Adaptive iterative learning control for MIMO nonlinear systems performing iteration-varying tasks

The present work aims to develop a novel adaptive iterative learning control(AILC) method for nonlinear multiple input multiple output (MIMO) systems that execute various control missions with iteration-varying magnitude-time scales. In order to reduce the variations of the systems, this work proposes a series of time scaling transformations to normalize the iteration-varying trial lengths. An AILC scheme is then developed for the transformed control systems on a uniform trial length, which is shown to be capable of ensuring the asymptotic convergence of the tracking error. In other words, the proposed AILC algorithm is able to relax the constraint in conventional ILC where the control task must remain the same in the iteration domain. Additionally, the basic assumption in classic ILC that the control system must repeat on a fixed finite period is also removed. The convergence analysis of the AILC is derived rigorously according to the composite energy function (CEF) methodology. It is shown that the newly developed learning control strategy works well for control plants with either time-invariant or time-varying parametric uncertainties. To show the effectiveness of the AILC, three examples are illustrated in the end. Meanwhile, the proposed learning method is also implemented to a traditional X–Y table system.     

Combined Observer-Controller Synthesis for Electro-Hydraulic Servo System with Modeling Uncertainties and Partial State Feedback

Modeling uncertainties including parameter uncertainty and unmodeled dynamics hinder the development of high-performance tracking controller for hydraulic servo system. The observation for the unknown state is another issue worthy of attention. In this paper, a new seamless observer-controller scheme for hydraulic servo system is proposed with partial feedback. The position signal and the pressure signal are firstly used to build an extended structure estimation system for the unknown state. The advantage of this estimation system is that the state observer provides an extended structure for the parameter adaptation compared to other state observers. Thus the parameter uncertainty can be handled. An adaptive robust controller is synthesized in this paper which includes the adaptive part and the robust part. The adaptive part is used to eliminate the parameter uncertainty. Then the residuals coming from the parameter adaption and the errors coming from the state observation are taken into consideration in the robust part. Moreover, the unmodeled dynamics is also handled by the robust part. Theoretical analysis proves that a prescribed transient performance and the final tracking accuracy can be guaranteed by the proposed observer-controller scheme in the presence of both parameter uncertainty and unmodeled dynamics. Furthermore, the convergence of the closed-loop controller-observer system is achieved with the parametric uncertainty existed only. Extensive comparative experiments performed on a hydraulic actuator demonstrate the effectiveness of the proposed observer-controller scheme.     

An adaptive iterative learning algorithm for boundary control of a coupled ODE–PDE two-link rigid–flexible manipulator

To perform repetitive tasks, this paper proposes an adaptive boundary iterative learning control (ILC) scheme for a two-link rigid–flexible manipulator with parametric uncertainties. Using Hamilton?s principle, the coupled ordinary differential equation and partial differential equation (ODE–PDE) dynamic model of the system is established. In order to drive the joints to follow desired trajectory and eliminate deformation of flexible beam simultaneously, boundary control strategy is added based on the conventional joints torque control. The adaptive iterative learning algorithm for boundary control scheme includes a proportional-derivative (PD) feedback structure and an iterative term. This novel controller is designed to deal with the unmodeled dynamics and other unknown external disturbances. Numerical simulations are provided to verify the performance of proposed controller in MATLAB.     

Experimental validation of a continuous-time MCSI algorithm with bounded adaptive gains

Model reference adaptive control algorithms with minimal controller synthesis have proven to be an effective solution to tame the behaviour of linear systems subject to unknown or time-varying parameters, unmodelled dynamics and disturbances. However, a major drawback of the technique is that the adaptive control gains might exhibit an unbounded behaviour when facing bounded disturbances. Recently, a minimal controller synthesis algorithm with an integral part and either parameter projection or σ-modification strategies was proposed to guarantee boundedness of the adaptive gains. In this article, these controllers are experimentally validated for the first time by using an electro-mechanical system subject to significant rapidly varying disturbances and parametric uncertainty. Experimental results confirm the effectiveness of the modified minimal controller synthesis methods to keep the adaptive control gains bounded while providing, at the same time, tracking performances similar to that of the original algorithm.     

Iterative learning control-based tracking synchronization for linearly coupled reaction-diffusion neural networks with time delay and iteration-varying switching topology

In this paper, the D-type iterative learning control (ILC) protocol based on the local neighbor information is designed to achieve tracking synchronization for linearly coupled reaction-diffusion neural networks in presence of time delay and iteration-varying switching topology under a repetitive environment. Firstly, based on non-collocated sensors and actuators network, the proposed D-type ILC update law can realize tracking synchronization by utilizing output tracking errors. Then, by virtue of the contraction mapping principle, the sufficient convergence conditions of tracking synchronization errors are presented under the fixed commutation topology. Subsequently, the synchronization conclusions are extended to the iteration-varying commutation topology scenario. Finally, two numerical examples are provided to verify the efficacy of the obtained results.     

