Observer-based Iterative and Repetitive Learning Control for a Class of Nonlinear Systems

In this paper, both output-feedback iterative learning control (ILC) and repetitive learning control (RLC) schemes are proposed for trajectory tracking of nonlinear systems with state-dependent time-varying uncertainties. An iterative learning controller, together with a state observer and a fully-saturated learning mechanism, through Lyapunov-like synthesis, is designed to deal with time-varying parametric uncertainties. The estimations for outputs, instead of system outputs themselves, are applied to form the error equation, which helps to establish convergence of the system outputs to the desired ones. This method is then extended to repetitive learning controller design. The boundedness of all the signals in the closed-loop is guaranteed and asymptotic convergence of both the state estimation error and the tracking error is established in both cases of ILC and RLC. Numerical results are presented to verify the effectiveness of the proposed methods.      

A multivariable MRAC scheme with application to a nonlinear aircraft model

This paper revisits the multivariable model reference adaptive control (MRAC) problem, by studying adaptive state feedback control for output tracking of multi-input multi-output (MIMO) systems. With such a control scheme, the plant-model matching conditions are much less restrictive than those for state tracking, while the controller has a simpler structure than that of an output feedback design. Such a control scheme is useful when the plant-model matching conditions for state tracking cannot be satisfied. A stable adaptive control scheme is developed based on LDS decomposition of the high-frequency gain matrix, which ensures closed-loop stability and asymptotic output tracking. A simulation study of a linearized lateral-directional dynamics model of a realistic nonlinear aircraft system model is conducted to demonstrate the scheme. This linear design based MRAC scheme is subsequently applied to a nonlinear aircraft system, and the results indicate that this linearization-based adaptive scheme can provide acceptable system performance for the nonlinear systems in a neighborhood of an operating point.     

H∞ decentralized fuzzy model reference tracking controldesign for nonlinear interconnected systems

In general, due to the interactions among subsystems, it is difficult to design an H_∞ decentralized controller for nonlinear interconnected systems. The model reference tracking control problem of nonlinear interconnected systems is studied via H_∞ decentralized fuzzy control method. First, the nonlinear interconnected system is represented by an equivalent Takagi-Sugeno type fuzzy model. A state feedback decentralized fuzzy control scheme is developed to override the external disturbances such that the H∞ model reference tracking performance is achieved. Furthermore, the stability of the nonlinear interconnected systems is also guaranteed. If states are not all available, a decentralized fuzzy observer is proposed to estimate the states of each subsystem for decentralized control. Consequently, a fuzzy observer-based state feedback decentralized fuzzy controller is proposed to solve the H_∞ tracking control design problem for nonlinear interconnected systems. The problem of H _∞ decentralized fuzzy tracking control design for nonlinear interconnected systems is characterized in terms of solving an eigenvalue problem (EVP). The EVP can be solved very efficiently using convex optimization techniques. Finally, simulation examples are given to illustrate the tracking performance of the proposed methods     

Predictor‐based repetitive learning control for a class of remote control nonlinear systems

In this paper, a repetitive learning control (RLC) approach is proposed for a class of remote control nonlinear systems satisfying the global Lipschitz condition. The proposed approach is to deal with the remote tracking control problem when the environment is periodic or repeatable over infinite time domain. Since there exist time delays in the two transmission channels: from the controller to the actuator and from the sensor to the controller, tracking a desired trajectory through a remote controller is not an easy task. In order to solve the problem caused by time delays, a predictor is designed on the controller side to predict the future state of the nonlinear system based on the delayed measurements from the sensor. The convergence of the estimation error of the predictor is ensured. The gain design of the predictor applies linear matrix inequality (LMI) techniques developed by Lyapunov Kravoskii method for time delay systems. The RLC law is constructed based on the feedback error from the predicted state. The overall tracking error tends to zero asymptotically over iterations. The proof of the stability is based on a constructed Lyapunov function related to the Lyapunov Kravoskii functional used for the proof of the predictor's convergence. By well incorporating the predictor and the RLC controller, the system state tracks the desired trajectory independent of the influence of time delays. A numerical simulation example is shown to verify the effectiveness of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.     

