brief paper zeros of structured linear systems this paper provides a detailed study of transmission zeros in the context of linear structured systems for such systems the entries of the state space model matrices are supposed to be either fixed zeros or free parameters a directed graph can be associated to such systems and structural properties can be studied i e properties which are valid for almost all values of the parameters we show that there exists two kinds of transmission zeros the parameter dependent ones and the constant ones which can only occur in zero moreover the constant transmission zeros can be directly obtained on the associated graph in terms of particular paths and cycles

approximating the least hypervolume contributor np hard in general but fast in practice the hypervolume indicator is an increasingly popular set measure to compare the quality of two pareto sets the basic ingredient of most hypervolume indicator based optimization algorithms is the calculation of the hypervolume contribution of single solutions regarding a pareto set we show that exact calculation of the hypervolume contribution is p hard while its approximation is np hard the same holds for the calculation of the minimal contribution we also prove that it is np hard to decide whether a solution has the least hypervolume contribution even deciding whether the contribution of a solution is at most 1 e times the minimal contribution is np hard this implies that it is neither possible to efficiently find the least contributing solution unless p np nor to approximate it unless np bpp nevertheless in the second part of the paper we present a fast approximation algorithm for this problem we prove that for arbitrarily given e d 0 it calculates a solution with contribution at most 1 e times the minimal contribution with probability at least 1 d though it cannot run in polynomial time for all instances it performs extremely fast on various benchmark datasets the algorithm solves very large problem instances which are intractable for exact algorithms e g 10 000 solutions in 100 dimensions within a few seconds

normal boundary intersection a new method for generating the pareto surface in nonlinear multicriteria optimization problems this paper proposes an alternate method for finding several pareto optimal points for a general nonlinear multicriteria optimization problem such points collectively capture the trade off among the various conflicting objectives it is proved that this method is independent of the relative scales of the functions and is successful in producing an evenly distributed set of points in the pareto set given an evenly distributed set of parameters a property which the popular method of minimizing weighted combinations of objective functions lacks further this method can handle more than two objectives while retaining the computational efficiency of continuation type algorithms this is an improvement over continuation techniques for tracing the trade off curve since continuation strategies cannot easily be extended to handle more than two objectives

input addition and leader selection for the controllability of graph based systems in this paper we consider dynamical graph based models which are well fitted for the structural analysis of complex systems a significant amount of work has been devoted to the controllability of such graph based models e g recently for multi agent systems or complex networks we study here the controllability through input addition in this framework we present several variants of this problem depending on the freedom which is left to the designer on the additional inputs we use a unified framework which allows us to encompass the different applications and representations large scale systems complex communications networks multi agent systems and provide convenient graph tools for their analysis our contribution is to characterize the structural modifications of the system resulting from an input addition or a leader selection and of the mechanisms which lead to controllability we provide information on the possible location of additional inputs and on the minimal number of inputs to be added for controllability

a graphical characterization of structurally controllable linear systems with dependent parameters one version of the concept of structural controllability defined for single input systems by lin and subsequently generalized to multi input systems by others states that a parameterized matrix pair a b whose nonzero entries are distinct parameters is structurally controllable if values can be assigned to the parameters that cause the resulting matrix pair to be controllable in this paper the concept of structural controllability is broadened to allow for the possibility that a parameter may appear in more than one location in the pair a b subject to a certain condition on the parameterization called the binary assumption an explicit graph theoretic characterization of such matrix pairs is derived

a simple criterion for structurally fixed modes we present a simple characterization of the maximum possible rank of the product of several real matrices when certain entries of the matrices are constrained to be zero our result relates this generic rank to the maximum number of independent information paths through the matrices and has as corollaries besides several previous attempts at this problem a new characterization of structurally fixed modes for linear time invariant dynamical systems furthermore our characterization translates immediately to an 0 n algorithm for calculating the generic rank and therefore detecting fixed modes by solving a network flow problem here n is the sum of the dimensions of the matrices kqvwords structurally fixed modes maximum flow generic rank decentralized systems

structural controllability and matrix nets abstract we establish structural controllability results for matrix pairs a b where a a 0 iai b b 0 i bi with the ai bi fixed and the i free scalar parameters the results characterize structural controllability in several ways via tests involving the checking of the rank or the evaluation of the determinant of various constant matrices formed from the ai bi a number of the results used as intermediate results tests for a full rank property of matrix nets i e tests that check if m m0 imi prescribed i variable has full rank for almost all i

