Adaptive compensation of uncertain Euler–Lagrange systems with multiple time-varying actuator faults

This work proposes the command tracking problem for uncertain Euler–Lagrange (EL) systems with multiple partial loss of effectiveness (PLOE) actuator faults. Compared to existing fault-tolerant controllers for EL systems, the proposed adaptive controller accounts for parametric uncertainties in the system and multiple time-varying actuator fault parameters. The proposed method can also handle an infinite number of fault cases. The closed-loop fault-tolerant system is treated as a switched dynamical system, and a switched system stability is established using multiple Lyapunov functions. It is shown that all signals are bounded in each sub-interval and at the switching instances, and asymptotic tracking can be obtained only for a finite number of fault occurrences, whereas tracking error is bounded for the infinite case. Finally, a simulation example on a robotic manipulator is presented to show the effectiveness of the proposed method.     

Robust Stability and Stabilization of a Class of Nonlinear Switched Discrete-Time Systems with Time-Varying Delays

In this paper, we investigate the problems of robust delay-dependent ℒ₂ gain analysis and feedback control synthesis for a class of nominally-linear switched discrete-time systems with time-varying delays, bounded nonlinearities and real convex bounded parametric uncertainties in all system matrices under arbitrary switching sequences. We develop new criteria for such class of switched systems based on the constructive use of an appropriate switched Lyapunov-Krasovskii functional coupled with Finsler’s Lemma and a free-weighting parameter matrix. We establish an LMI characterization of delay-dependent conditions under which the nonlinear switched delay system is robustly asymptotically stable with an ℒ₂-gain smaller than a prescribed constant level. Switched feedback schemes, based on state measurements, output measurements or by using dynamic output feedback, are designed to guarantee that the corresponding switched closed-loop system enjoys the delay-dependent asymptotic stability with an ℒ₂ gain smaller than a prescribed constant level. All the developed results are expressed in terms of convex optimization over LMIs and tested on representative examples.     

Robust analysis of discrete linear shift invariant systems represented by an interval matrix (Poster Presentation)

In this paper we describe a new bound in order to guaranteed the robust stability of a discrete linear shift invariant system which is represented by an interval matrix. This bound is based in the bound of Juang. The uncertainties are represented by an interval matrix. The system is represented in state variables with parametric uncertainty in the A matrix. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A computationally efficient robust tube based MPC for linear switched systems

This article considers the robust regulation problem for a class of constrained linear switched systems with bounded additive disturbances. The proposed solution extends the existing robust tube based model predictive control (RTBMPC) strategy for non-switched linear systems to switched systems. RTBMPC utilizes nominal model predictions, together with tightened sets constraints, to obtain a control policy that guarantees robust stabilization of the dynamic systems in presence of bounded uncertainties. In this work, similar to RTBMPC for non-switched systems, a disturbance rejection proportional controller is used to ensure that the closed loop trajectories of the switched linear system are bounded in a tube centered on the nominal system trajectories. To account for the uncertainty related to all sub-systems, the gain of this controller is chosen to simultaneously stabilize all switching dynamics. The switched system RTBMPC requires an on-line solution of a Mixed Integer Program (MIP), which is computationally expensive. To reduce the complexity of the MIP, a sub-optimal design with respect to the previous formulation is also proposed that uses the notion of a pre-terminal set in addition to the usual terminal set to ensure stability. The RTBMPC design with the pre-terminal set aids in determining the trade-off between the complexity of the control algorithm with the performance of the closed-loop system while ensuring robust stability. Simulation examples, including a Three-tank benchmark case study, are presented to illustrate features of the proposed MPC.     