Iterative learning control for output‐constrained nonlinear systems with input quantization and actuator faults

In this work, we propose a novel iterative learning control algorithm to deal with a class of nonlinear systems with system output constraint requirements and quantization effects on the system control input. Actuator faults have also been considered, which include multiplicative, additive, and stuck actuator faults. To the best of our knowledge, this is the first reported work in the iterative learning control literature to deal with quantization effects for the control input of nonlinear systems under the effects of actuator faults and system output constraints. Under the proposed scheme, using backstepping design and composite energy function approaches in the analysis, we show that uniform convergence of the state tracking errors can be guaranteed over the iteration domain, and the constraint requirement on the system output will not be violated at all time. In the end, a simulation study on a single‐link robot model is presented to demonstrate the effectiveness of the proposed scheme.     

离散时间部分状态反馈模型参考自适应控制

本文针对线性不确定性系统, 给出了部分状态反馈直接模型参考自适应控制设计方案以及详细的系统稳 定性、输出跟踪性能分析. 控制器设计基于降维观测器和参数化方法. 此方案采用反馈控制, 反馈信号不仅仅依赖 全状态信息或者输出信号, 而是任意不超过系统维数的可测信号. 因此, 部分状态反馈控制是包含状态反馈、输出 反馈控制的新的控制方案, 缓解了状态反馈对状态信息的限制, 降低了输出反馈控制结构的复杂性. 通过引入辅助 信号, 本文证明了输出匹配条件的存在性、所有闭环系统信号的有界性以及渐近输出跟踪性能. 仿真结果验证了该 方案的有效性.     

Adaptive finite‐time fault‐tolerant tracking control for a class of MIMO nonlinear systems with output constraints

In this work, we present a novel adaptive finite‐time fault‐tolerant control algorithm for a class of multi‐input multi‐output nonlinear systems with constraint requirement on the system output tracking error. Both parametric and nonparametric system uncertainties can be effectively dealt with by the proposed control scheme. The gain functions of the nonlinear systems under discussion, especially the control input gain function, can be not fully known and state‐dependent. Backstepping design with a tan‐type barrier Lyapunov function and a new structure of stabilizing function is presented. We show that under the proposed control scheme, finite‐time convergence of the output tracking error into a small set around zero is guaranteed, while the constraint requirement on the system output tracking error will not be violated during operation. An illustrative example on a robot manipulator model is presented in the end to further demonstrate the effectiveness of the proposed control scheme. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive neural output feedback tracking control for a class of nonlinear systems

In this paper, an adaptive neural output feedback control scheme based on backstepping technique and dynamic surface control (DSC) approach is developed to solve the tracking control problem for a class of nonlinear systems with unmeasurable states. Firstly, a nonlinear state observer is designed to estimate the unmeasurable states. Secondly, in the controller design process, radial basis function neural networks (RBFNNs) are utilised to approximate the unknown nonlinear functions, and then a novel adaptive neural output feedback tracking control scheme is developed via backstepping technique and DSC approach. It is shown that the proposed controller ensures that all signals of the closed-loop system remain bounded and the tracking error converges to a small neighbourhood around the origin. Finally, two numerical examples and one realistic example are given to illustrate the effectiveness of the proposed design approach.     

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.     

Iterative learning of model reference adaptive controller for uncertain nonlinear systems with only output measurement

In this paper, a model reference adaptive control strategy is used to design an iterative learning controller for a class of repeatable nonlinear systems with uncertain parameters, high relative degree, initial output resetting error, input disturbance and output noise. The class of nonlinear systems should satisfy some differential geometric conditions such that the plant can be transformed via a state transformation into an output feedback canonical form. A suitable error model is derived based on signals filtered from plant input and output. The learning controller compensates for the unknown parameters, uncertainties and nonlinearity via projection type adaptation laws which update control parameters along the iteration domain. It is shown that the internal signals remain bounded for all iterations. The output tracking error will converge to a profile which can be tuned by design parameters and the learning speed is improved if the learning gain is large.     

