Robust reliable L2 – L∞ control for continuous‐time systems with nonlinear actuator failures

This article examines the reliable L₂ – L_∞ control design problem for a class of continuous‐time linear systems subject to external disturbances and mixed actuator failures via input delay approach. Also, due to the occurrence of nonlinear circumstances in the control input, a more generalized and practical actuator fault model containing both linear and nonlinear terms is constructed to the addressed control system. Our attention is focused on the design of the robust state feedback reliable sampled‐data controller that guarantees the robust asymptotic stability of the resulting closed‐loop system with an L₂ – L_∞ prescribed performance level γ > 0, for all the possible actuator failure cases. For this purpose, by constructing an appropriate Lyapunov–Krasovskii functional (LKF) and utilizing few integral inequality techniques, some novel sufficient stabilization conditions in terms of linear matrix inequalities (LMIs) are established for the considered system. Moreover, the established stabilizability conditions pave the way for designing the robust reliable sampled‐data controller as the solution to a set of LMIs. Finally, as an example, a wheeled mobile robot trailer model is considered to illustrate the effectiveness of the proposed control design scheme. © 2016 Wiley Periodicals, Inc. Complexity 21: 309–319, 2016     

Complex impure systems: Sheaves,freeways, and chains

Fundamental to the approach of Complex Impure Systems is the definition of the concept of an s‐impure set as a set of perceptual beliefs or denotative significances (relative beings) of material and/or energetic real objects (absolute beings). But any Subject not only the subject S perceives objects O as significances, and he perceives the existing relations between these significances or, alternatively, he infers them. The study of these relations, conceived not as a singular relation between singular objects, but as sheaves of relations in both directions and forming relational freeways, will be studied here. In this work, we approach the structure of the system, from a synchronous point of view, as a first approach to this class of systems. © 2016 Wiley Periodicals, Inc. Complexity 21: 387–400, 2016     

Crisis in complex social systems: A social theory view illustrated with the chilean case

The article argues that crises are a distinctive feature of complex social systems. A quest for connectivity of communication leads to increase systems' own robustness by constantly producing further connections. When some of these connections have been successful in recent operations, the system tends to reproduce the emergent pattern, thereby engaging in a non‐reflexive, repetitive escalation of more of the same communication. This compulsive growth of systemic communication in crisis processes, or logic of excess, resembles the dynamic of self‐organized criticality. Accordingly, we first construct the conceptual foundations of our approach. Second, we present three core assumptions related to the generative mechanism of social crises, their temporal transitions (incubation, contagion, restructuring), and the suitable modeling techniques to represent them. Third, we illustrate the conceptual approach with a percolation model of the crisis in Chilean education system. © 2016 Wiley Periodicals, Inc. Complexity 21: 13–23, 2016     

LMI‐based criterion for the robust guaranteed cost control of uncertain switched neutral systems with time‐varying mixed delays and nonlinear perturbations by dynamic output feedback

This article reports on an investigation into robust guaranteed cost control (GCC) for uncertain switched neutral systems (USNSs) with interval time‐varying mixed delays and nonlinear perturbations via dynamic output feedback. Delay‐dependent sufficient conditions are suggested to guarantee the robust exponential stability and to obtain robust GCC for USNSs using the average dwell time approach and the piecewise Lyapunov function technique in terms of a set of linear matrix inequalities. The problem of uncertainty in the system model is solved by deploying the Yakubovich lemma. Lastly, two examples (i.e., a numerical example and the water‐quality dynamic model for the Nile River) are given to verify the efficiency of the propounded theories. © 2016 Wiley Periodicals, Inc. Complexity 21: 555–578, 2016     

Fuzzy guaranteed cost output tracking control for fuzzy discrete‐time systems with different premise variables

This article investigates the problem of output tracking control for a class of discrete‐time interval type‐2 (IT2) fuzzy systems subject to mismatched premise variables. Based on the IT2 Takagi–Sugeno (T–S) fuzzy model, the criterion to design the desired controller is obtained, which guarantees the closed‐loop system to be asymptotically stable and satisfies the predefined cost function. Moreover, the controller to be designed does not need to share the same premise variables of the system, which enhances the flexibility of controller design and reduces the conservativeness. Finally, two examples are provided to demonstrate the effectiveness of the method proposed in this article. © 2015 Wiley Periodicals, Inc. Complexity 21: 265–276, 2016     

