Spline Based Pseudo‐Inversion of Sampled Data Non‐Minimum Phase Systems for an Almost Exact Output Tracking

This paper considers the problem of achieving a very accurate tracking of a pre‐specified desired output trajectory , for linear, multiple input multiple output, non‐minimum phase and/or non hyperbolic, sampled data, and closed loop control systems. The proposed approach is situated in the general framework of model stable inversion and introduces significant novelties with the purpose of reducing some theoretical and numerical limitations inherent in the methods usually proposed. In particular, the new method does not require either a preactuation or null initial conditions of the system. The desired and the corresponding sought input are partitioned in a transient component ( and u_t(k), respectively) and steady‐state ( and u_s(k), respectively). The desired transient component is freely assigned without requiring it to be null over an initial time interval. This drastically reduces the total settling time. The structure of u_t(k) is a priori assumed to be given by a sampled smoothing spline function. The spline coefficients are determined as the least‐squares solution of the over‐determined system of linear equations obtained imposing that the sampled spline function assumed as reference input yield the desired output over a properly defined transient interval. The steady‐state input u_s(k) is directly analytically computed exploiting the steady‐state output response expressions for inputs belonging to the same set of .     

Low Frequency Sensitivity Function Constraints for Nonlinear ‐stable Networked Control

The paper derives a robust networked controller design method for systems with saturation where the delay is large and uncertain, as in one‐directional data flow‐control. A classical linear H_∞ criterion is first formulated in terms of the sensitivity and complementary sensitivity functions. A new asymptotic constraint is then derived, which specifies the minimum amount of low frequency gain that is needed in the sensitivity function to conclude on non‐linear closed loop ‐stability using the Popov criterion. This result guides the selection of the design criterion, thereby adjusting the linear controller design for better handling of delay and saturation. The controller design method then uses gridding to pre‐compute a subset of the stability region. Based on the pre‐computed region, a robust ‐stable controller can be selected. Alternatively, an adaptive controller could recompute ‐stable controllers on‐line using the pre‐computed region. Simulations show that the controller meets the specified stability and performance requirements.     

Robust Stochastic Stability and Control for Uncertain Singular Markovian Jump Systems with Multiplicative Noise

This paper focuses on the problems of robust stability and stabilization and robust control for uncertain singular Markovian jump systems with (x,v)‐dependent noise. The parameter uncertainties appearing in state, input, disturbance as well as diffusion terms are assumed to be time‐varying but norm‐bounded. Based on the approach of generalized quadratic stability, the memoryless state feedback controller is designed for the robust stabilization problem, which ensures that the resulting closed‐loop system has an impulse‐free solution and is asymptotically stable in the mean square. Furthermore, the results of robust control problem are derived. The desired state feedback controller is presented, which not only meets the requirement of robust stabilization but also satisfies a prescribed performance level. The obtained results are formulated in terms of strict LMIs. What we have obtained can be viewed as corresponding extensions of existing results on uncertain singular systems. A numerical example is finally given to demonstrate the application of the proposed method.     

Reliable Decentralized Supervisors for Discrete‐Event Systems Under Communication Delays: Existence and Verification

A reliable decentralized supervisory control framework for discrete‐event systems is proposed to deal with possible actuation failures and communication delays. We mainly focus on the existence of such a controller that the control performance can be guaranteed even in face of local supervisor failures and communication delays. Especially, the existence of k‐reliable decentralized supervisors under communication delays is characterized by the notion of k‐reliable together with . In addition, the verification for k‐reliable decentralized supervisors is investigated by developing a constructive methodology to test the k‐reliable . It is shown that for a given number of distributed components, the existence of such k‐reliable decentralized supervisors can be checked with a polynomial complexity in the size of the state space.     

r‐consensus control for higher‐order multi‐agent systems with digraph

This paper studies a consensus problem for lth (l ≥ 2) order multi‐agent systems with digraph, namely, for a fixed r (0 ≤ r ≤ l ? 1), the rth derivative of the states x_i of agents are convergent to a constant value and, for every k (0 ≤ k ≤ l ? 1), are convergent to zeros. A new concept of r‐consensus is introduced and new consensus protocols are proposed for solving such an r‐consensus problem. A sufficient and necessary condition for r‐consensus is obtained. As special cases, criteria for third‐order systems are given, in which the exact relationship between feedback gains is established. Finally, an illustrative example is given to demonstrate the effectiveness of these protocols.     

