Adaptive backstepping repetitive learning control design for nonlinear discrete‐time systems with periodic uncertainties

This paper addresses a tracking problem for uncertain nonlinear discrete‐time systems in which the uncertainties, including parametric uncertainty and external disturbance, are periodic with known periodicity. Repetitive learning control (RLC) is an effective tool to deal with periodic unknown components. By using the backstepping procedures, an adaptive RLC law with periodic parameter estimation is designed. The overparameterization problem is overcome by postponing the parameter estimation to the last backstepping step, which could not be easily solved in robust adaptive control. It is shown that the proposed adaptive RLC law without overparameterization can guarantee the perfect tracking and boundedness of the states of the whole closed‐loop systems in presence of periodic uncertainties. In addition, the effectiveness of the developed controller is demonstrated by an implementation example on a single‐link flexible‐joint robot. Copyright © 2014 John Wiley & Sons, Ltd.     

Adaptive robust control of nonlinear systems with dynamic uncertainties

In this paper, the discontinuous projection‐based adaptive robust control (ARC) approach is extended to a class of nonlinear systems subjected to parametric uncertainties as well as all three types of nonlinear uncertainties—uncertainties could be state‐dependent, time‐dependent, and/or dynamic. Departing from the existing robust adaptive control approach, the proposed approach differentiates between dynamic uncertainties with and without known structural information. Specifically, adaptive robust observers are constructed to eliminate the effect of dynamic uncertainties with known structural information for an improved steady‐state output tracking performance—asymptotic output tracking is achieved when the system is subjected to parametric uncertainties and dynamic uncertainties with known structural information only. In addition, dynamic normalization signals are introduced to construct ARC laws to deal with other uncertainties including dynamic uncertainties without known structural information not only for global stability but also for a guaranteed robust performance in general. Copyright © 2008 John Wiley & Sons, Ltd.     

Iterative learning control for non‐repetitive trajectory tracking of robot manipulators with joint position constraints and actuator faults

In this work, we present a novel iterative learning control (ILC) scheme for a class of joint position constrained robot manipulator systems with both multiplicative and additive actuator faults. Unlike most ILC literature that requires identical reference trajectory from trail to trail, in this work the reference trajectory can be non‐repetitive over the iteration domain without assuming the identical initial condition. A tan‐type Barrier Lyapunov Function is proposed to deal with the constraint requirements which can be both time and iteration varying, with ILC update laws adopted to learn the iteration‐invariant system uncertainties, and robust methods used to compensate the iteration and time varying actuator faults and disturbances. We show that under the proposed ILC scheme, uniform convergence of the full state tracking error beyond a small time interval in each iteration can be guaranteed over the iteration domain, while the constraint requirements on the joint position vector will not be violated during operation. An illustrative example on a two degree‐of‐freedom robotic manipulator is presented to demonstrate the effectiveness of the proposed control scheme. Copyright © 2016 John Wiley & Sons, Ltd.     

Mode‐independent H∞ filtering for discrete‐time Markov jump linear system with parametric uncertainties and quantized measurements

This paper is concerned with the problem of H_∞ filtering for discrete‐time Markov jump linear system with parametric uncertainties and quantized measurements, when the jumping mode information is not accessible. By converting the quantized errors into a sector‐bounded nonlinearity, the parametric uncertainties and measurements quantization are dealt with in a unified framework. The mode‐independent H_∞ filter is designed, and sufficient conditions are established via Lyapunov function approach, such that for all possible uncertain parameters and quantization errors, the resulting filtering error system is robustly stochastically stable and achieves a guaranteed H_∞ filtering error performance index. A numerical example is provided to demonstrate the feasibility and effectiveness of the proposed approach. Copyright © 2015 John Wiley & Sons, Ltd.     

Composite learning fuzzy synchronization for incommensurate fractional‐order chaotic systems with time‐varying delays

This paper presents a composite learning fuzzy control to synchronize two different uncertain incommensurate fractional‐order time‐varying delayed chaotic systems with unknown external disturbances and mismatched parametric uncertainties via the Takagi‐Sugeno fuzzy method. An adaptive controller together with fractional‐order composite learning laws is designed based on both a parallel distributed compensation technology and a fractional Lyapunov criterion. The boundedness of all variables in the closed‐loop system and the Mittag‐Leffler stability of tracking error can be guaranteed. T‐S fuzzy systems are provided to tackle unknown nonlinear functions. The distinctive features of the proposed approach consist in the following: (1) a supervisory control law is designed to compensate the lumped disturbances; (2) both the prediction error and the tracking error are used to estimate the unknown fuzzy system parameters; (3) parameter convergence can be ensured by an interval excitation condition. Finally, the feasibility of the proposed control strategy is demonstrated throughout an illustrative example.     