fixed modes in parametrized systems several necessary graph theoretic conditions are presented for a parametrized system nut to have structurally fixed modus under output feedback of some arbitrarily specified pattern the criteria are formulated by the aid of a new graph which represents the couplings inherent in the system as well as the admissible feedback pattern for the special class of structured systems the conditions turn out to be also sufficient

regularity conditions via quasi relative interior in convex programming we give some new regularity conditions for fenchel duality in separated locally convex vector spaces written in terms of the notion of quasi interior and quasi relative interior respectively we provide also an example of a convex optimization problem for which the classical generalized interior point conditions given so far in the literature cannot be applied while the one given by us is applicable by using a technique developed by magnanti we derive some duality results for the optimization problem with cone constraints and its lagrange dual problem and we show that a duality result recently given in the literature for this pair of problems has self contradictory assumptions

sms emoa multiobjective selection based on dominated hypervolume abstract the hypervolume measure or s metric is a frequently applied quality measure for comparing the results of evolutionary multiobjective optimisation algorithms emoa the new idea is to aim explicitly for the maximisation of the dominated hypervolume within the optimisation process a steady state emoa is proposed that features a selection operator based on the hypervolume measure combined with the concept of non dominated sorting the algorithm s population evolves to a well distributed set of solutions thereby focussing on interesting regions of the pareto front the performance of the devised s metric selection emoa sms emoa is compared to state of the art methods on two and three objective benchmark suites as well as on aeronautical real world applications

on simultaneous optimization of smart structures part ii algorithms and examples five algorithms for the simultaneous optimal design of smart structural systems are presented these algorithms are developed based on sequential mathematical programming and guided random search techniques being applied to multidisciplinary optimization in which both structural layout and controller parameters are involved a method to prevent singularities when updating the structural layout is suggested two adaptive trusses are optimised and comparison is made for the different optimal schemes on the basis of iteration histories and major results achieved all of the five algorithms are shown efficient in improving the truss s performance with respect to robustness and controllability the results show that the greatest improvement in all the performance indicators is achieved using a genetic algorithm whilst the most efficient scheme is seen to be a novel hybrid combining sequential linear programming with simulated annealing

survey generic properties and control of linear structured systems a survey in this survey paper we consider linear structured systems in state space form where a linear system is structured when each entry of its matrices like a b c and d is either a fixed zero or a free parameter the location of the fixed zeros in these matrices constitutes the structure of the system indeed a lot of man made physical systems which admit a linear model are structured a structured system is representative of a class of linear systems in the usual sense it is of interest to investigate properties of structured systems which are true for almost any value of the free parameters therefore also called generic properties interestingly a lot of classical properties of linear systems can be studied in terms of genericity moreover these generic properties can in general be checked by means of directed graphs that can be associated to a structured system in a natural way we review here a number of results concerning generic properties of structured systems expressed in graph theoretic terms by properties we mean here system specific properties like controllability the finite and infinite zero structure and so on as well as solvability issues of certain classical control problems like disturbance rejection input output decoupling and so on in this paper we do not try to be exhaustive but instead by a selection of results we would like to motivate the reader to appreciate what we consider as a wonderful modelling and analysis tool we emphasize the fact that this modelling technique allows us to get a number of important results based on poor information on the system only moreover the graph theoretic conditions are intuitive and are easy to check by hand for small systems and by means of well known polynomially bounded combinatorial techniques for larger systems

about structural controllability of interconnected dynamical systems the concepts of structural controllability for a linear time invariant dynamical system are extended to multivariable systems consisting of interconnected subsystems the graph theoretic method based on the cactus notion is used to find sufficient conditions for the pair a b of the global system to be structurally controllable in terms of the structure of the interconnections

existence of optimal solutions and duality results under weak conditions in this paper we consider an ordinary convex program with no qualification conditions such as slater s condition and for which the optimal set is neither required to be compact nor to be equal to the sum of a compact set and a linear space it is supposed only that the infimum is finite a very wide class of convex functions is exhibited for which the optimum is always attained and is equal to the supremum of the ordinary dual program additional results concerning the existence of optimal solutions in the non convex case are also given

