Robust reliable dissipative filtering for Markovian jump nonlinear systems with uncertainties

This paper investigates the problem of robust reliable dissipative filtering for a class of Markovian jump nonlinear systems with uncertainties and time‐varying transition probability matrix described by a polytope. Our main attention is focused on the design of a reliable dissipative filter performance for the filtering error system such that the resulting error system is stochastically stable and strictly dissipative. By introducing a novel augmented Lyapunov–Krasovskii functional, a new set of sufficient conditions is obtained for the existence of reliable dissipative filter design in terms of linear matrix inequalities (LMIs). More precisely, a sufficient LMI condition is derived for reliable dissipative filtering that unifies the conditions for filtering with passivity and H_∞ performances. Moreover, the filter gains are characterized in terms of solution to a set of linear matrix inequalities. Finally, two numerical examples are provided to demonstrate the effectiveness and potential of the proposed design technique. Copyright © 2016 John Wiley & Sons, Ltd.     

Implementation of a square‐root filtering approach in marginalized particle filters for mixed linear/nonlinear state‐space models

Marginalized particle filter (MPF) takes advantage of both Kalman filter and particle filter frameworks to estimate nonlinear state‐space models with reduced number of calculations in comparison to particle filter. However, due to existence of Kalman filter framework inside MPF, some limitations are introduced in implementation of MPF especially in embedded systems with finite numerical accuracies. In this paper, for the first time, we propose a novel square‐root filtering strategy for MPFs to alleviate these restrictions using modified factorization. Typical square‐root Kalman filters cannot be employed inside MPF due to the presence of minus operations in some equations of MPF. However, our method can be easily implemented inside the MPF structure. The proposed method can be used in any application that employs MPFs to estimate the mixed linear/nonlinear state‐space models. In order to demonstrate its usefulness, we employed the proposed square‐root filtering method inside a marginalized particle extended Kalman filter (MP‐EKF) structure, which was specifically designed for ECG denoising. The experimental results showed that, in the field of ECG denoising, the square‐root MP‐EKF performs more consistently than MP‐EKF in white Gaussian noises.     

filtering for switched discrete‐time systems under asynchronous switching: A dwell‐time dependent Lyapunov functional method

In this article, the filtering problem for switched discrete‐time linear systems under asynchronous switching is addressed in the framework of dwell time, where ‘asynchronous switching’ covers more general and practical cases, for example, the switching lags caused by mode identification process are taken into consideration. Firstly, a novel dwell‐time dependent Lyapunov function (DTDLF) is introduced to solve stability and ?₂ gain analysis problems. The main advantage of DTDLF approach is that the derived conditions are all convex in system matrices, so it is convenient to be applied into filter design with performance instead of weighted performance as many other previous results. Thus, on the basis of DTLDF, a dwell‐time dependent filter with time‐varying structure is proposed to achieve the desirable non‐weighted filtering performance. It is notable that the proposed approach can also easily characterize the relationships among filtering performance, dwell time, and asynchronous time. Two examples are provided to validate the theoretical findings in this paper. Copyright © 2014 John Wiley & Sons, Ltd.     

and filter design for polytopic continuous‐time Markov jump linear systems with uncertain transition rates

This paper addresses the problems of and full‐order filter design for continuous‐time Markov jump linear systems subject to uncertainties. Different from the available methods in the literature, the main novelty of the proposed approach is the possibility of computing bounds to the and norms of the augmented system composed by the uncertain Markov jump linear system plus the robust filter through Lyapunov matrices depending polynomially on the uncertainties affecting independently the matrices of each operation mode and the transition rate matrix. By means of a suitable representation of the uncertainties, the proposed filter design conditions are expressed in terms of linear matrix inequality relaxations associated with searches on scalar parameters. As an additional flexibility, the conditions can be used to synthesize filters with partial, complete, or null Markov mode availability. Numerical experiments illustrate that the proposed approach is more general and can be less conservative than the available methods. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

