Determinization and minimization of finite acyclic automata by incremental techniques

The determinization of a nondeterministic finite automaton (FA) is the process of generating a deterministic FA (DFA) equivalent to (sharing the same regular language of) . The minimization of is the process of generating the minimal DFA equivalent to . Classical algorithms for determinization and minimization are available in the literature for several decades. However, they operate monolithically, assuming that the FA to be either determinized or minimized is given once and for all. By contrast, we consider determinization and minimization in a dynamic context, where augments over time: after each augmentation, determinization and minimization of into is required. Using classical monolithic algorithms to solve this problem is bound to poor performance. An algorithm for incremental determinization and minimization of acyclic finite automata, called IDMA, is proposed. Despite being conceived within the narrow domain of model‐based diagnosis and monitoring of active systems, the algorithm is general‐purpose in nature. Experimental evidence indicates that IDMA is far more efficient than classical algorithms in solving incremental determinization and minimization problems. Copyright © 2015 John Wiley & Sons, Ltd.     

An Efficient Algorithm for Determining an Aesthetic Shape Connecting Unorganized 2D Points

We present anefficient algorithm for determining an aesthetically pleasing shape boundary connecting all the points in a given unorganized set of 2D points, with no other information than point coordinates. By posing shape construction as a minimisation problem which follows the Gestalt laws, our desired shape is non‐intersecting, interpolates all points and minimizes a criterion related to these laws. The basis for our algorithm is an initial graph, an extension of the Euclidean minimum spanning tree but with no leaf nodes, called as the minimum boundary complex . and can be expressed similarly by parametrizing a topological constraint. A close approximation of , termed can be computed fast using a greedy algorithm. is then transformed into a closed interpolating boundary in two steps to satisfy ’s topological and minimization requirements. Computing exactly is an NP (Non‐Polynomial)‐hard problem, whereas is computed in linearithmic time. We present many examples showing considerable improvement over previous techniques, especially for shapes with sharp corners. Source code is available online.     

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.     

Weighted control with ‐stability constraint for switched positive linear systems

This paper is concerned with the problem of control with ‐stability constraint for a class of switched positive linear systems. The ‐stability means that all the poles of each subsystem of the resultant closed‐loop system belong to a prescribed disk in the complex plane. A sufficient condition is derived for the existence of a set of state‐feedback controllers, which guarantees that the closed‐loop system is not only positive and exponentially stable with each subsystem ‐stable but also has a weighted performance for a class of switching signals with average dwell time greater than a certain positive constant. Both continuous‐time and discrete‐time cases are considered, and all of the obtained conditions are formulated in terms of linear matrix inequalities, whose solution also yields the desired controller gains and the corresponding minimal average dwell time. Numerical examples are given to illustrate the effectiveness of the presented approach.Copyright © 2012 John Wiley & Sons, Ltd.     

Mixed control of hidden Markov jump systems

In this work, we study the mixed control for Markov jump linear systems with hidden Markov parameters. The hidden Markov process is denoted by , where the nonobservable component θ(k) represents the mode of operation of the system, whereas represents the observable component provided by a detector. The goal is to obtain design techniques for mixed control problems, with the controllers depending only on the estimate , for problems formulated in 3 different forms: (i) minimizing an upper bound on the norm subject to a given restriction on the norm; (ii) minimizing an upper bound on the norm, while limiting the norm; and (iii) minimizing a weighted combination of upper bounds of both the and norms. We propose also new conditions for synthesizing robust controllers under parametric uncertainty in the detector probabilities and in the transition probabilities. The so‐called cluster case for the mixed control problem is also analyzed under the detector approach. The results are illustrated by means of 2 numerical examples.     

Polynomial time approximation algorithms for proportionate open‐shop scheduling

This paper deals with the presentation of polynomial time (approximation) algorithms for a variant of open‐shop scheduling, where the processing times are only machine‐dependent. This variant of scheduling is called proportionate scheduling and its applications are used in many real‐world environments. This paper develops three polynomial time algorithms for the problem. First, we present a polynomial time algorithm that solves the problem optimally if , where n and m denote the numbers of jobs and machines, respectively. If, on the other hand, , we develop a polynomial time approximation algorithm with a worst‐case performance ratio of that improves the bound existing for general open‐shops. Next, in the case of , we take into account the problem under consideration as a master problem and convert it into a simpler secondary approximation problem. Furthermore, we formulate both the master and secondary problems, and compare their complexity sizes. We finally present another polynomial time algorithm that provides optimal solution for a special case of the problem where .     

