Transfer learning for high‐precision trajectory tracking through adaptive feedback and iterative learning

Robust and adaptive control strategies are needed when robots or automated systems are introduced to unknown and dynamic environments where they are required to cope with disturbances, unmodeled dynamics, and parametric uncertainties. In this paper, we demonstrate the capabilities of a combined adaptive control and iterative learning control (ILC) framework to achieve high‐precision trajectory tracking in the presence of unknown and changing disturbances. The adaptive controller makes the system behave close to a reference model; however, it does not guarantee that perfect trajectory tracking is achieved, while ILC improves trajectory tracking performance based on previous iterations. The combined framework in this paper uses adaptive control as an underlying controller that achieves a robust and repeatable behavior, while the ILC acts as a high‐level adaptation scheme that mainly compensates for systematic tracking errors. We illustrate that this framework enables transfer learning between dynamically different systems, where learned experience of one system can be shown to be beneficial for another different system. Experimental results with two different quadrotors show the superior performance of the combined ‐ILC framework compared with approaches using ILC with an underlying proportional‐derivative controller or proportional‐integral‐derivative controller. Results highlight that our ‐ILC framework can achieve high‐precision trajectory tracking when unknown and changing disturbances are present and can achieve transfer of learned experience between dynamically different systems. Moreover, our approach is able to achieve precise trajectory tracking in the first attempt when the initial input is generated based on the reference model of the adaptive controller.     

Adaptive neural network asymptotic tracking control for a class of stochastic nonlinear systems with unknown control gains and full state constraints

This article addresses the issue of adaptive intelligent asymptotic tracking control for a class of stochastic nonlinear systems with unknown control gains and full state constraints. Unlike the existing systems in the literature in which the prior knowledge of the control gains is available for the controller design, the salient feature of our considered system is that the control gains are allowed to be unknown but have a positive sign. By introducing an auxiliary virtual controller and employing the new properties of Numbness functions, the major technique difficulty arising from the unknown control gains is overcome. At the same time, the -type barrier Lyapunov functions are introduced to prevent the violation of the state constraints. What's more, neural networks' universal online approximation ability and gain suppression inequality technology are combined in the frame of adaptive backstepping design, so that a new control method is proposed, which cannot only realize the asymptotic tracking control in probability, but also meet the requirement of the full state constraints imposed on the system. In the end, the simulation results for a practical example demonstrate the effectiveness of the proposed control method.     

Hybrid-triggered fault detection filter design for networked Takagi–Sugeno fuzzy systems subject to persistent heavy noise disturbance

In the network environment, the single time-triggered scheme wastes limited bandwidth resources due to all the sampled data are transmitted to the networks, and the single event-triggered scheme may increase system error because of ignoring factors such as changes in network utilization. To reduce the design conservatism, this paper is concerned with the hybrid-triggered L₁ fault detection filter design for a class of nonlinear networked control systems (NCSs) described by Takagi–Sugeno (T-S) fuzzy model. Taking the effects of time-triggered scheme and event-triggered scheme into consideration simultaneously, we construct a fuzzy fault detection system. New results on stability and L₁ performance are proposed for fuzzy fault detection system by exploiting the Lyapunov–Krasovskii functional and by means of the integral inequality method. Specially, attention is focused on the design of fault detection filter that guarantees a prescribed L₁ noise attenuation level . Finally, two examples are presented to demonstrate the effectiveness of the proposed method.     

An adaptive learning and control architecture for mitigating sensor and actuator attacks in connected autonomous vehicle platoons

In this paper, we develop an adaptive control algorithm for addressing security for a class of networked vehicles that comprise a formation of human‐driven vehicles sharing kinematic data and an autonomous vehicle in the aft of the vehicle formation receiving data from the preceding vehicles through wireless vehicle‐to‐vehicle communication devices. Specifically, we develop an adaptive controller for mitigating time‐invariant state‐dependent adversarial sensor and actuator attacks while guaranteeing uniform ultimate boundedness of the closed‐loop networked system. Furthermore, an adaptive learning framework is presented for identifying the state space model parameters based on input‐output data. This learning technique utilizes previously stored data as well as current data to identify the system parameters using a relaxed persistence of excitation condition. The effectiveness of the proposed approach is demonstrated by an illustrative numerical example involving a platoon of connected vehicles.     