minimizing convergence error in multi agent systems via leader selection a supermodular optimization approach in a leader follower multi agent system mas the leader agents act as control inputs and influence the states of the remaining follower agents the rate at which the follower agents converge to their desired states as well as the errors in the follower agent states prior to convergence are determined by the choice of leader agents in this paper we study leader selection in order to minimize convergence errors experienced by the follower agents which we define as a norm of the distance between the follower agents intermediate states and the convex hull of the leader agent states by introducing a novel connection to random walks on the network graph we show that the convergence error has an inherent supermodular structure as a function of the leader set supermodularity enables development of efficient discrete optimization algorithms that directly approximate the optimal leader set provide provable performance guarantees and do not rely on continuous relaxations we formulate two leader selection problems within the supermodular optimization framework namely the problem of selecting a fixed number of leader agents in order to minimize the convergence error as well as the problem of selecting the minimum size set of leader agents to achieve a given bound on the convergence error we introduce algorithms for approximating the optimal solution to both problems in static networks dynamic networks with known topology distributions and dynamic networks with unknown and unpredictable topology distributions our approach is shown to provide significantly lower convergence errors than existing random and degree based leader selection methods in a numerical study

some equivalent results with yakubovich s s lemma this paper presents an elementary proof of nonstrict finsler s theorem and discusses five closely related theorems yakubovich s s lemma yuan s alternative theorem nonstrict finsler s theorem strict finsler s theorem and finsler calabi s theorem this paper discusses how one is related with another at the end of this article we present some extensions of these results to an infinite dimensional vector space

linear time approximation for maximum weight matching the maximum cardinality and maximum weight matching problems can be solved in o m n time a bound that has resisted improvement despite decades of research here m and n are the number of edges and vertices in this article we demonstrate that this m n barrier can be bypassed by approximation for any e 0 we give an algorithm that computes a 1 e approximate maximum weight matching in o me 1 log e 1 time that is optimal linear time for any fixed e our algorithm is dramatically simpler than the best exact maximum weight matching algorithms on general graphs and should be appealing in all applications that can tolerate a negligible relative error

key node selection in minimum cost control of complex networks abstract finding the key node set that is connected with a given number of external control sources for driving complex networks from initial state to any predefined state with minimum cost known as minimum cost control problem is critically important but remains largely open by defining an importance index for each node we propose revisited projected gradient method extension r pgme in monte carlo scenario to determine key node set it is found that the importance index of a node is strongly correlated to occurrence rate of that node to be selected as a key node in monte carlo realizations for three elementary topologies erd s renyi and scale free networks we also discover the distribution patterns of key nodes when the control cost reaches its minimum specifically the importance indices of all nodes in an elementary stem show a quasi periodic distribution with high peak values in the beginning and end of a quasi period while they approach to a uniform distribution in an elementary cycle we further point out that an elementary dilation can be regarded as two elementary stems whose lengths are the closest and the importance indices in each stem present similar distribution as in an elementary stem our results provide a better understanding and deep insight of locating the key nodes in different topologies with minimum control cost

minimum cost input output design for large scale linear structural systems in this paper we provide optimal solutions to two different but related input output design problems involving large scale linear dynamical systems where the cost associated to each directly actuated measured state variable can take different values but is independent of the input output performing the task under these conditions we first aim to determine and characterize the input output placement that incurs in the minimum cost while ensuring that the resulting placement achieves structural controllability observability further we address a constrained variant of the above problem in which we seek to determine the minimum cost placement configuration among all possible input output placement configurations that ensures structural controllability observability with the lowest number of directly actuated measured state variables we develop new graph theoretical characterizations of cost constrained input selections for structural controllability and properties that enable us to address both problems by reduction to a weighted maximum matching problem efficiently addressed by algorithms with polynomial time complexity in the number of state variables finally we illustrate the obtained results with an example

newton s method with a model trust region modification a modified newton method for unconstrained minimization is presented and analyzed the modification is based upon the model trust region approach this report contains a thorough analysis of the locally constrained quadratic minimizations that arise as subproblems in the modified newton iteration several promising alternatives are presented for solving these subproblems in ways that overcome certain theoretical difficulties exposed by this analysis very strong convergence results are presented concerning the minimization algorithm in particular the explicit use of second order information is justified by demonstrating that the iterates converge to a point which satisfies the second order necessary conditions for minimization with the exception of very pathological cases this occurs whenever the algorithm is applied to problems with continuous second partial derivatives