Adaptive prescribed performance control for hydraulic system with disturbance compensation

In this article, an adaptive prescribed performance controller is developed for hydraulic system with uncertainties. An extraordinary feature is that better prescribed performance control can be achieved by compensating the uncertainties including parameter uncertainties and disturbances. For this reason, the transformation of system output error is realized by a prescribed performance function, which is employed to constrain the boundary of tracking error and convergence rate, then the tracking error of the original system with a priori prescribed performance can be realized by stabilizing the transformed system. Adaptive control is employed to solve the system parametric uncertainties; extended state observers are built to estimate the multiple disturbances. Based on the backstepping method, they are integrated into the design of the novel controller to guarantee prescribed tracking error performance. The stability analysis of the proposed controller is carried out via the Lyapunov theory. Finally, experimental results indicate good performance of the proposed algorithm.     

Discrete‐time periodic adaptive control for parametric systems with non‐sector nonlinearities

In this paper, a periodic adaptive control approach is proposed for a class of discrete‐time parametric systems with non‐sector nonlinearities. The proposed periodic adaptive control law is characterized by either one‐period delayed parametric updating or two‐period delayed parametric updating when input gain contains periodic unknowns. Logarithmic‐type discrete Lyapunov function is employed to handle the difficulties caused by the uncertainties that do not satisfy the linear growth condition. Some extensions to nonlinear systems with multiple unknown parameters and time‐varying input gain, tracking tasks, as well as higher‐order systems in canonical form, are also discussed. Copyright © 2013 John Wiley & Sons, Ltd.     

Composite energy function‐based iterative learning control for systems with nonparametric uncertainties

In this work, we propose new iterative learning control (ILC) schemes that deal with nonlinear multi‐input multi‐output systems under alignment condition with nonparametric uncertainties. A major contribution of this work is to remove the classical resetting condition. Another major contribution of this work is to deal with norm‐bounded nonlinear uncertainties that satisfy local Lipschitz condition, in particular to deal with nonlinear uncertain state‐dependent input gain matrix that could be non‐square left invertible and local Lipschitzian. Two types of composite energy function are proposed to facilitate the ILC design and property analysis. Through rigorous analysis, we show that the new ILC schemes proposed warrant the asymptotical tracking convergence of system states. In the end, an illustrative example is provided to demonstrate the efficacy of the proposed ILC scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

Online data‐driven composite adaptive backstepping control with exact differentiators

This paper presents an online data‐driven composite adaptive backstepping control for a class of parametric strict‐feedback nonlinear systems with mismatched uncertainties, where both tracking errors and prediction errors are utilized to update parametric estimates. Hybrid exact differentiators are applied to obtain the derivatives of virtual control inputs such that the complexity problem of integrator backstepping can be avoided. Closed‐loop tracking error equations are integrated in a moving‐time window to generate prediction errors such that online recorded data can be utilized to improve parameter adaptation. Semiglobal asymptotic stability of the closed‐loop system is rigorously established by the time‐scales separation and Lyapunov synthesis. The proposed composite adaptation can not only avoid the application of identification models and linear filters resulting in a simpler control structure, but also suppress parametric uncertainties and external perturbations via the time‐interval integral. Simulation results have demonstrated that the proposed approach possesses superior control performances under both noise‐free and noisy‐measurement environments. Copyright © 2015 John Wiley & Sons, Ltd.     

Learning‐based iterative modular adaptive control for nonlinear systems

In this paper, we study the problem of adaptive trajectory tracking control for a class of nonlinear systems with structured parametric uncertainties. We propose to use an iterative modular approach: we first design a robust nonlinear state feedback that renders the closed‐loop input‐to‐state stable (ISS). Here, the input is considered to be the estimation error of the uncertain parameters, and the state is considered to be the closed‐loop output tracking error. Next, we propose an iterative adaptive algorithm, where we augment this robust ISS controller with an iterative data‐driven learning algorithm to estimate online the parametric uncertainties of the model. We implement this method with two different learning approaches. The first one is a data‐driven multiparametric extremum seeking method, which guarantees local convergence results, and the second is a Bayesian optimization‐based method called Gaussian Process Upper Confidence Bound, which guarantees global results in a compact search set. The combination of the ISS feedback and the data‐driven learning algorithms gives a learning‐based modular indirect adaptive controller. We show the efficiency of this approach on a two‐link robot manipulator numerical example.     