Output feedback adaptive robust control of hydraulic actuator with friction and model uncertainty compensation

This paper studies output feedback control of hydraulic actuators with modified continuous LuGre model based friction compensation and model uncertainty compensation. An output feedback adaptive robust controller is constructed which combines the adaptive control part and the robust control part seamlessly. The adaptive part is constructed to handle the parametric uncertainties existed in the model. The residuals coming from parameter adaption and the unmodeled dynamics are taken into consideration by the robust part. Since only the position signal is available, the velocity, pressure, and internal friction states are obtained by observation or estimation. The errors coming from observation and estimation are also dealt with the robust part. Furthermore, the convergence of the closed-loop controller–observer scheme is achieved by the Lyapunov method in the presence of parametric uncertainties only. Extensive comparative experiments performed on a hydraulic actuator demonstrate the effectiveness of the proposed controller–observer scheme.     

Consensus for heterogeneous networked multi-agent systems with switching topology and time-varying delays

This paper investigates consensus problem for heterogeneous discrete linear time-invariant (LTI) multi-agent systems subjected to time-varying network communication delays and switching topology. A new two-stage consensus protocol is proposed based on stochastic, indecomposable and aperiodic (SIA) matrix and pseudo predictive scheme. With pseudo predictive scheme the network delay is compromised. Consensus analysis based on seminorm is provided. Results give conditions for such systems with periodic switching topology and time-varying delays to reach consensus. Highlights of the paper include: the protocol can be implemented in a distributed manner; the pseudo predictive approach requires less computation and communication; the verification of consensus convergence does not require the global information about the communication topology; the protocol allows delay to be time-varying, topology to dynamically and asymmetrically switch and system mode to be unstable. Numerical and practical examples demonstrate the effectiveness of the theoretical results.     

On hyper-exponential stability and stabilization of linear systems by bounded linear time-varying controllers

Hyper-exponential stability analysis and hyper-exponential stabilization of linear systems by bounded linear time-varying feedback are investigated in this paper. On the one hand, we propose some Lyapunov-like hyper-exponential stability theorems (both global and local) based on the comparison principle and the concepts of hyper-exponentially stable functions and hyper-exponentially increasing functions. On the other hand, we establish methods to design bounded linear time-varying controllers such that hyper-exponential stability of linear time-invariant systems can be guaranteed. The key design tool is the utilization of a time-varying parameter contained in the controller and the properties of solution to a parametric Lyapunov equation. Both state feedback and observer-based output feedback are accommodated. As a further result, hyper-exponential semi-global stabilization for linear systems by bounded controls is discussed. Finally, the validity of the proposed schemes is illustrated through numerical simulations on spacecraft rendezvous control system.     

Event-triggered adaptive control of multi-agent systems with saturated input and partial state constraints

In this paper, we study the consensus tracking control problem of a class of strict-feedback multi-agent systems (MASs) with uncertain nonlinear dynamics, input saturation, output and partial state constraints (PSCs) which are assumed to be time-varying. An adaptive distributed control scheme is proposed for consensus achievement via output feedback and event-triggered strategy in directed networks containing a spanning tree. To handle saturated control inputs, a linear form of the control input is adopted by transforming the saturation function. The radial basis function neural network (RBFNN) is applied to approximate the uncertain nonlinear dynamics. Since the system outputs are the only available data, a high-gain adaptive observer based on RBFNN is constructed to estimate the unmeasurable states. To ensure that the constraints of system outputs and partial states are never violated, a barrier Lyapunov function (BLF) with time-varying boundary function is constructed. Event-triggered control (ETC) strategy is applied to save communication resources. By using backstepping design method, the proposed distributed controller can guarantee the boundedness of all system signals, consensus tracking with a bounded error and avoidance of Zeno behavior. Finally, the correctness of the theoretical results is verified by computer simulation.     