Optimal inventory and insurance decisions for a supply chain financing system with downside risk control

This research considers a supply chain financing system consisting of a capital‐constrained retailer, a supplier and a risk‐averse bank. The retailer may be subject to credit limit because of the bank's downside risk control, and hence, credit insurance should be needed to enhance his financing ability. This paper develops a mathematical optimization model by incorporating insurance policy into the well‐known newsvendor financing model. The optimal inventory and insurance decisions under different scenarios, that is, no insurance, insurance with symmetric information and insurance with asymmetric information, are derived. This work also discusses how the retailer's capital level, the bank's risk aversion, and the insurer's loading factor affect the optimal inventory and insurance decisions. The results show that the retailer will use credit insurance if he is sufficiently capital‐constrained or the insurer's risk loading factor is low enough. Moreover, credit insurance can bring Pareto improvement to the supply chain financing system, which verifies the prevalence of credit insurance in practice. Several numerical experiments are presented to examine the sensitivities of key parameters. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust sampled‐data control of uncertain switched neutral systems with probabilistic input delay

This article focuses on the robust sampled‐data control for a class of uncertain switched neutral systems based on the average dwell‐time approach. In particular, the system is considered with probabilistic input delay using sampled state vectors, which are described by the stochastic variables with a Bernoulli distributed white sequence and time‐varying norm‐bounded uncertainties. By constructing a novel Lyapunov–Krasovskii functional which involves the lower and upper bounds of the delay, a new set of sufficient conditions are derived in terms of linear matrix inequalities for ensuring the robust exponential stability of the uncertain switched neutral system about its equilibrium point. Moreover, based on the stability criteria, a state feedback sampled‐data control law is designed for the considered system. Finally, a numerical example based on the water‐quality dynamic model for the Nile River is given to illustrate the effectiveness of the proposed design technique. © 2015 Wiley Periodicals, Inc. Complexity 21: 308–318, 2016     

A higher‐order PDE‐based image registration approach

This paper addresses the problem of image registration with higher‐order partial differential equation (PDE) methods. From the study of existing affine‐linear and non‐linear methods, a new framework is proposed that unifies common image registration methods within a generic formulation. Currently image registration strategies are classified into either affine‐linear or non‐linear methods subject to the underlying transformations. The new approach combines both strategies to obtain proper approximations which are invariant under global geometrical distortion (shearing), anisotropic resolution (scale changes), as well as rotation and translation. To achieve this favourable property, a modified gradient flow approach is proposed which uses an operator with a kernel consisting of affine‐linear transformations. An approximation with finite differences leads to a large singular linear system. The pseudo‐inverse solution of this system can be computed efficiently by augmenting the singular system to a regular system. Numerical experiments show the improvements compared to unmodified gradient flow approaches. Copyright © 2005 John Wiley & Sons, Ltd.     

Robust consensus of nonlinear multi‐agent systems via reliable control with probabilistic time delay

In this paper, the consensus problem of uncertain nonlinear multi‐agent systems is investigated via reliable control in the presence of probabilistic time‐varying delay. First, the communication topology among the agents is assumed to be directed and fixed. Second, by introducing a stochastic variable which satisfies Bernoulli distribution, the information of probabilistic time‐varying delay is equivalently transformed into the deterministic time‐varying delay with stochastic parameters. Third, by using Laplacian matrix properties, the consensus problem is converted into the conventional stability problem of the closed‐loop system. The main objective of this paper is to design a state feedback reliable controller such that for all admissible uncertainties as well as actuator failure cases, the resulting closed‐loop system is robustly stable in the sense of mean‐square. For this purpose, through construction of a suitable Lyapunov–Krasovskii functional containing four integral terms and utilization of Kronecker product properties along with the matrix inequality techniques, a new set of delay‐dependent consensus stabilizability conditions for the closed‐loop system is obtained. Based on these conditions, the desired reliable controller is designed in terms of linear matrix inequalities which can be easily solved by using any of the effective optimization algorithms. Moreover, a numerical example and its simulations are included to demonstrate the feasibility and effectiveness of the proposed control design scheme. © 2016 Wiley Periodicals, Inc. Complexity 21: 138–150, 2016     