regularity controllability observability of an nds with descriptor form subsystems and generalized lfts abstract this paper investigates regularity controllability and observability for a networked dynamic system nds with its subsystems being described in a descriptor form and system matrices of each subsystem being represented by a generalized linear fractional transformation glft of its parameters except a well posedness condition no any other constraints are put on either parameters or connections of a subsystem based on the kronecker canonical form kcf of a matrix pencil some matrix rank based necessary and sufficient conditions are established respectively for the regularity and complete controllability observability of the nds in which the associated matrix depends affinely on both subsystem parameters and subsystem connections these conditions keep the property that all the involved numerical computations are performed on each subsystem independently which is attractive in the analysis and synthesis of a large scale nds moreover some explicit and easily checkable requirements are derived for subsystem dynamics parameters with which a completely controllable observable nds can be constructed more easily

analysis of linear structured systems using a primal dual algorithm in this paper we give a polynomial algorithm to compute the infinite structure of a structured system a directed graph is associated with such structured systems the infinite zero orders can be computed on the associated graph via the determination of the minimal length of vertex disjoint input output paths this search corresponds to a minimum cost flow determination on an appropriate directed graph the proposed algorithm is based on the primal dual algorithm linked to linear programming this polynomial algorithm is one of the most efficient for this type of problem moreover it allows an iterative determination of the generic infinite structure which is a key tool for solving numerous control problems

on almost invariant subspaces of structural systems and decentralized control graph theoretic conditions are obtained for a structured system to have the property that the supremal l sub p almost invariant controllability subspace is generically the entire state space and that the infimal sup l sub p almost conditional invariant complementary observability subspace is generically the zero subspace the conditions are used to determine stabilizability of structured interconnected systems by means of decentralized feedback control although the obtained graph theoretic conditions are conservative they are considered satisfactory to the extent that the benefits of easy testability involving only binary calculations outweigh the conservativeness in the results

stable zero duality gaps in convex programming complete dual characterisations with applications to semidefinite programs the zero duality gap that underpins the duality theory is one of the central ingredients in optimisation in convex programming it means that the optimal values of a given convex program and its associated dual program are equal it allows in particular the development of efficient numerical schemes however the zero duality gap property does not always hold even for finite dimensional problems and it frequently fails for problems with non polyhedral constraints such as the ones in semidefinite programming problems over the years various criteria have been developed ensuring zero duality gaps for convex programming problems in the present work we take a broader view of the zero duality gap property by allowing it to hold for each choice of linear perturbation of the objective function of the given problem globalising the property in this way permits us to obtain complete geometric dual characterisations of a stable zero duality gap in terms of epigraphs and conjugate functions for convex semidefinite programs we establish necessary and sufficient dual conditions for stable zero duality gaps as well as for a universal zero duality gap in the sense that the zero duality gap property holds for each choice of constraint right hand side and convex objective function zero duality gap results for second order cone programming problems are also given our approach makes use of elegant conjugate analysis and fenchel s duality

optimum feedback patterns in multivariable control systems abstract the following problem is considercd given a multivariable system with m inputs and r outputs and an r m matrix whose non negative i j th element represents the cost of setting up a feedback link from the jth output to the ith input sind a set of feedback links with minimum total cost which does not give rise to sixed modes utilizing the graph theoretic characterization of structurally sixed modes the problem is decomposed into two subproblems which are then solved by using concepts and results from network theory a combination of the optimum solutions of the subproblems provides a suboptimal solution to the original problem

a distance based approach to strong target control of dynamical networks this paper deals with controllability of dynamical networks it is often unfeasible or unnecessary to fully control large scale networks which motivates the control of a prescribed subset of agents of the network this specific form of output control is known under the name target control we consider target control of a family of linear control systems associated with a network and provide both a necessary and a sufficient topological condition under which the network is strongly targeted controllable furthermore a leader selection algorithm is presented to compute leader sets achieving target control

on the complexity of the constrained input selection problem for structural linear systems this paper studies the problem of given the structure of a linear time invariant system and a set of possible inputs finding the smallest subset of input vectors that ensures system s structural controllability we refer to this problem as the minimum constrained input selection mincis problem since the selection has to be performed on an initial given set of possible inputs we prove that the mincis problem is np hard which addresses a recent open question of whether there exist polynomial algorithms in the size of the system plant matrices that solve the mincis problem to this end we show that the associated decision problem to be referred to as the cis of determining whether a subset of a given collection of inputs with a prescribed cardinality exists that ensures structural controllability is np complete further we explore in detail practically important subclasses of the mincis obtained by introducing more specific assumptions either on the system dynamics or the input set instances for which systematic solution methods are provided by constructing explicit reductions to well known computational problems the analytical findings are illustrated through examples in multi agent leader follower type control problems