Robust real-time parameter estimation for linear systems affected by external noises and uncertainties

A robust adaptive parameter estimation method, based on the application of a full-order filter capable of rejecting exogenous disturbances, is proposed in this article. A linear matrix inequality condition is proposed to synthesize the desired robust filter, assuming the presence of a known input control with constraints. The filter uses the output of the system to estimate the desired signal that will be employed in the adaptive estimation procedure and, to assure robustness to exogenous noise and unstructured uncertainties, the guaranteed cost is minimized in the synthesis condition. The filtered signals are then applied to an adaptive procedure to estimate the unknown system's internal parameters, which is also proposed in this article. It is shown that lower values for the guaranteed cost from the disturbance input to the error output of the filter imply more accurate estimations of the parameters. The efficiency of the proposed estimation technique is illustrated through a simulated model and a physical system has been considered to validate real-time estimation.     

Finite‐time dissipativity‐based filter design for networked control systems

This paper investigates the problem of finite‐time boundedness and dissipativity‐based filter design for networked control systems together with parameter uncertainties and random packet dropouts. The packet transmission information is defined by using Bernoulli distributed white sequence which characterizes the measurement conditions. Some new sufficient conditions are established to ensure that the filtering error system is stochastically finite‐time bounded and strictly finite‐time dissipative. These sufficient conditions to design the filter parameters are derived by using linear matrix inequalities and reciprocally convex approach. Finally, an example is given to validate the effectiveness of the proposed filter design.     

A robust adaptive control architecture for disturbance rejection and uncertainty suppression with L ∞ transient and steady‐state performance guarantees

In this paper, a new adaptive control architecture for linear and nonlinear uncertain dynamical systems is developed to address the problem of high‐gain adaptive control. Specifically, the proposed framework involves a new and novel controller architecture involving a modification term in the update law that minimizes an error criterion involving the distance between the weighted regressor vector and the weighted system error states. This modification term allows for fast adaptation without hindering system robustness. In particular, we show that the governing tracking closed‐loop system error equation approximates a Hurwitz linear time‐invariant dynamical system with input–output signals. This key feature of our framework allows for robust stability analysis of the proposed adaptive control law using system theory. We further show that by properly choosing the design parameters in the modification term, we can guarantee a desired bandwidth of the adaptive controller, guaranteed transient closed‐loop performance, and an a priori characterization of the size of the ultimate bound of the closed‐loop system trajectories. Several illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

LPNN-based approach for LASSO problem via a sequence of regularized minimizations

In compressive sampling theory, the least absolute shrinkage and selection operator (LASSO) is a representative problem. Nevertheless, the non-differentiable constraint impedes the use of Lagrange programming neural networks (LPNNs). We present in this article the -LPNN model, a novel algorithm that tackles the LASSO minimization together with the underlying theory support. First, we design a sequence of smooth constrained optimization problems, by introducing a convenient differentiable approximation to the non-differentiable -norm constraint. Next, we prove that the optimal solutions of the regularized intermediate problems converge to the optimal sparse signal for the LASSO. Then, for every regularized problem from the sequence, the -LPNN dynamic model is derived, and the asymptotic stability of its equilibrium state is established as well. Finally, numerical simulations are carried out to compare the performance of the proposed -LPNN algorithm with both the LASSO-LPNN model and a standard digital method.     

Robust adaptive passivity-based PIλD control

In this article, we develop proportional, fractional-integral, and derivative () controllers for the regulation and tracking problems of nonlinear systems. The analytic results are obtained by extending the passivity-based approach to include fractional operators. Robustness under parametric uncertainty is dealt with by a combination with an adaptive scheme. It is also shown their robustness under additive noise and their robustness under uncertainty in the derivation order. The advantages in the controlled system performance and in the control energy consumption in comparison to classic PI and proportional integral derivative controllers are illustrated for the quadratic boost converter and a benchmark system in the literature.     