Application of generally weighted moving average method to tracking signal state space model

In predicting time series, if a trend includes a structural break, then a state space model can be applied to revise the predictive method. Some scholars suggest that restricted damped trend models yield excellent prediction results by automatically revising unforeseen structural break factors in the prediction process. Restricted damped trend models add a smoothed error statistic to a local‐level model and use the exponentially weighted moving average (EWMA) method to make corrections. This paper applies the generally weighted moving average (GWMA) concept and method to a restricted damped trend model that changes the smoothed error statistic from the EWMA form to the GWMA form and adds the correction parameter λ, which distinguishes three situations , , and . The original restricted damped trend model applies only to , enabling the model to capture situations in which and increases its generality. This paper also compares the effect of various parameter values on the predictive model and finds the range of parameter settings that optimize the model.     

Design and analysis of wideband U‐slot patch antenna with U‐shaped parasitic elements

A single layer single probe‐fed wideband microstrip antenna is presented and investigated. By cutting a U‐slot in the rectangular patch, and by incorporating two identical U‐shaped parasitic patches around both the radiating edges and the nonradiating edges of the rectangular patch, three resonant frequencies are excited to form the wideband performance. Details of the antenna design is presented. The measured and simulated results are in good agreement, the measured impedance bandwidth is GHz ( GHz), or centered at GHz, which covers WLAN GHz ( GHz), WLAN GHz ( GHz), and WIMAX GHz ( GHz) bands. The measured peak gains at the three resonant frequencies are dB, dB, and dB, respectively. An equivalent circuit model which is based on the transmission line theory, the asymmetric coupled microstrip lines theory, and the π‐network theory is established. This equivalent circuit model is used to give an insight into the wideband mechanism of the proposed antenna, and is also used to explain why the three resonant frequencies shift at the variations of different parameters from a physical point of view. The error analysis is given to demonstrate the validity of the equivalent circuit model.     

Graphical tuning method of FOPID controllers for fractional order uncertain system achieving robust ‐stability

This paper focuses on the graphical tuning method of fractional order proportional integral derivative (FOPID) controllers for fractional order uncertain system achieving robust ‐stability. Firstly, general result is presented to check the robust ‐stability of the linear fractional order interval polynomial. Then some alternative algorithms and results are proposed to reduce the computational effort of the general result. Secondly, a general graphical tuning method together with some computational efficient algorithms are proposed to determine the complete set of FOPID controllers that provides ‐stability for interval fractional order plant. These methods will combine the results for fractional order parametric robust control with the method of FOPID ‐stabilization for a fixed plant. At last, two important extensions will be given to the proposed graphical tuning methods: determine the ‐stabilizing region for fractional order systems with two kinds of more general and complex uncertainty structures: multi‐linear interval uncertainty and mixed‐type uncertainties. Numerical examples are followed to illustrate the effectiveness of the method. Copyright © 2015 John Wiley & Sons, Ltd.     

Dual approaches to strictly positive real controller synthesis with a performance using linear matrix inequalities

The synthesis of controllers that minimize a performance index subject to a strictly positive real (SPR) constraint is considered. Two controller synthesis methods are presented that are then combined into an iterative algorithm. Each method synthesizes optimal SPR controllers by posing a convex optimization problem where constraints are enforced via linear matrix inequalities. Additionally, each method fixes the controller state‐feedback gain matrix and finds an observer gain matrix such that an upper bound on the closed‐loop ‐norm is minimized and the controller is SPR. The first method retools the standard ‐optimal control problem by using a common Lyapunov matrix variable to satisfy both the criteria and the SPR constraint. The second method overcomes bilinear matrix inequality issues associated with the performance and the SPR constraint by employing a completing the square method and an overbounding technique. Both synthesis methods are used within an iterative scheme to find optimal SPR controllers in a sequential manner. Comparison of our synthesis methods to existing methods in the literature is presented. Copyright © 2012 John Wiley & Sons, Ltd.     

Enhancing Bayesian Estimators for Removing Camera Shake

The aim of removing camera shake is to estimate a sharp version x from a shaken image y when the blur kernel k is unknown. Recent research on this topic evolved through two paradigms called and . only solves for k by marginalizing the image prior, while recovers both x and k by selecting the mode of the posterior distribution. This paper first systematically analyses the latent limitations of these two estimators through Bayesian analysis. We explain the reason why it is so difficult for image statistics to solve the previously reported failure. Then we show that the leading methods, which depend on efficient prediction of large step edges, are not robust to natural images due to the diversity of edges. , although much more robust to diverse edges, is constrained by two factors: the prior variation over different images, and the ratio between image size and kernel size. To overcome these limitations, we introduce an inter‐scale prior prediction scheme and a principled mechanism for integrating the sharpening filter into . Both qualitative results and extensive quantitative comparisons demonstrate that our algorithm outperforms state‐of‐the‐art methods.     