Characterization of Stochastic Mean‐Field Type Index

index of mean‐field stochastic differential equations (SDE) is investigated in this paper. For systems with state‐ and input‐dependent noise, we obtain a sufficient condition of index larger than some λ>0 via the solvability of differential Riccati equations (DRE). Especially, a necessary and sufficient condition is given for mean‐field SDE with state‐dependent noise, which generalize the corresponding results of classical stochastic systems to the mean‐field stochastic models.     

Improved Adaptive Controller Synthesis of Piecewise‐Affine Systems

This paper considers the adaptive control problem for piecewise affine systems (PWS), a novel synthesis framework is presented based on the piecewise quadratic Lyapunov function (PQLF) instead of the common quadratic Lyapunov function to achieve the less conservatism. First, by designing the projection‐type piecewise adaptive law, the problem of the adaptive control of PWS can be reduced to the control problem of augmented piecewise systems. Then, we construct the piecewise affine control law for augmented piecewise systems in such a way that the PQLF can be employed to establish the stability and performance. In particular, the Reciprocal Projection Lemma is employed to formulate the synthesis condition as linear matrix inequalities (LMIs), which enables the proposed PQLF approach to be numerically solvable. Finally, an engineering example is shown to illustrate the synthesis results.     

Revisiting bounded context block‐sorting transformations

The Burrows–Wheeler Transform (BWT ) produces a permutation of a string X, denoted X^?, by sorting the n cyclic rotations of X into full lexicographical order and taking the last column of the resulting n×n matrix to be X^?. The transformation is reversible in time. In this paper, we consider an alteration to the process, called k‐BWT , where rotations are only sorted to a depth k. We propose new approaches to the forward and reverse transform, and show that the methods are efficient in practice. More than a decade ago, two algorithms were independently discovered for reversing k‐BWT , both of which run in time. Two recent algorithms have lowered the bounds for the reverse transformation to and, respectively. We examine the practical performance for these reversal algorithms. We find that the original approach is most efficient in practice, and investigates new approaches, aimed at further speeding reversal, which store precomputed context boundaries in the compressed file. By explicitly encoding the context boundaries, we present an reversal technique that is both efficient and effective. Finally, our study elucidates an inherently cache‐friendly – and hitherto unobserved – behavior in the reverse k‐BWT , which could lead to new applications of the k‐BWT transform. In contrast to previous empirical studies, we show that the partial transform can be reversed significantly faster than the full transform, without significantly affecting compression effectiveness. Copyright © 2011 John Wiley & Sons, Ltd.     

Quantized Filtering for Continuous‐Time Markovian Jump Systems with Deficient Mode Information

This paper investigates the problem of quantized filtering for a class of continuous‐time Markovian jump linear systems with deficient mode information. The measurement output of the plant is quantized by a mode‐dependent logarithmic quantizer, and the deficient mode information in the Markov stochastic process simultaneously considers the exactly known, partially unknown, and uncertain transition rates. By fully exploiting the properties of transition rate matrices, together with the convexification of uncertain domains, a new sufficient condition for quantized performance analysis is first derived, and then two approaches, namely, the convex linearization approach and iterative approach, to the filter synthesis are developed. It is shown that both the full‐order and reduced‐order filters can be obtained by solving a set of linear matrix inequalities (LMIs) or bilinear matrix inequalities (BMIs). Finally, two illustrative examples are given to show the effectiveness and less conservatism of the proposed design methods.     

Quasi‐Time‐Dependent Controller for Discrete‐Time Switched Linear Systems With Mode‐Dependent Average Dwell‐Time

This paper is concerned with the stability and stabilization problem of a class of discrete‐time switched systems with mode‐dependent average dwell time (MDADT). A novel Lyapunov function, which is both mode‐dependent (MD) and quasi‐time‐dependent (QTD), is established. The new established Lyapunov function is allowed to increase at some certain time instants. A QTD controller is designed such that the system is globally uniformly asymptotically stable (GUAS) and has a guaranteed performance index. The new QTD robust controller designed in this paper is less conservative than the mode independent one which is frequently considered in literatures. Finally, a numerical example and a practical example are provided to illustrate the effectiveness of the developed results.      