A new method for control of nonlinear state-dependent switched systems

In this paper, a new method for the control of input-affine nonlinear switched systems is introduced. The system switching conditions are assumed to be state-dependent, rather than the simpler input-dependent case. The main contribution of this research is that the effects of switched dynamics are interpreted as a model uncertainty bounded within a polynomial of states norms, with unknown coefficients. In order to prevent extra conservativeness, coefficients are tuned adaptively, so that a minimal state-varying bound could be achieved. This is unlike the conventional sliding mode control (SMC) scheme, where the existence of a constant and usually large upper bound must be presumed. To address the challenge of coping with such a new concept of uncertainty, an extended form of the original adaptive fuzzy sliding mode control scheme is proposed. Adaptation laws are used to tune a fuzzy controller and also real-time estimation of the instantaneous bound of uncertainties. Closed-loop stability is guaranteed by proposing a group of multiple Lyapunov functions (MLF) with tunable parameters. Except for the mild condition that the largest difference between the magnitudes of the sub-manifolds of the switched system is bounded by a polynomial of states with uncertain coefficients, the proposed method has the distinct advantage that no information about the dynamic equations or switching conditions is required in the control design stage. The proposed method is applied to the two challenging case studies, depicting the outstanding effectiveness of the method.     

Delay-dependent BIBO stability analysis of switched uncertain neutral systems

This paper presents the analysis of delay-dependent bounded input bounded output (BIBO) stability for a class of switched uncertain neutral systems. The uncertainty is assumed to be of structured linear fractional form which includes the norm-bounded uncertainty as a special case. First, by introducing the general variation-of-constants formula of neutral systems with perturbation, the BIBO stability property of general linear switched neutral systems with perturbation is established. Next, combining the general variation-of-constants formula with the state-dependent switching rule, new approaches are presented to design the feedback controller and the switching rules. Furthermore, the BIBO stability criteria are obtained in terms of the so-called Lyapunov–Metzler linear matrix inequalities (LMIs). Finally, simulation examples are given to demonstrate the effectiveness and the potential of the proposed techniques in this paper.     

Sensitivity and stability analysis in DEA with bounded uncertainty

Measurement errors, incomplete information and noisy input and output data create difficulties in assessing the efficiency of data envelopment analysis (DEA). Previous studies have addressed uncertainty using interval analysis to extend the classical DEA problem to the case of bounded uncertainties. This paper proposes an approach to analyze the sensitivity and stability radius. By assuming that the data vary within a bounded interval, all of the decision making units (DMUs) can be classified as \(\hbox {E}^{++}, \hbox {E}^{+},\) and \(\hbox {E}^{-}\). To determine how sensitive these classifications are to possible data perturbations, the paper develops programs to calculate the stability radius within which the percentage data variation does not change the class of efficiency unit. In addition, the data changes are applied to not only the DMU that is being evaluation but also all of the DMUs and the various input and output subsets.     

Robust synchronization of impulsively-coupled complex switched networks with parametric uncertainties and time-varying delays

This paper presents a general impulsively-coupled complex switched network (ICCSN) model with parametric uncertainties and multiple Time-varying Delays in both the linear and nonlinear terms. The model is more general than those in the literature in that it contains switching behaviors on nodes and impulsive effects in the whole topology. Robust synchronization of ICCSNs with parametric uncertainties and time-varying delays is investigated. Based on the Lyapunov stability theory, delay-independent synchronization conditions for ICCSNs with uncertainties and delays are obtained. In addition, we consider five special synchronization cases: ICCSNs with delays in both the linear and nonlinear terms, ICCSNs with parametric uncertainties and delays either in the linear or in the nonlinear term, ICCSNs without switching behaviors but with parametric uncertainties and delays, and impulsively-switched-coupled complex switched network with uncertainties and delays. A systematic-design procedure is presented, and a numerical example is carried out to demonstrate the effectiveness of the proposed synchronization strategy. A comparative study of the maximum impulsive intervals for synchronization is presented for all special cases.     

Sliding Mode Techniques for Robust Trajectory Tracking as well as State and Parameter Estimation

Practical applications are often affected by uncertainties—more precisely bounded and stochastic disturbances. These have to be considered in robust control procedures to prevent a system from being unstable. Common sliding mode control strategies are often not able to cope with the mentioned impacts simultaneously, because they assume that the considered system is only affected by matched uncertainty. Another problem is the offline computation of the switching amplitude. Under these assumptions, important nonlinear system properties cannot be taken into account within the mathematical model of the system. Therefore, this paper presents sliding mode techniques, that on the one hand are able to consider bounded as well as stochastic uncertainties simultaneously, and on the other hand are not limited to the matched case. Firstly, a sliding mode control procedure taking into account both classes of uncertainty is shown. Additionally, a sliding mode observer for the simultaneous estimation of non-measurable system states and uncertain but bounded parameters is described despite stochastic disturbances. This is possible by using intervals for states and parameters in the resulting stochastic differential equations. Therefore, the Itô differential operator is involved and the system’s stability can be verified despite uncertainties and disturbances for both control and observer procedures. This operator is used for the online computation of the variable structure part gain (matrix of switching amplitudes) which is advantageous in contrast to common sliding mode procedures.     