Positive invariant set estimation of adaptive controller in the presence of input saturation

For a class of linear dynamical systems with constant unknown parameters, an adaptive control scheme is developed that provides stable adaptation in the presence of input magnitude constraints. Whereas for open‐loop stable systems the results are global, for open‐loop unstable systems, the problem of nonconservative estimation of the nonempty positive invariant set is cast into an LMI framework, which can be efficiently solved numerically via convex optimization. To achieve this, a standard result toward invariant set characterization is appropriately extended to accommodate bounded disturbance and model uncertainties. In addition to closed‐loop stability, performance bounds of the adaptive closed‐loop system are analyzed, and the degradation due to the possible control deficiency is quantified. Simulation examples of aerospace applications are included to illustrate the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust neuro‐adaptive cooperative control of multi‐agent port‐controlled Hamiltonian systems

This paper presents the distributed cooperative tracking control of the multi‐agent port‐controlled Hamiltonian (PCH) systems that are networked through a directed graph. Controller is made robust against the parametric uncertainties using neural networks. Dynamics of the the proposed novel neural network tuning law is driven by both the position and the velocity errors owing to the information preserving filtering of the Hamiltonian gradient. In addition, the PCH structure of the closed‐loop system is preserved and the controller achieves the disturbance attenuation objective. Simulations are performed on a group of robotic manipulators to demonstrate the efficacy of the proposed controller. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust nonlinear adaptation algorithms for multitask prediction networks

High fidelity behavior prediction of intelligent agents is critical in many applications, which is challenging due to the stochasticity, heterogeneity, and time-varying nature of agent behaviors. Prediction models that work for one individual may not be applicable to another. Besides, the prediction model trained on the training set may not generalize to the testing set. These challenges motivate the adoption of online adaptation algorithms to update prediction models in real-time to improve the prediction performance. This article considers online adaptable multitask prediction for both intention and trajectory. The goal of online adaptation is to improve the performance of both intention and trajectory predictions with only the feedback of the observed trajectory. We first introduce a generic -step adaptation algorithm of the multitask prediction model that updates the model parameters with the trajectory prediction error in recent steps. Inspired by extended Kalman filter (EKF), a base adaptation algorithm modified EKF with forgetting factor (MEKF) is introduced. In order to improve the performance of MEKF, generalized exponential moving average filtering techniques are adopted. Then this article introduces a dynamic multiepoch update strategy to effectively utilize samples received in real time. With all these extensions, we propose a robust online adaptation algorithm: MEKF with moving average and dynamic multiepoch strategy (MEKF_{MA − ME} ). We empirically study the best set of parameters to adapt in the multitask prediction model and demonstrate the effectiveness of the proposed adaptation algorithms to reduce the prediction error.     

Enhanced adaptive control for a benchmark piezoelectric‐actuated system via fuzzy approximation

This paper investigates the problem of the high precision tracking control of piezoelectric actuators (PEAs) without using the inverse of the uncertain hysteresis. Based on fuzzy system approximator and particle swarm optimization (PSO) algorithm, a proposed enhanced adaptive controller is developed. The proposed controller provides fast and robust adaptation simultaneously with guaranteed desired transient performance. Moreover, it has a simple form and requires fewer adaptation parameters. The adaptation gain is determined via PSO algorithm. The proposed controller is tested on a lab‐scale PEA system. Experimental results with comparative studies with different techniques have been developed. The simulation results reveal that the proposed controller outperforms the other controllers in terms of normalized root‐mean‐square and maximum tracking errors for different frequencies.     

Robust adaptive dynamic surface control for linear time‐varying systems

In this paper, robust output‐feedback tracking control is considered for a class of linear time‐varying plants whose time‐varying parameters are unknown bounded with bounded derivatives and output is affected by unknown bounded additive disturbances. Using adaptive dynamic surface control technique, the proposed scheme possesses the following advantages: (1) the design procedure is simple and the control law is easy to be implemented, and (2) by introducing an initialization technique, together with adjusting some design parameters, the performance of system tracking error can be guaranteed regardless of the time variation. It is proved that with the proposed scheme, all the closed‐loop signals are semi‐globally uniformly ultimately bounded. Simulation results are presented to demonstrate the effectiveness of the proposed scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

Reliable H∞ control for 2-D discrete switched systems with state delays and actuator failures

This article is concerned with the reliable H_∞ control problem against actuator failures for discrete two-dimensional (2-D) switched systems with state delays and actuator faults described by the second Fornasini-Marchesini (FM) state-space model. By resorting to the average dwell time (ADT) approach, also by constructing an appropriate Lyapunov-Krasovskii functional and using the Wirtinger inequality, some sufficient conditions for the exponential stability analysis and weighted H_∞ performance of the given system are derived. Then, based on the obtained conditions, a reliable H_∞ controller design approach is presented such that the resulting closed-loop system is exponentially stable with a weighted H_∞ performance , not only when all actuators are in normal conditions, but also in the case of some actuator failures. Finally, two numerical examples are examined to demonstrate the effectiveness of the proposed results.     