H∞ output tracking fuzzy control for nonlinear systems with time-varying delay

This paper proposes an observer-based output tracking control via virtual desired reference model for a class of nonlinear systems with time-varying delay and disturbance. First, the Takagi–Sugeno fuzzy model represents the nonlinear system with time-varying delay and disturbance. Then we design an observer to estimate immeasurable states and controller to drive the error between estimated state and virtual desired variables (VDVs) to zero such that the overall control output tracking system has H_∞ control performance. Using Lyapunov–Krasovskii functional, we derive sufficient conditions for stability. The advantages of the proposed output control system are (i) systematic approach to derive VDVs for controller design; (ii) relaxes need for real reference model; (iii) drops need for information of equilibrium; (iv) relaxed condition is provided via three-step procedure to find observer and controller gain. We carry out simulation using a continuous stirred tank reactor system where the effectiveness of the proposed controller is demonstrated by satisfactory numerical results.     

Approximate local output regulation for nonlinear distributed parameter systems

Output regulation for a class of nonlinear infinite-dimensional systems, called regular nonlinear systems (RNS), is the subject of this work. For the plants in this class, the linearization at the origin is an exponentially stable regular linear system (RLS). The plants are driven by a control input and a disturbance signal. Well-posedness of the plants for small initial states, control inputs and disturbance signals is established and it is shown that if the control input and the disturbance signal for a plant are T-periodic, then so are its state and output (asymptotically). On the basis of this characterization, an approximate local output regulator problem for multi-input multi-output (MIMO) plants in the RNS class is addressed. Given a plant, the regulation objective is to ensure that a finite number of harmonics of a T-periodic reference signal and the plant output are identical whenever the reference signal, the T-periodic disturbance signal for this plant and the initial state are small. An internal model based output feedback control scheme is proposed for an exponentially stable RLS for tracking reference signals, which are a finite sum of functions that are a product of a sinusoid and a polynomial in time. This scheme merely uses the transfer function gains of the RLS at the poles of the Laplace transform of the reference signal and practically requires no other data. Using the proposed control scheme, a linear finite-dimensional controller is designed for a MIMO nonlinear plant in the RNS class using minimal plant information. The resulting closed-loop system is rigorously analyzed to establish that the controller achieves the regulation objective. The efficacy of the control design is illustrated numerically using the model of a cable coupled to a point mass via a nonlinear spring.     

Flyback CCM inverter for AC module applications: iterative learning control and convergence analysis

This paper presents an iterative learning controller (ILC) for an interleaved flyback inverter operating in continuous conduction mode (CCM). The flyback CCM inverter features small output ripple current, high efficiency, and low cost, and hence it is well suited for photovoltaic power applications. However, it exhibits the non-minimum phase behaviour, because its transfer function from control duty to output current has the right-half-plane (RHP) zero. Moreover, the flyback CCM inverter suffers from the time-varying grid voltage disturbance. Thus, conventional control scheme results in inaccurate output tracking. To overcome these problems, the ILC is first developed and applied to the flyback inverter operating in CCM. The ILC makes use of both predictive and current learning terms which help the system output to converge to the reference trajectory. We take into account the nonlinear averaged model and use it to construct the proposed controller. It is proven that the system output globally converges to the reference trajectory in the absence of state disturbances, output noises, or initial state errors. Numerical simulations are performed to validate the proposed control scheme, and experiments using 400-W AC module prototype are carried out to demonstrate its practical feasibility.     

Observer‐based adaptive robust control of a class of nonlinear systems with dynamic uncertainties