Asymptotic disturbance attenuation properties for uncertain switched linear systems

In this paper, the disturbance attenuation properties in the sense of uniformly ultimate boundedness are investigated for a class of switched linear systems with parametric uncertainties and exterior disturbances. The aim is to characterize the conditions under which the switched system can achieve a finite disturbance attenuation level. First, arbitrary switching signals are considered, and a necessary and sufficient condition is given. Secondly, conditions on how to restrict the switching signals to achieve finite disturbance attenuation levels are investigated. Two cases are considered here that depend on whether all the subsystems are uniformly ultimately bounded or not. Both discrete-time and continuous-time switched systems are considered, and the techniques are based on multiple polyhedral Lyapunov functions and their extensions.     

Stabilization of switched linear systems by a controller of variable structure

We study the state stabilization problem for switched linear systems operating under parametric uncertainty and bounded coordinate disturbances. To solve the problem, we suggest an algorithmfor constructing a controller of variable structure on the basis of methods of simultaneous stabilization theory.     

一类奇异跳跃系统的鲁棒稳定性研究

研究了一类奇异跳跃系统的鲁棒稳定和镇定问题.在所研究的系统中,假设系数和转移率的不确定项范数有界.通过构造Lyapunov-Krasovskii函数,得到的充分条件可以保证系统在一定程度不确定性的影响下,是正则,无脉冲和均值意义下随机稳定的.最后,算例说明了所给方法的有效性.     

An Improved Delay-Dependent Criterion for Asymptotic Stability of Uncertain Dynamic Systems with Time-Varying Delays

In this paper, the problem of stability analysis for uncertain dynamic systems with time-varying delays is considered. The parametric uncertainties are assumed to be bounded in magnitude. Based on the Lyapunov stability theory, a new delay-dependent stability criterion for the system is established in terms of linear matrix inequalities, which can be solved easily by various efficient convex optimization algorithms. Two numerical examples are illustrated to show the effectiveness of proposed method.     

Robust Stability Criteria for Uncertain Neutral Systems with Interval Time-Varying Delay

In this paper, we consider the problem of robust stability of a class of linear uncertain neutral systems with interval time-varying delay under (i) nonlinear perturbations in state, and (ii) time-varying parametric uncertainties using Lyapunov-Krasovskii approach. By constructing a candidate Lyapunov-Krasovskii (LK) functional, that takes into account the delay-range information appropriately, less conservative robust stability criteria are proposed in terms of linear matrix inequalities (LMI) to compute the maximum allowable bound for the delay-range within which the uncertain neutral system under consideration remains asymptotically stable. The reduction in conservatism of the proposed stability criterion over recently reported results is attributed to the fact that time-derivative of the LK functional is bounded tightly without neglecting any useful terms using a minimal number of slack matrix variables. The analysis, subsequently, yields a stability condition in convex LMI framework, that can be solved non-conservatively at boundary conditions using standard LMI solvers. The effectiveness of the proposed stability criterion is demonstrated through standard numerical examples.     

Exponential stability of simultaneously triangularizable switched systems with explicit calculation of a common Lyapunov function

In this note, a common quadratic Lyapunov function is explicitly calculated for a linear hybrid system described by a family of simultaneously triangularizable matrices. The explicit construction of such a function allows not only obtaining an estimate of the convergence rate of the exponential stability of the switched system under arbitrary switching but also calculating an upper bound for the output during its transient response. Furthermore, the presented result is then extended to the case where the system is affected by parametric uncertainty, providing the corresponding results in terms of the nominal matrices and uncertainty bounds.     