The Mixed Robust /FTS Control Problem Analysis and State Feedback Control

In this paper we deal with the mixed  /finite‐time stability control problem. More specifically, given an open loop uncertain linear system, we provide a necessary and sufficient condition for quadratic input‐output finite‐time stability with an  bound. Exploiting this result we also give a sufficient condition to solve the related synthesis problem via state‐feedback. The property of quadratic input‐output finite‐time stability with an  bound implies that the system under consideration satisfies an  performance bound between the disturbance input and the controlled output and, at the same time, is input‐output finite‐time stable for all admissible uncertainties. This condition requires the solution of a feasibility problem constrained by a pair of differential linear matrix inequalities (LMIs) coupled with a time‐varying LMI. The proposed technique is illustrated by means of both a numerical and a physical example.     

Dynamic Output‐Feedback Control for T‐S Fuzzy Systems with Input Time‐Varying Delay

This paper considers the problem of the control for T‐S fuzzy systems with input time‐varying delay via dynamic output feedback. Firstly, by applying the reciprocally convex approach, new delay‐dependent sufficient condition for performance analysis is obtained. Then, a less conservative condition for the existence of the controllers is given in terms of linear matrix inequalities (LMIs). Moreover, in the considered system, the time‐delay term is included in the measured output. This results in the difficulty in designing the controllers being increased and the obtained results being applied to a wider class of fuzzy systems than the most existing ones. The main contribution of this work lies in the application of the reciprocally convex inequality and the time‐delay term included in the measured output. Finally, the advantages and effectiveness of the present results are shown by several numerical examples.     

Computational and structural analysis of the contour of graphs

Let be a finite, simple, and connected graph. The closed interval of a set is the set of all vertices lying on a shortest path between any pair of vertices of S. The set S is geodetic if . The eccentricity of a vertex v is the number of edges in the greatest shortest path between v and any vertex w of G. A vertex v is a contour vertex if no neighbor of v has eccentricity greater than v. The contour of G is the set formed by the contour vertices of G. We consider two problems: the problem of determining whether the contour of a graph class is geodetic; the problem of determining if there exists a graph such that is not geodetic. We obtain a sufficient condition that is useful for both problems; we prove a realization theorem related to problem and show two infinite families such that is not geodetic. Using computational tools, we establish the minimum graphs for which is not geodetic; and show that all graphs with , and all bipartite graphs with , are such that is geodetic.     

A new dual‐mode wideband circularly polarized rectangular dielectric resonator antenna coupled with stubs and asymmetric ground plane for WiMAX applications

In this article, a new radiating stub microstrip feed has been investigated with asymmetrical ground plane for generation of circular polarization (CP) in a dielectric resonator antenna (DRA). Here, asymmetrical ground plane and 3 radiating stubs with microstrip feed line are used for generation of 2 different modes namely TE_11δ and TE_12δ in rectangular DRA. By using mode matching concepts, these modes are responsible for enhancing the impedance bandwidth (TE_12δ ie, and ) and axial ratio (AR) bandwidth (TE_11δ ie, and ) in proposed antenna. Designed antenna offers measured input impedance bandwidth (|S₁₁| < ?10 dB) and AR bandwidth (AR < 3‐dB) of 44.78%, ranging from 4.6 to 6.9 GHz and 23.32%, ranging from 4.6 to 6.9 GHz, respectively. It has been observed that proposed antenna shows left‐handed CP fields in boresight direction with average gain of 3.15 dBic and radiation efficiency of 90.54%. Designed antenna is suitable for Wi‐MAX (3.3‐3.7 GHz) applications.     

Reset Control Systems With Time‐Varying Delay: Delay‐Dependent Stability And Gain Performance Improvement

This paper considers the stability analysis of reset control systems with time‐varying delay. Based on sector reset conditions, delay‐dependent exponential stability and finite gain stability conditions are proposed, and piecewise Lyapunov functions are used such that less conservative results can be obtained, moreover, gain performance improvement results are presented to show the advantage of reset control. Numerical examples are given to show the effectiveness.     

