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.     

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.     

Adaptive output feedback regulation for a class of uncertain feedforward nonlinear systems

In this paper, we solve the problem of global output feedback regulation for uncertain feedforward nonlinear systems. The nonlinear functions, in the class of systems under consideration, are assumed to be dominated by an input‐output function multiplied by an unknown parameter and a linear unmeasured states. Contrarily to the previous works, the interval of the output's power has been expanded from to . A numerical example is provided to illustrate the effectiveness of the proposed design scheme. Copyright © 2016 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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Fault estimation and tolerant control for discrete‐time switched systems with sojourn probabilities

This paper addresses the issue of fault estimation and accommodation for a discrete‐time switched system with actuator faults. Here, we assume that the sojourn probabilities are known a priori. By using the reduced‐order observer method, the sojourn probability approach, and the Lyapunov technique, a fault estimation algorithm is obtained for the considered system. The main objective of this work is to design a dynamic output feedback fault‐tolerant controller based on the obtained fault estimation information such that the closed‐loop discrete‐time switched system with available sojourn probabilities is robustly mean‐square stable and satisfies a prescribed mixed and passivity disturbance attenuation level in the presence of actuator faults. More precisely, a dynamic output feedback fault‐tolerant controller is established in terms of linear matrix inequalities. Finally, numerical examples are provided to illustrate the usefulness and effectiveness of the proposed design technique.     

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.     

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.     

Mixed and passive filtering for linear switched systems with average dwell time

In this paper, a new performance index is proposed for switched systems. The new performance index can be viewed as the mixed weighted and passivity performance. This new performance index covers the weighted performance and the passivity performance as special cases. Based on this new performance index, the weighted filtering problem and the passive filtering problem of linear switched systems with unstable subsystems are solved in a unified framework. The states of the filtering error system constructed by the augmentation technique will be divergent when unstable subsystems are activated. To overcome this problem, a set of mode‐dependent filters of a Luenberger‐like observer type is constructed. The multiple Lyapunov function approach and the average dwell‐time technique are employed to solve the mixed filtering problem. New sufficient conditions for the existence of mixed and passive filters are developed, which ensure the filtering error system to be asymptotically stable with a prescribed mixed and passivity performance index. Moreover, the desired mixed and passive filters can be constructed by solving a set of linear matrix inequalities. Finally, numerical examples are given to demonstrate the applicability and advantage of the obtained results.     

Excitation and steam‐valving coordinated robust controller design for multi‐machine power systems based on the multi‐index nonlinear robust control approach

This paper proposes a novel multi‐index nonlinear robust control (MNRC) approach for multi‐machine power systems. The MNRC approach combines multi‐index nonlinear control with the control theory. With the multi‐index nonlinear control, which selects the output functions as arithmetic combination of state variables, multiple performance indices of the controlled system can be achieved simultaneously in the nonlinear control framework. The control is able to ensure that the system possess the desired robust performance during disturbance. Then, excitation and steam‐valving coordinated robust controllers are developed based on the MNRC approach for multi‐machine power systems. The effectiveness of the proposed robust controller is evaluated by a six‐machine power system simulation. Simulation results show that the expected dynamic and steady‐state performances of power system can be achieved with the MNRC approach. Meanwhile, it is able to achieve the prescribed system performance despite the presence of disturbances. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Random adaptive control for cluster synchronization of complex networks with distinct communities

In this paper, we investigate the cluster synchronization for complex networks with time‐varying delayed couplings, stochastic disturbance, and non‐identical nodes in different clusters. Based on randomly occurring controllers, some Bernoulli stochastic variables are introduced to describe the controllers, then, a fraction of nodes in clusters, which have direct connections to the other clusters, is controlled, and the states of the whole dynamical networks can be globally forced to the objective cluster states. Sufficient conditions are derived to guarantee the realization of the mean square cluster synchronization pattern for all initial values by means of Lyapunov stability theory, It differential formula, and LMI approach. Besides, by designing the randomly occurring adaptive update law, some suitable control gains are obtained. Finally, numerical simulations are also given to demonstrate the effectiveness and validity of the main result. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Event-triggered adaptive backstepping tracking control for a class of nonlinear fractional order systems

This article investigates the problem of event-trigger based adaptive backstepping control for a class of nonlinear fractional order systems. By introducing an appropriate transformation of frequency distributed model, the fractional-order indirect Lyapunov method with is obtained. In addition, the event-triggered adaptive controller is developed by employing the event-triggered control approach. Meanwhile, by the proposed adaptive control scheme, all the closed-loop signals are globally uniformly bounded, and the tracking error converges to a small neighborhood of the origin. Finally, simulation results are provided to testify the availability of the presented controller.     

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.