Robust synchronization of singular complex switched networks with parametric uncertainties and unknown coupling topologies via impulsive control

This paper presents a general model of singular complex switched networks, in which the nodes can be singular dynamic systems and switching behaviors act on both nodes and edges. The parametric uncertainties and unknown coupling topologies are also considered in this model. Two robust synchronization schemes are discussed respectively. In one scheme, the network is synchronized to a homogeneous orbit and in the other one the network is synchronized to a weighted average of all the nodes. Based on the Lyapunov stability theory, different robust synchronization conditions for the two schemes are obtained for this singular complex switched network model via impulsive control. The similarities and differences between these synchronization conditions for the two schemes are discussed. In addition, three useful robust results for the special cases of the singular complex switched networks are presented. Two systematic-design procedures are presented for the two schemes, and three numerical examples are provided for illustrations.     

Interval Methods for Real-Time Capable Robust Control of Solid Oxide Fuel Cell Systems

Reliable control strategies for complex dynamic systems have to account for stability and robustness despite the presence of both parameter uncertainty and measurement errors. In addition, such control strategies have to comply with performance specifications that can be described either by the minimization of suitable cost functions or by direct specifications of desired reference trajectories. To handle bounded uncertainty and errors in a reliable way, it is possible to include the use of interval analysis in real-time control environments. Previous work has shown that approaches based on the general methodology of sliding mode and predictive control are promising options in this context. This paper presents a comparison of the properties of interval extensions of both types of control procedures for the thermal subsystem of a high-temperature solid oxide fuel cell. Representative simulation results conclude this contribution.     

Almost Sure Stability Analysis of Parametric Roll in Random Seas Based on Top Lyapunov Exponent

Stability analysis of the upright position of a ship in random head or following seas is presented. Such seas lead to parametric excitation of roll motion due to periodic variations of the righting lever. The development of simple criteria for the occurrence of parametric induced roll motion in random seas is of major interest for improvement of the international code on intact stability provided by the International Maritime Organization. The stability analysis in random seas is based on the calculation of the top Lyapunov exponent using the fact, that a negative top Lyapunov exponent yields no roll motion. With this findings, roll motion can be excluded for specific sea states. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Delay‐dependent robust reliable control for uncertain switched neutral systems

This article investigates the robust reliable control problem for a class of uncertain switched neutral systems with mixed interval time‐varying delays. The system under study involves state time‐delay, parameter uncertainties and possible actuator failures. In particular, the parameter uncertainties is assumed to satisfy linear fractional transformation formulation and the involved state delay are assumed to be randomly time varying which is modeled by introducing Bernoulli distributed sequences. The main objective of this article is to obtain robust reliable feedback controller design to achieve the exponential stability of the closed‐loop system in the presence of for all admissible parameter uncertainties. The proposed results not only applicable for the normal operating case of the system, but also in the presence of certain actuator failures. By constructing an appropriate Lyapunov–Krasovskii functional, a new set of criteria is derived for ensuring the robust exponential stability of the closed‐loop switched neutral system. More precisely, zero inequality approach, Wirtinger's based inequality, convex combination technique and average dwell time approach are used to simplify the derivation in the main results. Finally, numerical examples with simulation result are given to illustrate the effectiveness and applicability of the proposed design approach. © 2015 Wiley Periodicals, Inc. Complexity 21: 224–237, 2016     

Dynamic analysis of Markovian jumping impulsive stochastic Cohen–Grossberg neural networks with discrete interval and distributed time-varying delays

In this paper, the dynamic analysis problem is considered for a new class of Markovian jumping impulsive stochastic Cohen–Grossberg neural networks (CGNNs) with discrete interval and distributed delays. The parameter uncertainties are assumed to be norm bounded and the discrete delay is assumed to be time-varying and belonging to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the Lyapunov–Krasovskii functional and stochastic stability theory, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities. Some asymptotic stability criteria are formulated by means of the feasibility of a linear matrix inequality (LMI), which can be easily calculated by LMI Toolbox in Matlab. A numerical example is provided to show that the proposed results significantly improve the allowable upper bounds of delays over some existing results in the literature.