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.     

Computation of lower bounds for the induced norm of LPV systems

Determining the induced norm of a linear parameter‐varying (LPV) system is an integral part of many analysis and robust control design procedures. Most prior work has focused on efficiently computing upper bounds for the induced norm. The conditions for upper bounds are typically based on scaled small‐gain theorems with dynamic multipliers or dissipation inequalities with parameter‐dependent Lyapunov functions. This paper presents a complementary algorithm to compute lower bounds for the induced norm. The proposed approach computes a lower bound on the gain by restricting the parameter trajectory to be a periodic signal. This restriction enables the use of recent results for exact calculation of the norm for a periodic linear time varying system. The proposed lower bound algorithm also returns a worst‐case parameter trajectory for the LPV system that can be further analyzed to provide insight into the system performance. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

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 .     

Decentralized consensus protocol for a class of high‐order multiagent systems

This paper proposes a consensus protocol for a class of high‐order multiagent systems under directed networks. It is supposed that each agent is exposed to an external disturbance additive to its control input. Based on the optimization theory, the consensus protocol gains are designed in order to attenuate the effects of the external disturbances on the performance of the multiagent system. The main problem of existing high‐order consensus protocols in the literature is the dependency of the design on the information of coupling matrices associated with networks topologies. Despite existing high‐order consensus protocols in the literature, the proposed consensus protocol can be designed in a fully decentralized manner based on no global information. The main idea of the design is to propose an control formulation in which the coupling information of the agents is considered as exogenous signals, while the coupling effects of these signals lead to achieving consensus in the multiagent system. Numerical examples verify the effectiveness of the proposed consensus protocol. Copyright © 2016 John Wiley & Sons, Ltd.     

Input‐output triggered control using ‐stability over finite horizons

This paper investigates stability of nonlinear control systems under intermittent information. Following recent results in the literature, we replace the traditional periodic paradigm, where the up‐to‐date information is transmitted and control laws are executed in a periodic fashion, with the event‐triggered paradigm. Building on the small gain theorem, we develop input–output triggered control algorithms yielding stable closed‐loop systems. In other words, based on the currently available (but outdated) measurements of the outputs and external inputs of a plant, a mechanism triggering when to obtain new measurements and update the control inputs is provided. Depending on the noise in the environment, the developed algorithm yields stable, asymptotically stable, and ‐stable (with bias) closed‐loop systems. Control loops are modeled as interconnections of hybrid systems for which novel results on ‐stability are presented. The prediction of a triggering event is achieved by employing ‐gains over a finite horizon. By resorting to convex programming, a method to compute ‐gains over a finite horizon is devised. Finally, our approach is successfully applied to a trajectory tracking problem for unicycles. Copyright © 2014 John Wiley & Sons, Ltd.     

Stability control and recurrent switching rules

Recently, it has been enlightened the interest of a class of switching rules with good properties, which are called eventually periodic: more precisely, it has been proven that a finite family of linear vector fields of can be stabilized by means of eventually periodic switching rules provided that it is asymptotically controllable and satisfies an additional finite time controllability condition. Unfortunately, simple examples point out that in general, eventually periodic switching rules are not robust with respect to state measurement errors. In this paper, we introduce a new type of switching rules with improved robustness properties, which are called recurrent switching rules. They are subject to the construction of a finite sequence of complete cones Γ₁, … ,Γ_H of . We shown that, if a stabilizing eventually periodic switching rule for is known, then Γ₁, … ,Γ_H can be constructed in such a way that is stabilized by any recurrent switching rule subject to Γ₁, … ,Γ_H. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

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

This paper investigates the problems of and state feedback control design for continuous‐time Markov jump linear systems. The matrices of each operation mode are supposed to be uncertain, belonging to a polytope, and the transition rate matrix is considered partly known. By appropriately modeling all the uncertain parameters in terms of a multi‐simplex domain, new design conditions are proposed, whose main advantage with respect to the existing ones is to allow the use of polynomially parameter‐dependent Lyapunov matrices to certify the mean square closed‐loop stability. Synthesis conditions are derived in terms of matrix inequalities with a scalar parameter. The conditions, which become LMIs for fixed values of the scalar, can cope with and state feedback control in both mode‐independent and mode‐dependent cases. Using polynomial Lyapunov matrices of larger degrees and performing a search for the scalar parameter, less conservative results in terms of guaranteed costs can be obtained through LMI relaxations. Numerical examples illustrate the advantages of the proposed conditions when compared with other techniques from the literature. Copyright © 2015 John Wiley & Sons, Ltd.