Stochastic high‐order internal model‐based adaptive TILC with random uncertainties in initial states and desired reference points

Many practical batch processes operate repetitively in industry and lack intermediate measurements for the interested process variables. Moreover, the initial states as well as the desired product objective often vary with different runs because of the existence of many uncertainties in practice. This work proposes a novel adaptive terminal iterative learning control method to deal with random uncertainties in desired terminal points and initial states. The run‐varying initial states are formulated by a stochastic high‐order internal model, which is further incorporated into the controller design. The desired terminal output is run dependent and is directly compensated like a feedback term in the controller. Only the system output at the endpoint of an operation is utilized to update the control signal. An estimation algorithm is designed to update the system Markov parameters as a whole. No explicit model information is involved in the controller design; thus, the proposed method is data driven and can be applied to nonlinear systems directly. Both the theoretical analysis and the simulation studies demonstrate the effectiveness of the proposed approach under random initial states and iteration‐varying referenced terminal points. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive fault tolerant control for a class of multi‐input multi‐output nonlinear systems with both sensor and actuator faults

Compared with the fault diagnosis, detection, and isolation literature, very few results are available to discuss control algorithms directly for multi‐input multi‐output nonlinear systems with both sensor and actuator faults in the fault tolerant control literature. In this work, we present a fault tolerant control algorithm to address the system output stabilization problem for a class of multi‐input multi‐output nonlinear systems with both parametric and nonparametric uncertainties, subject to sensor and actuator faults that can be both multiplicative and additive. All elements of the sensor measurements and actuator components can be faulty. Besides, the control input gain function is not fully known. Backstepping method is used in the analysis and control design. We show that under the proposed control scheme, uniformly ultimate boundedness of the system output is guaranteed, while all closed‐loop system signals stay bounded. In the cases where the sensor faults are only multiplicative, exponential convergence of the system state variables into small neighbourhoods around zero is guaranteed. An illustrative example on a robot manipulator model is presented in the end to further demonstrate the effectiveness of the proposed control scheme.     

Design of a power system stabilizer using decentralized adaptive model following tracking control approach

This paper presents the design of a power system stabilizer using decentralized adaptive model following tracking control (DAMFTC) approach to damp oscillations of generators in transient response subjected to uncertainties and generating fault actuators. The power system is represented as a collection of interconnected dynamical subsystems each described by a set of differential/algebraic equations using a clear representation of load voltage magnitude with matched and unmatched time‐varying uncertainties. All adaptive learning algorithms in this control system are derived in the sense of Lyapunov stability analysis subject to state errors due to uncertainties and fault section, so that stability and robustness of the closed‐loop system are ensured and asymptotic‐state tracking can be achieved. An adaptive bound estimation algorithm is investigated to relax the requirement for the bound of uncertainties. The effectiveness of the proposed approach is demonstrated by distributing a detailed simulation of the three‐machine nine‐bus system with nonlinear interactions, uncertainties, and fault actuators. The simulation includes the effects of network and stator transients. Copyright © 2009 John Wiley & Sons, Ltd.     

Model‐free fault‐tolerant control approach for uncertain state‐constrained linear systems with actuator faults

This paper investigates the robust adaptive fault‐tolerant control problem for state‐constrained continuous‐time linear systems with parameter uncertainties, external disturbances, and actuator faults including stuck, outage, and loss of effectiveness. It is assumed that the knowledge of the system matrices, as well as the upper bounds of the disturbances and faults, is unknown. By incorporating a barrier‐function like term into the Lyapunov function design, a novel model‐free fault‐tolerant control scheme is proposed in a parameter‐dependent form, and the state constraint requirements are guaranteed. The time‐varying parameters are adjusted online based on an adaptive method to prevent the states from violating the constraints and compensate automatically the uncertainties, disturbances, and actuator faults. The time‐invariant parameters solved by using data‐based policy iteration algorithm are introduced for helping to stabilize the system. Furthermore, it is shown that the states converge asymptotically to zero without transgression of the constraints and all signals in the resulting closed‐loop system are uniformly bounded. Finally, two simulation examples are provided to show the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive stabilization of state-constrained uncertain nonholonomic system via dynamic surface control

In this presented work, a systematic adaptive stabilization control strategy is proposed for nonholonomic system with parametric uncertainties and full-state constraints. To facilitate the handling of state constraints, the original constrained nonholonomic system is converted into a new unconstrained system by state-dependent function transformations including discontinuous state scalings. The adaptive control algorithm is elaborated by cleverly combing the tuning function design approach with switching control strategy. In stability analysis, it is shown that the designed stabilization control method can realize the desired stabilization control aims and full-state constraints. Simulation is carried out to demonstrate the effectiveness of the control scheme.     

An adaptive robust observer for velocity estimation in an electro‐hydraulic system

This paper proposes the design of an observer to estimate the velocity of an electro‐hydraulic system by using pressure measurements only. The difficulties involved in the design of an observer for such a system include the highly nonlinear system dynamics, severe parametric uncertainties such as large variation of inertial load and unmatched model uncertainties. In order to address these issues, a nonlinear model‐based adaptive robust observer is designed to estimate the velocity. The contributions of the proposed work is twofold. First, it introduces a novel coordinate transformation to reconstruct the velocity estimate. And second, from a structural viewpoint, the design has two important features: (i) an underlying robust filter structure, which can attenuate the effect of uncertain nonlinearities such as friction and disturbances on the velocity estimation, and (ii) an adaptation mechanism to reduce the extent of parametric uncertainties. Experimental results on the swing motion control of an electro‐hydraulic robot arm demonstrate the effectiveness of the proposed observer. Copyright © 2012 John Wiley & Sons, Ltd.     

