strict feedback form via a backstepping technique has been proposed. It is assumed that system output and its derivatives are available. By virtue of the observability concept, it is shown that for this class of systems there exists a one-to-one map, which maps output and its derivatives to system states. By means of this mapping and using linearly parametrised approximators, such as fuzzy logic systems or neural networks, the uncertain nonlinear dynamics and unavailable states are estimated. The proposed adaptive controller guarantees that the closed-loop system is uniformly ultimately bounded and the influence of minimum approximation error on the L ₂-norm of the output tracking error is attenuated arbitrarily. The effectiveness of the proposed scheme has been demonstrated through simulation results.     

Almost disturbance decoupling of MIMO nonlinear systems and application to chemical processes

The problem of almost disturbance decoupling is considered for a class of nonlinear systems with unmeasurable time-varying disturbances. A structure, called nested lower triangular form, is introduced, which contains lower triangular form as a special case. The backstepping design technique is applied to construct an H_∞ feedback controller which achieves internal stability of the closed-loop system and renders a bounded L₂ gain from the disturbance input to the output. The application of the developed design method is illustrated through a two continuous stirred tank reactor example, which can be put into the nested lower triangular form.     

Adaptive output feedback tracking control for a class of uncertain switched nonlinear systems under arbitrary switching

This paper investigates the problem of adaptive output feedback tracking for uncertain switched nonlinear systems, under arbitrary switching. First, an adaptive output feedback controller is designed, which ensures the boundedness of all the closed-loop signals. Then, a novel adaptive-based robust output feedback control is proposed to drive the tracking error to zero, in which the bound of disturbances is not required to be known in advance. Both control algorithms are based on the common Lyapunov function method, without any restrictions on dwell time. To evaluate the performance of the proposed output feedback control schemes, a numerical example is presented and discussed.     

Predictor-based neural dynamic surface control for distributed formation tracking of multiple marine surface vehicles with improved transient performance基于预估器神经网络动态面的海洋航行器分布式队形跟踪

In this paper, we investigate the distributed formation tracking problem of multiple marine surface vehicles with model uncertainty and time-varying ocean disturbances induced by wind, waves, and ocean currents. The objective is to achieve a collective tracking with a time-varying trajectory, which can only be accessed by a fraction of follower vehicles. A novel predictor-based neural dynamic surface control design approach is proposed to develop the distributed adaptive formation controllers. We use prediction errors, rather than tracking errors, to construct the neural adaptive laws, which enable the fast identification of the vehicle dynamics without incurring high-frequency oscillations in control signals. We establish the stability properties of the closed-loop network via Lyapunov analysis, and quantify the transient performance by deriving the truncated L₂ norms of the derivatives of neural weights, which we demonstrate to be smaller than the classical neural dynamic surface control design approach. We also extend the above result to the distributed formation tracking using the relative position information of vehicles, and the advantage is that the velocity information of neighbors and leader are required. Finally, we give the comparative studies to illustrate the performance improvement of the proposed method.     

Performance analysis for bounded persistent disturbances in PD/PID-controlled robotic systems with its experimental demonstrations

This paper is concerned with performance analysis of proportional-derivative/proportional-integral-derivative (PD/PID) controller for bounded persistent disturbances in a robotic manipulator. Even though the notion of input-to-state stability (ISS) has been widely used to deal with the effect of disturbances in control of a robotic manipulator, the corresponding studies cannot be directly applied to the treatment of persistent disturbances occurred in robotic manipulators. This is because the conventional studies relevant to ISS consider the H_∞ performance for robotic systems, which is confined to the treatment of decaying disturbances, i.e. the disturbances those in the L₂ space. To deal with the effect of persistent disturbances in robotic systems, we first provide a new treatment of ISS in the L_∞ sense because bounded persistent disturbances should be intrinsically regarded as elements of the L_∞ space. We next derive state-space representations of trajectory tracking control in the robotic systems which allow us to define the problem formulations more clearly. We then propose a novel control law that has a PD/PID control form, by which the trajectory tracking system satisfies the reformulated ISS. Furthermore, we can obtain a theoretical argument about the L_∞ gain from the disturbance to the regulated output through the proposed control law. Finally, experimental studies for a typical 3-degrees of freedom robotic manipulator are given to demonstrate the effectiveness of the method introduced in this paper.     

Approximation-based adaptive tracking control of nonlinear pure-feedback systems with time-varying output constraints

An adaptive neural network control problem of completely non-affine pure-feedback systems with a time-varying output constraint and external disturbances is investigated. For the controller design, we presents an appropriate Barrier Lyapunov Function (BLF) considering both the time-varying output constraint and the control direction nonlinearities induced from the implicit function theorem and mean value theorem. From an error transformation, the BLF dependent on the time-varying constraint is transformed into the explicitly time-independent BLF. Based on the explicitly time-independent BLF, an adaptive dynamic surface control scheme using the function approximation technique is designed to ensure both the constraint satisfaction and the desired tracking ability. It is shown that all signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error converges to an adjustable neighborhood of the origin while the time-varying output constraint is never violated.     

Adaptive robust output tracking of uncertain strict-feedback nonlinear time-delay systems via control schemes with simple structure

The output tracking control problem is considered for a class of uncertain strict-feedback nonlinear systems with time-varying delays. In the paper, the time-varying delays are assumed to be any non-negative continuous and bounded functions, and it is not necessary for their derivatives to be less than one. It is also assumed that the upper bounds of nonlinear delayed state perturbations and external disturbances are unknown. On the basis of backstepping algorithm, a novel design method is proposed by which some simple adaptive robust output tracking control schemes are synthesised. The proposed design method can avoid the repeated differentiation problem which appears in using the conventional backstepping algorithm, and need not know all the nonlinear upper bound functions of uncertainties, which are repeatedly employed at each step of the backstepping algorithm. In particular, it is not necessary to know any information on the time-varying delays to construct our simple output tracking control schemes. It is also shown that the tracking error can converge uniformly exponentially towards a neighbourhood of the origin. Finally, a numerical example and its simulations are provided to demonstrate the design procedure of the simple method proposed in the paper.