A novel unknown input observer-based fault detection with application to a two-stage chemical reactor

This article presents a new method of fault detection for the two-stage chemical reactor system. The process can be carried out effectively in the presence of the time-delay and the unknown inputs and the parameter uncertainties by using the observer-based method technique. In order to detect the actuator fault, a novel unknown input observer is employed as the residual generator. Multi-objective optimization techniques and a new performance index are adopted to ensure the robustness and sensitivity of the fault detection observer. Then the problem of fault detection is reduced to the problem of model matching. Furthermore, sufficient conditions are obtained to guarantee that the error system is asymptotically stable with an performance by means of the Lyapunov function technique. Finally, a two-stage chemical system is borrowed to demonstrate the effectiveness of the obtained methods.     

An enhanced state estimation for linear parabolic PDE systems with mobile sensors

This paper studies an enhanced state estimation problem of distributed parameter processes modeled by a linear parabolic partial differential equation using mobile sensors. The proposed estimation scheme contains a state estimator and the guidance of mobile sensors, where the spatial domain is decomposed into multiple subdomains according to the number of sensors and each sensor is capable of moving within the respective subdomain. The state estimator is desired to make the state estimation error system exponentially stable while providing an performance bound. The mobile sensor guidance is used to enhance the transient performance of the error system. By the Lyapunov direct technique, an integrated design of state estimator and mobile sensor guidance laws is developed in the form of bilinear matrix inequalities (BMIs) to meet the desired design objectives. Moreover, to make the performance bound as small as possible, a suboptimal enhanced state estimation problem is formulated as a BMI optimization one, which can be solved via an iterative linear matrix inequality algorithm. Finally, numerical simulations are given to show the effectiveness of the proposed method.     

Adaptive dynamic programming for tracking design of uncertain nonlinear systems with disturbances and input constraints

In this paper, the tracking controller is designed for uncertain nonlinear systems with external disturbances and input constraints. A discounted nonquadratic function is introduced, which encodes the constrained input into the performance. The key difficulty for tracking control is the requirement of solving the tracking Hamilton‐Jacobi‐Isaacs equation, which is a partial differential equation. It is impossible or extremely difficult to solve analytically even in simple cases. To overcome the difficulty, an online model‐free integral reinforcement learning (IRL) algorithm is proposed to learn online in real time the solution to the tracking Hamilton‐Jacobi‐Isaacs equation without requiring any knowledge of system dynamics. To implement it, critic‐actor‐disturbance neural networks (NNs) are built, and the 3 NNs are updated simultaneously. Stability and convergence analyses are shown by the Lyapunov method. In addition, a robust term is added to the controller to attenuate the effect of NN approximation errors, which leads to the asymptotic stability of the closed‐loop systems. Finally, 2 simulation examples show the effectiveness of the proposed algorithm.     

Input-to-state learning of recurrent neural networks with delay and disturbance

This article deals with the issue of input-to-state stabilization for recurrent neural networks with delay and external disturbance. The goal is to design a suitable weight-learning law to make the considered network input-to-state stable with a predefined -gain. Based on the solution of linear matrix inequalities, two schemes for the desired learning law are presented via using decay-rate-dependent and decay-rate-independent Lyapunov functionals, respectively. It is shown that, in the absence of external disturbance, the proposed learning law also guarantees the exponential stability of the network. To illustrate the applicability of the present weight-learning law, two numerical examples with simulations are given.     

Composite adaptive anti‐disturbance resilient control for Markovian jump systems with partly known transition rate and multiple disturbances

In this paper, the problem of composite adaptive anti‐disturbance resilient control is investigated for Markovian jump systems with partly known transition rate and multiple disturbances. The considered multiple disturbances include two types: one is external disturbance, while the other is an unexpected nonlinear signal which is described as a nonlinear function. Composite adaptive disturbance observers are constructed to estimate these disturbances, and the estimations are applied to feedforward compensation. Then a composite adaptive anti‐disturbance resilient controller is obtained. Furthermore, some sufficient conditions are presented in terms of linear matrix inequalities such that the closed‐loop system is stochastically stable with performance. Finally, a numerical example and an application example are given to illustrate the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.