Dissipative sampled‐data control of uncertain nonlinear systems with time‐varying delays

This article investigates the delay‐dependent robust dissipative sampled‐data control problem for a class of uncertain nonlinear systems with both differentiable and non‐differentiable time‐varying delays. The main purpose of this article is to design a retarded robust control law such that the resulting closed‐loop system is strictly (Q, S, R)‐dissipative. By introducing a suitable Lyapunov–Krasovskii functional and using free weighting matrix approach, some sufficient conditions for the solvability of the addressed problem are derived in terms of linear matrix inequalities. From the obtained dissipative result, we deduce four cases namely, H_∞ performance, passivity performance, mixed H_∞, and passivity performance and sector bounded performance of the considered system. From the obtained result, it is concluded that based on the passivity performance it is possible to obtain the controller with less control effort, and also the minimum H_∞ performance and the maximum allowable delay for achieving stabilization conditions can be obtained via the mixed H_∞ and passivity control law. Finally, simulation studies based on aircraft control system are performed to verify the effectiveness of the proposed strategy. © 2015 Wiley Periodicals, Inc. Complexity 21: 142–154, 2016     

Dissipative analysis for discrete‐time systems via fault‐tolerant control against actuator failures

This article investigates the problem of robust dissipative fault‐tolerant control for discrete‐time systems with actuator failures. Based on the Lyapunov technique and linear matrix inequality (LMI) approach, a set of delay‐dependent sufficient conditions is developed for achieving the required result. A design scheme for the state‐feedback reliable dissipative controller is established in terms LMIs which can guarantee the asymptotic stability and dissipativity of the resulting closed‐loop system with actuator failures. In addition, the proposed controller not only stabilize the fault‐free system but also to guarantee an acceptable performance of the faulty system. Also as special cases, robust H_∞ control, passivity control, and mixed H_∞ and passivity control with the prescribed performances under given constraints can be obtained for the considered systems. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed fault‐tolerant control technique. © 2016 Wiley Periodicals, Inc. Complexity 21: 579–592, 2016     

Relaxed fuzzy observer‐based output feedback control synthesis of discrete‐time nonlinear control systems

This work develops the development of observer‐based output feedback control design of discrete‐time nonlinear systems in the form of Takagi–Sugeno fuzzy model. Lately, previous results have been improved in virtue of a two‐step method. From a technical point of view, it is not flawless and related problems have not been completely resolved. In this study, more advanced two‐steps approach is further developed while the relative sizes among different normalized fuzzy weighting functions are utilized by introducing some additional matrix variables. As a result of the above work, those main defects of the existing method can be redressed and a desired solution in aspect of not only reducing the conservatism but also alleviating the computation complexity is provided for some special cases. Moreover, the effectiveness of the proposed result is shown at length by means of an illustrative example. © 2016 Wiley Periodicals, Inc. Complexity 21: 593–601, 2016     

Modeling networked systems using the topologically distributed bounded rationality framework

In networked systems research, game theory is increasingly used to model a number of scenarios where distributed decision making takes place in a competitive environment. These scenarios include peer‐to‐peer network formation and routing, computer security level allocation, and TCP congestion control. It has been shown, however, that such modeling has met with limited success in capturing the real‐world behavior of computing systems. One of the main reasons for this drawback is that, whereas classical game theory assumes perfect rationality of players, real world entities in such settings have limited information, and cognitive ability which hinders their decision making. Meanwhile, new bounded rationality models have been proposed in networked game theory which take into account the topology of the network. In this article, we demonstrate that game‐theoretic modeling of computing systems would be much more accurate if a topologically distributed bounded rationality model is used. In particular, we consider (a) link formation on peer‐to‐peer overlay networks (b) assigning security levels to computers in computer networks (c) routing in peer‐to‐peer overlay networks, and show that in each of these scenarios, the accuracy of the modeling improves very significantly when topological models of bounded rationality are applied in the modeling process. Our results indicate that it is possible to use game theory to model competitive scenarios in networked systems in a way that closely reflects real world behavior, topology, and dynamics of such systems. © 2016 Wiley Periodicals, Inc. Complexity 21: 123–137, 2016     