Decentralized adaptive fault tolerant control for a class of interconnected systems with nonlinear multisource disturbances

In this paper, a decentralized adaptive backstepping control scheme is proposed for a class of interconnected systems with nonlinear multisource disturbances and actuator faults. The nonlinear multisource disturbances comprise of two parts: one is the time-varying parameterized uncertainty; the other is the dynamic unexpected signal formulated by a nonlinear exogenous system. For each subsystem, the disturbances are compensated by an adaptive controller based on several dynamic signals and the bound estimation approach. Moreover, the effect of the actuator faults is tackled in spite of the fact that the faults may change in different cases infinite times. Meanwhile, through several smooth functions, the interactions among the subsystems are successfully disposed. As a result, the tracking errors can converge to an arbitrarily small value by choosing the design parameters appropriately. The proof of the closed-loop system stability is completed. Several illustrative examples are employed to demonstrate the effectiveness of the proposed method.     

Dynamical robust H∞ filtering for nonlinear uncertain systems: An LMI approach

In this paper, a new approach to robust H_∞ filtering for a class of nonlinear systems with time-varying uncertainties is proposed in the LMI framework based on a general dynamical observer structure. The nonlinearities under consideration are assumed to satisfy local Lipschitz conditions and appear in both state and measured output equations. The admissible Lipschitz constants of the nonlinear functions are maximized through LMI optimization. The resulting H_∞ observer guarantees asymptotic stability of the estimation error dynamics with prespecified disturbance attenuation level and is robust against time-varying parametric uncertainties as well as Lipschitz nonlinear additive uncertainty.     

Type-B Nussbaum function-based fault-tolerant control for a class of strict-feedback nonlinear systems

This paper studies the fault-tolerant control (FTC) problem of a class of strict-feedback nonlinear systems. First, we put forward a key theorem which shows that type-B Nussbaum functions can be extended to the cases containing multiple Nussbaum functions in the same Lyapunov inequality under certain conditions. Then, by using the techniques of Nussbaum functions and adaptive control, a new fault-tolerant control scheme is proposed. Compared with the previous work, this paper considers unknown time-varying control coefficients and unknown time-varying fault coefficients of actuators. It is proved that all the signals of the closed-loop system are globally bounded and the tracking error converges to zero asymptotically. Finally, simulations are provided to verify the effectiveness of the proposed control scheme.     

Leader-following consensus control of multiple nonholomomic mobile robots: An iterative learning adaptive control scheme

In this paper, the distributed iterative learning control for nonholonomic mobile robots with a time-varying reference is investigated, in which the mobile robots are with parametric uncertainties and are not fully actuated. Besides, the control gains of mobile robots are unknown. The leader is with a time-varying reference trajectory, and there is no need to assume that the time-varying reference is linearly parameterized by a set of known functions. A distributed control scheme is designed for each mobile robot based on a set of local compensatory filters designed by its neighborhood information. Stability analysis is established through a set of composite energy function. The uniform convergence of the consensus errors can be guaranteed. An example is given to show that our designed control law is effective.     

Adaptive fault-tolerant control for continuous-time Markovian jump systems with signal quantization

This paper investigates the adaptive fault-tolerant control problem for a class of continuous-time Markovian jump systems with digital communication constraints, parameter uncertainty, disturbance and actuator faults. In this study, the exact information for actuator fault, disturbance and the unparametrisable time-varying stuck fault are totally unknown. The dynamical uniform quantizer is utilized to perform the design work and the mismatched initializations at the coder and decoder sides are also considered. In this paper, a novel quantized adaptive fault-tolerant control design method is proposed to eliminate the effects of actuator fault, parameter uncertainty and disturbance. Moreover, it can be proved that the solutions of the overall closed-loop system are uniformly bounded, which is asymptotically stable almost surely. Finally, numerical examples are provided to verify the effectiveness of the new methodology.     

Stabilization irrespective of bounds of uncertain variations for linear uncertain systems with delays

In this study, the stabilizability irrespective of the bounds of uncertain parameters and time delays is investigated for linear uncertain delay systems. For uncertain systems without delays, a linear time-varying or time-invariant uncertain system has been shown to be stabilizable independent of the bounds of uncertain variations if and only if the system has a particular geometric configuration called an antisymmetric stepwise configuration (ASC) or a generalized antisymmetric stepwise configuration (GASC), respectively. In this study, fundamental approaches to investigating the stabilizability of delay systems with specific uncertainty structures such as ASCs or GASCs are presented. For a class of 3-dimensional systems, it is shown here that if a linear time-varying or time-invariant uncertain delay system has an ASC or a GASC, respectively, then the system can be stabilized, however large the given bounds of delays and uncertain parameters might be.     