In this paper, a discontinuous projection‐based adaptive robust control (ARC) scheme is constructed for a class of nonlinear systems in an extended semi‐strict feedback form by incorporating a nonlinear observer and a dynamic normalization signal. The form allows for parametric uncertainties, uncertain nonlinearities, and dynamic uncertainties. The unmeasured states associated with the dynamic uncertainties are assumed to enter the system equations in an affine fashion. A novel nonlinear observer is first constructed to estimate the unmeasured states for a less conservative design. Estimation errors of dynamic uncertainties, as well as other model uncertainties, are dealt with effectively via certain robust feedback control terms for a guaranteed robust performance. In contrast with existing conservative robust adaptive control schemes, the proposed ARC method makes full use of the available structural information on the unmeasured state dynamics and the prior knowledge on the bounds of parameter variations for high performance. The resulting ARC controller achieves a prescribed output tracking transient performance and final tracking accuracy in the sense that the upper bound on the absolute value of the output tracking error over entire time‐history is given and related to certain controller design parameters in a known form. Furthermore, in the absence of uncertain nonlinearities, asymptotic output tracking is also achieved. Copyright © 2001 John Wiley & Sons, Ltd.     

Adaptive Fuzzy Backstepping Tracking Control for Flexible Robotic Manipulator

In this paper, an adaptive fuzzy state feedback control method is proposed for the single-link robotic manipulator system. The considered system contains unknown nonlinear function and actuator saturation. Fuzzy logic systems (FLSs) and a smooth function are used to approximate the unknown nonlinearities and the actuator saturation, respectively. By combining the command-filter technique with the backstepping design algorithm, a novel adaptive fuzzy tracking backstepping control method is developed. It is proved that the adaptive fuzzy control scheme can guarantee that all the variables in the closed-loop system are bounded, and the system output can track the given reference signal as close as possible. Simulation results are provided to illustrate the effectiveness of the proposed approach.      

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.     

严格反馈互联系统分散式backstepping自适应迭代学习控制

基于Lyapunov分析方法,针对具有严格反馈形式的非线性互联系统,本文设计了一种分散式backstepping自适应迭代学习控制器.子系统之间的互联项为所有子系统输出项线性有界,为每个子系统设计的控制器仅采用该子系统的信息,不需要子系统之间相互传递信息.在控制器中,引入在时间轴和迭代轴上同时更新的自适应参数,以补偿子系统之间的互联项影响.通过采用本文给出的控制器,可使得每个子系统的输出跟踪相应的参考模型输出,仿真结果验证了本文算法的有效性.     

On Repetitive Learning Control for Periodic Tracking Tasks

In this note, a repetitive learning control (RLC) approach is proposed to deal with periodic tracking tasks for nonlinear dynamical systems with nonparametric uncertainties. We address two fundamental issues associated with the learning control methodology: The existence of the solution, and learning convergence property. Applying the existence theorem of the neutral differential difference equation, and using Lyapunov-Krasovskii functional, the existence of the solution and learning convergence can be proven rigorously. A further extension of the RLC to cascade systems is also explored     

Output tracking for nonlinear stochastic systems by iterative learning control

An iterative learning control (ILC) algorithm, which in essence is a stochastic approximation algorithm, is proposed for output tracking for nonlinear stochastic systems with unknown dynamics and unknown noise statistics. The nonlinear function of the system dynamics is allowed to grow up as fast as a polynomial of any degree, but the system is linear with respect to control. It is proved that the ILC generated by the algorithm a.s. converges to the optimal one at each time t/spl isin/[0,1,...,N] and the output tracking error is asymptotically minimized in the mean square sense as the number of iterates tends to infinity, although the convergence rate is rather slow. The only information used in the algorithm is the noisy observation of the system output and the reference signal y/sub d/(t). When the system state equation is free of noise and the system output is realizable, then the exact state tracking is asymptotically achieved and the tracking error is purely due to the observation noise.     

Iterative learning control design with high‐order internal model for discrete‐time nonlinear systems

In this paper, a high‐order internal model (HOIM)‐based iterative learning control (ILC) scheme is proposed for discrete‐time nonlinear systems to tackle the tracking problem under iteration‐varying desired trajectories. By incorporating the HOIM that is utilized to describe the variation of desired trajectories in the iteration domain into the ILC design, it is shown that the system output can converge to the desired trajectory along the iteration axis within arbitrarily small error. Furthermore, the learning property in the presence of state disturbances and output noise is discussed under HOIM‐based ILC with an integrator in the iteration axis. Two simulation examples are given to demonstrate the effectiveness of the proposed control method. Copyright © 2016 John Wiley & Sons, Ltd.