Modular‐based adaptive control of uncertain nonlinear time‐varying systems with piecewise jumping parameters

Nonlinear time‐varying systems exist widely in practice. Therefore, it is of great theoretical importance and practical value to investigate the problem of controlling such systems. However, the results available in developing adaptive control to address such a problem are still limited. Especially a majority of them are restricted to be slowly time‐varying linear systems. This paper presents a modular‐based adaptive control scheme for parametric strict feedback nonlinear time‐varying systems. The parameters considered include both continuous and piecewise time‐varying parameters, and they are not necessarily restricted to be slowly time‐varying or infrequent jumping. The technique of adaptive backstepping with nonlinear damping is employed in the control design module, while the parameter projection algorithm is performed on the parameter estimation module. It is proved that the uniform boundedness of all closed‐loop system signals can be guaranteed with the proposed control scheme. The performance of the tracking error in the mean square sense with respect to the parameter variation rate is also established. Furthermore, perfect asymptotically tracking can be achieved when the varying rates of unknown parameters are in the space. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

A robust output error identifier for continuous‐time systems

This paper shows that the adaptive output error identifier for linear time‐invariant continuous‐time systems proposed by Bestser and Zeheb is robust vis‐à‐vis finite energy measurement noise. More precisely, it is proven that the map from the noise to the estimation error is –stable—provided a tuning parameter is chosen sufficiently large. A procedure to determine the required minimal value of this parameter is also given. If the noise is exponentially vanishing, asymptotic convergence to zero of the prediction error is achieved. Instrumental for the establishment of the results is a suitable decomposition of the error system equations that allows us to strengthen—to strict—the well‐known passivity property of the identifier. The estimator neither requires fast adaptation, a dead‐zone, nor the knowledge of an upperbound on the noise magnitude, which is an essential requirement to prove stability of standard output error identifiers. To robustify the estimator with respect to non‐square integrable (but bounded) noises, a prediction error‐dependent leakage term is added in the integral adaptation. –stability of the modified scheme is established under a technical assumption. A simulated example, which is unstable for the equation error identifier and the output error identifier of Bestser and Zeheb, is used to illustrate the noise insensitivity property of the new scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

Integrated design of fault detection,isolation, and control for continuous‐time Markovian jump systems

In this paper, the problem of integrated fault detection, isolation, and control design of continuous‐time Markovian jump linear systems with uncertain transition probabilities is introduced and addressed for the first time in the literature. A single Markovian jump module designated as the integrated fault detection, isolation, and control under a mixed robust framework is considered to simultaneously achieve the desired detection, isolation, and control objectives. Conventional mixed robust approaches to the fault detection and isolation problem lead to conservative results due to the selection of identical Lyapunov matrices. Consequently, the extended linear matrix inequality methodology is utilized in this work to reduce the conservativeness of standard approaches by introducing additional matrix variables so that the coupling of Lyapunov matrices with the system matrices is eliminated. Simulation results for an application to the GE F‐404 aircraft engine system illustrate the effectiveness and capabilities of our proposed design methodologies. Comparisons with relevant work in the literature are also provided to demonstrate the advantages of our proposed solutions.     

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.     

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.     

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.     

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.     

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.     

An improved finite frequency approach to robust filter design for LTI systems with polytopic uncertainties

In this paper, the finite frequency robust filtering problem (‐FFRFP), design of a robust filter minimizing the norm from the disturbance input to the estimation error evaluated over a prescribed finite frequency domain, is considered for continuous‐time and discrete‐time linear time‐invariant (LTI) systems with polytopic parameter uncertainties. By means of the generalized Kalman–Yakubovich–Popov (KYP) lemma in combination with a result known as Finsler's lemma, the ‐FFRFP is cast as a linear matrix inequality (LMI) optimization. Examples are given to demonstrate that the proposed condition can achieve improvement over the previous ones in the literature. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

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.