Disturbance Observer‐Based Elegant Anti‐Disturbance Control for Stochastic Systems with Multiple Disturbances

Disturbance observer‐based elegant anti‐disturbance control (DOBEADC) scheme is proposed for a class of stochastic systems with nonlinear dynamics and multiple disturbances. The stochastic disturbance observer based on pole placement is constructed to estimate disturbance which is generated by an exogenous system. Then, composite DOBC and controller is designed to guarantee the composite system is mean‐square stable and its performance satisfies a prescribed level. Finally, simulations on an A4D aircraft model show the effectiveness of the proposed approaches.     

Robust Partially Mode Delay‐Dependent ℋ∞ Output Feedback Control of Discrete‐Time Networked Control Systems

In this paper, a methodology for designing an output feedback controller for discrete‐time networked control systems has been considered. More precisely, network‐induced delays between the sensor and the controller is modelled by a Markov chain with transition probabilities which are not assumed to be fully known. The systems parameter uncertainties are assumed to be norm‐bounded and possibly time‐varying. To the best of the authors knowledge, the problem of designing a partially mode delay‐dependent output feedback controller for NCSs with partially known transition probability matrix has not been investigated in the literature. Based on the Lyapunov‐Krasovskii functional approach, sufficient conditions for the existence of a robust partially mode delay‐dependent output feedback controller are given in terms of bilinear matrix inequalities which can be solved using a cone complementarity linearization algorithm. The proposed design methodology differs from the existing design methodologies in that dynamic output feedback controllers are parameterized by both modes and transition probabilities, as opposed to the existing design approaches which parameterize controllers by modes only. The results obtained reduce to the existing results on fully known transition matrices when transition probabilities are fully known. It is shown that the proposed methodology can be applied to real world systems. The proposed design methodology is verified by using a DC servo motor system where the plant and the controller are connected via a cellular network with partially known transition probability matrix.     

state estimation with fading measurements,randomly varying nonlinearities and probabilistic distributed delays

In this paper, the state estimation problem is investigated for a class of discrete‐time stochastic systems in simultaneous presence of three network‐induced phenomena, namely, fading measurements, randomly varying nonlinearities and probabilistic distributed delays. The channel fading is characterized by the ?th‐order Rice fading model whose coefficients are mutually independent random variables with given probability density functions. Two sequences of random variables obeying the Bernoulli distribution are utilized to govern the randomly varying nonlinearities and probabilistic distributed delays. The purpose of the problem addressed is to design an state estimator such that the dynamics of the estimation errors is stochastically stable and the prespecified disturbance rejection attenuation level is guaranteed. Through intensive stochastic analysis, sufficient conditions are established under which the addressed state estimation problem is recast as a convex optimization one that can be solved via the semi‐definite program method. Finally, a simulation example is provided to show the usefulness of the proposed state estimation scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

Another view on q‐rung orthopair fuzzy sets

In this paper, two new approaches have been presented to view q‐rung orthopair fuzzy sets. In the first approach, these can viewed as L‐fuzzy sets, whereas the second approach is based on the notion of orbits. Uncertainty index is the quantity , which remains constant for all points in an orbit. Certain operators can be defined in q‐ROF sets, which affect when applied to some q‐ROF sets. Operators , , and have been defined. It is studied that how these operators affect when applied to some q‐ROF set A.     

Full complexity analysis of the diameter‐constrained reliability

Let be a simple graph with nodes and links, a subset of “terminals,” a vector , and a positive integer d, called “diameter.” We assume that nodes are perfect but links fail stochastically and independently, with probabilities . The “diameter‐constrained reliability” (DCR) is the probability that the terminals of the resulting subgraph remain connected by paths composed of d links, or less. This number is denoted by . The general DCR computation belongs to the class of ‐hard problems, since it subsumes the problem of computing the probability that a random graph is connected. The contributions of this paper are twofold. First, a full analysis of the computational complexity of DCR subproblems is presented in terms of the number of terminal nodes and the diameter d. Second, we extend the class of graphs that accept efficient DCR computation. In this class, we include graphs with bounded co‐rank, graphs with bounded genus, planar graphs, and, in particular, Monma graphs, which are relevant to robust network design.