A co-design methodology for cyber-physical systems under actuator fault and cyber attack

This paper investigates the controller design problem of cyber-physical systems (CPSs) to ensure the reliability and security when actuator faults in physical layers and attacks in cyber layers occur simultaneously. The actuator faults are time-varying, which cover bias fault, outage, loss of effectiveness and stuck. Besides that, some state-dependent cyber attacks are launched in control input commands and system measurement data channels, which may lead state information to the opposite direction. A novel co-design controller scheme is constructed by adopting a new Lyapunov function, Nussbaum-type function, and direct adaptive technique, which may further relax the requirements of actuator/sensor attacks information. It is proven that the states of the closed-loop system asymptotically converge to zero even if actuator faults, actuator attacks and sensor attack are time-varying and co-existing. Finally, simulation results are presented to show the effectiveness of the proposed control method.     

An improved design strategy for approximation-based adaptive event-triggered tracking of a class of uncertain nonlinear systems

This paper presents an improved adaptive design strategy for neural-network-based event-triggered tracking of uncertain strict-feedback nonlinear systems. An adaptive tracking scheme based on state variables transmitted from the sensor-to-controller channel is designed via only single neural network function approximator, regardless of unknown nonlinearities unmatched in the control input. Contrary to the existing multiple-function-approximators-based event-triggered backstepping control results with multiple triggering conditions dependent on all error surfaces, the proposed scheme only requires one triggering condition using a tracking error and thus can overcome the problem of the existing results that all virtual controllers with multiple function approximators should be computed in the sensor part. This leads to achieve the structural simplicity of the proposed event-triggered tracker in the presence of unmatched and unknown nonlinearities. Using the impulsive system approach and the error transformation technique, it is shown that all the signals of the closed-loop system are bounded and the tracking error is bounded within pre-designable time-varying bounds in the Lyapunov sense.     

Design of switching path-planning control for obstacle avoidance of mobile robot

Generally speaking, the mobile robot is capable of sensing its surrounding environment, interpreting the sensed information to obtain the knowledge of its location and the environment, and planning a real-time trajectory to reach the object. In this process, the issue of obstacle avoidance is a fundamental topic to be challenged. Thus, a switching path-planning control scheme is designed without detailed environmental information, large memory size, and heavy computation burden in this study for the obstacle avoidance of a mobile robot. In this scheme, the robot can gradually approach its object according to the motion tracking mode, obstacle avoidance mode, self-rotation mode, and robot state selection designed by learning and expert rules for enhancing the tracking speed and adapting to different environments. The effectiveness of the proposed adaptive path-planning control scheme is verified by numerical simulations and experimental results of a differential-driving mobile robot under the possible occurrence of obstacle shapes.     

Trajectory tracking double two-loop adaptive neural network control for a Quadrotor

In this paper, the development and experimental validation of a novel double two-loop nonlinear controller based on adaptive neural networks for a quadrotor are presented. The proposed controller has a two-loop structure: an outer loop for position control and an inner loop for attitude control. Similarly, both position and orientation controllers also have a two-loop design with an adaptive neural network in each inner loop. The output weight matrices of the neural networks are updated online through adaptation laws obtained from a rigorous error convergence analysis. Thus, a training stage is unnecessary prior to the neural network implementation. Additionally, an integral action is included in the controller to cope with constant disturbances. The error convergence analysis guarantees the achievement of the trajectory tracking task and the boundedness of the output weight matrix estimation errors. The proposed scheme is designed such that an accurate knowledge of the quadrotor parameters is not needed. A comparison against the proposed controller and two other well-known schemes is presented. The obtained results showed the functionality of the proposed controller and demonstrated robustness to parametric uncertainty.     

High dynamic adaptive robust control of load emulator with output feedback signal

This paper is concerned with the high performance adaptive robust control problem for an aircraft load emulator (LE). High dynamic capability is a key performance index of load emulator. However, physical load emulators exist a lot of nonlinearities and modeling uncertainties, which are the main obstacles for achieving high performance of load emulator. To handle the modeling uncertainty and achieve adjustable model-based compensation, firstly, the mathematical model of the load emulator is built, and then a nonlinear adaptive robust controller only with output feedback signal is proposed to improve the tracking accuracy and dynamic response capability. The controller is constructed based on the adaptive robust control framework with necessary design modifications required to accommodate uncertainties and nonlinearities of hydraulic load emulator. In this approach, nonlinearities are canceled by output feedback signal; and modeling errors, including parametric uncertainties and uncertain nonlinearities, are dealt with adaptive control and robust control respectively. The resulting controller guarantees a prescribed disturbance attenuation capability in general while achieving asymptotic output tracking in the absence of time-varying uncertainties. Experimental results are obtained to verify the high performance nature of the proposed control strategy, especially the high dynamic capability.