Precision motion control of a small launching platform with disturbance compensation using neural networks

A kind of launching platform driven by two permanent magnet synchronous motors which is used to launch kinetic load to hit the target always faces strong parameter uncertainties and strong external disturbance such as the air current impulsion which would degrade their tracking accuracy greatly. In this paper, a practical method which combines adaptive robust control with neural network‐based disturbance observer is proposed for high‐accuracy motion control of the launching platform. The proposed controller not only accounts for the parametric uncertainties but also takes the external disturbances into account. Adaptive control is designed to compensate the former, while neural network‐based disturbance observer is designed to compensate the latter respectively and both of them are integrated together via a feedforward cancellation technique. A new kind of parametric adaptation and weight adaptation strategy is designed by using the linear combination of the system's tracking error and the weight estimation error as a driving signal for parametric adaptation and disturbance approximation. The stability of the novel control scheme is analyzed via a Lyapunov method and this method presents a prescribed output tracking performance in the presence of both parameter uncertainties and unmodeled nonlinearities. Extensive comparative simulation and experimental results are obtained to verify the high‐performance of the proposed control strategy. Copyright © 2016 John Wiley & Sons, Ltd.     

Data‐driven bounded‐error fault detection

In this paper, a new data‐driven fault‐detection method is proposed. This method is based on a new nonparametric system identification approach, which constitutes the principal contribution to this work. The fault‐detection method is a parametric model‐free approach that can be applied to nonlinear systems that work at various operating points. Not only can the fault‐detection process be applied to the steady state of each operating point, but it can also be applied to the transient state resulting from a change in the operating point. In order to detect faults, the proposed method uses an interval predictor based on bounded‐error techniques. The utilization of techniques based on bounded error enables system uncertainties to be included in an explicit way. This in turn leads to the possibility of obtaining interval predictions of the behaviour of the system, which include information on the reliability of the prediction itself. In order to show the effectiveness of the fault‐detection method, two examples are presented: in the form of a simulated process (counter‐flow shell‐and‐tube heat‐exchanger system) and an example of a real application (two‐tanks system). A comparison with two fault‐detection methods has also been included. Copyright © 2013 John Wiley & Sons, Ltd.     

Global adaptive regulation control for a class of nonlinear systems with unknown control coefficients

This paper is concerned with the global asymptotic regulation control problem for a class of nonlinear uncertain systems with unknown control coefficients. The allowed class of uncertainties include unmeasured input‐to‐state stable (ISS) and/or weaker integral ISS (iISS) inverse dynamics, parametric uncertainties, and uncertain nonlinearities. By using the Nussbaum‐type gain technique and changing the ISS/integral ISS inverse dynamics supply rates, we design a dynamic output feedback controller which could guarantee that the system states are asymptotically regulated to the origin from any initial conditions, and the other signals are bounded in closed‐loop systems. The numerical example of a simple pendulum with all unknown parameters and without velocity measurement illustrates our theoretical results. The simulation results demonstrate its efficacy. Copyright © 2015 John Wiley & Sons, Ltd.     

A new command governor architecture for transient response shaping

In this paper, we develop a control framework for stabilization and command following of nonlinear uncertain dynamical systems. The proposed methodology consists of a new command governor architecture and an adaptive controller. The command governor is a dynamical system that adjusts the trajectory of a given command to follow an ideal reference system capturing a desired closed‐loop dynamical system behavior in transient time. Specifically, we show that the controlled nonlinear uncertain dynamical system can approach the ideal reference system by choosing the design parameter of the command governor. In addition, an adaptive element is used to asymptotically assure that the error between the controlled nonlinear uncertain dynamical system and the ideal reference system is reduced in long term. Therefore, the proposed methodology not only has closed‐loop transient and steady‐state performance guarantees but can also shape the transient response by adjusting the trajectory of the given command with the command governor. We highlight that there exists a trade‐off between the adaptive controller's learning rate and the command governor's design parameter. This key feature of our framework allows rapid suppression of system uncertainties without resorting to a high learning rate in the adaptive controller. Furthermore, we discuss the robustness properties of the proposed approach with respect to high‐frequency dynamical system content such as measurement noise and ∕ or unmodeled dynamics. A numerical example is provided to demonstrate the efficacy of the proposed architecture. Copyright © 2012 John Wiley & Sons, Ltd.