Sampled‐data reliable stabilization of T‐S fuzzy systems and its application

In this article, based on sampled‐data approach, a new robust state feedback reliable controller design for a class of Takagi–Sugeno fuzzy systems is presented. Different from the existing fault models for reliable controller, a novel generalized actuator fault model is proposed. In particular, the implemented fault model consists of both linear and nonlinear components. Consequently, by employing input‐delay approach, the sampled‐data system is equivalently transformed into a continuous‐time system with a variable time delay. The main objective is to design a suitable reliable sampled‐data state feedback controller guaranteeing the asymptotic stability of the resulting closed‐loop fuzzy system. For this purpose, using Lyapunov stability theory together with Wirtinger‐based double integral inequality, some new delay‐dependent stabilization conditions in terms of linear matrix inequalities are established to determine the underlying system's stability and to achieve the desired control performance. Finally, to show the advantages and effectiveness of the developed control method, numerical simulations are carried out on two practical models. © 2016 Wiley Periodicals, Inc. Complexity 21: 518–529, 2016     

Estimates of blow‐up times of a system of semilinear SPDEs

In this paper, blow‐up property to a system of nonlinear stochastic PDEs driven by two‐dimensional Brownian motions is investigated. The lower and upper bounds for blow‐up times are obtained. When the system parameters satisfy certain conditions, the explicit solutions of a related system of random PDEs are deduced, which allows us to use Yor's formula to obtain the distribution functions of several blow‐up times. Particularly, the impact of noises on the life span of solutions is studied as the system parameters satisfy different conditions. Copyright © 2016 John Wiley & Sons, Ltd.     

A new result on robust H∞ control for uncertain time‐delay singular systems via sliding mode control

This article is devoted to designing linear sliding surface and adaptive sliding mode controller for a class of singular time‐delay systems with parametric uncertainties and external disturbance. In terms of linear matrix inequalities (LMIs), a sufficient criteria of H_∞ performance, and admissibility for considered sliding motion restricted to linear sliding surface is achieved, and the controller which guarantees the finite‐time reachability of the predesigned sliding surface is then developed, respectively. Finally, three examples show the effectiveness of the proposed result. © 2016 Wiley Periodicals, Inc. Complexity 21: 165–177, 2016     

Robust dissipativity and passivity analysis for discrete‐time stochastic neural networks with time‐varying delay

In this article, we consider the problem of robust dissipativity and passivity analysis for a class of general discrete‐time recurrent neural networks (NNs) with time‐varying delays. The NN under consideration is subject to time‐varying and norm bounded parameter uncertainties. By the latest free‐weighting matrix method, an appropriate Lyapunov–Krasovskii functional and using stochastic analysis technique a sufficient condition is established to ensure that the NNs under consideration is strictly ‐dissipative. The derived conditions are presented in terms of linear matrix inequalities. Numerical examples and its simulations are given to demonstrate the effectiveness of the results. © 2014 Wiley Periodicals, Inc. Complexity 21: 47–58, 2016     

The effect of prey refuge and time delay on a diffusive predator‐prey system with hyperbolic mortality

In this article, we investigate the effect of prey refuge and time delay on a diffusive predator‐prey system with Holling II functional response and hyperbolic mortality subject to Neumann boundary condition. More precisely, we study Turing instability of positive equilibrium by using refuge as parameter, instability and Hopf bifurcation induced by time delay. In addition, by the theory of normal form and center manifold, we derive conditions for determining the bifurcation direction and the stability of the bifurcating periodic solution. © 2016 Wiley Periodicals, Inc. Complexity 21: 446–459, 2016     

Adaptive fuzzy backstepping control for a class of MIMO switched nonlinear systems with unknown control directions

In this article, an adaptive fuzzy output tracking control approach is proposed for a class of multiple‐input and multiple‐output uncertain switched nonlinear systems with unknown control directions and under arbitrary switchings. In the control design, fuzzy logic systems are used to identify the unknown switched nonlinear systems. A Nussbaum gain function is introduced into the control design and the unknown control direction problem is solved. Under the framework of the backstepping control design, fuzzy adaptive control and common Lyapunov function stability theory, a new adaptive fuzzy output tracking control method is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed‐loop system are bounded and the tracking error remains an adjustable neighborhood of the origin. A numerical example is provided to illustrate the effectiveness of the proposed approach. © 2015 Wiley Periodicals, Inc. Complexity 21: 155–166, 2016