necessary and sufficient condition for local minima of a class of nonconvex quadratic programs the author 1992 1993 earlier studied the equivalence of a class of 0 1 quadratic programs and their relaxed problems thus a class of combinatorial optimization problems can be solved by solving a class of nonconvex quadratic programs in this paper a necessary and sufficient condition for local minima of this class of nonconvex quadratic programs is given this will be the foundation for study of algorithms

on the controllability and observability of networked dynamic systems some necessary and sufficient conditions are obtained for the controllability and observability of a networked system with linear time invariant lti dynamics the topology of this system is fixed but arbitrary and every subsystem is permitted to have different dynamics these conditions essentially depend only on transmission zeros of every subsystem and the subsystem connection matrix which makes them attractive in the analysis and synthesis of a large scale networked system as an application these conditions are utilized to characterize systems whose steady estimation accuracy with the distributed predictor of zhou 2013 is equal to that of the lumped kalman filter it has been made clear that to guarantee this equivalence the steady update gain matrix of the kalman filter must be block diagonal

global practical tracking for high order uncertain nonlinear systems with unknown control directions this paper addresses the global practical tracking problem for a class of high order uncertain nonlinear systems with unknown control directions under fairly weak conditions although the stabilization problem has been studied for the systems the tracking problem remains unsolved up to now mainly because of the essential differences between stabilization and tracking problems when control directions are unknown in this paper by introducing a novel coordinate transformation and new updating laws an approach is presented for the first time to design a continuous adaptive controller to make the tracking error prescribed arbitrarily small after a finite time and simultaneously to keep all the closed loop states bounded it is worth emphasizing that the proposed adaptive tracking control design scheme is motivated by the recent tracking works inspired by the ideas of universal control and dead zone and obtained by the approaches of nussbaum gain and adding a power integrator most importantly this paper removes the basic assumption that the control directions are precisely known in the related tracking works without additional conditions imposed on the systems and the reference signal

a survey of the s lemma in this survey we review the many faces of the s lemma a result about the correctness of the s procedure the basic idea of this widely used method came from control theory but it has important consequences in quadratic and semidefinite optimization convex geometry and linear algebra as well these were all active research areas but as there was little interaction between researchers in these different areas their results remained mainly isolated here we give a unified analysis of the theory by providing three different proofs for the s lemma and revealing hidden connections with various areas of mathematics we prove some new duality results and present applications from control theory error estimation and computational geometry

composability and controllability of structural linear time invariant systems distributed verification abstract motivated by the development and deployment of large scale dynamical systems often comprised of geographically distributed smaller subsystems we address the problem of verifying their controllability in a distributed manner specifically we study controllability in the structural system theoretic sense structural controllability in which rather than focusing on a specific numerical system realization we provide guarantees for equivalence classes of linear time invariant systems on the basis of their structural sparsity patterns i e the location of zero nonzero entries in the plant matrices towards this goal we first provide several necessary and or sufficient conditions that ensure that the overall system is structurally controllable on the basis of the subsystems structural pattern and their interconnections the proposed verification criteria are shown to be efficiently implementable i e with polynomial time complexity in the number of the state variables and inputs in two important subclasses of interconnected dynamical systems similar where every subsystem has the same structure and serial where every subsystem outputs to at most one other subsystem secondly we provide an iterative distributed algorithm to verify structural controllability for general interconnected dynamical system i e it is based on communication among physically interconnected subsystems and requires only local model and interconnection knowledge at each subsystem

an alternative formulation for a new closed cone constraint qualification abstract we give an alternative formulation for the so called closed cone constraint qualification cccq related to a convex optimization problem in banach spaces recently introduced in the literature this new formulation allows to prove in a simple way that cccq is weaker than some generalized interior point constraint qualifications given in the past by means of some insights from the theory of conjugate duality we also show that strong duality still holds under some weaker hypotheses than the ones considered so far in the literature

structure at infinity of structured descriptor systems and its applications the generic structure at infinity of the transfer matrix of a descriptor system is investigated under the physically reasonable assumption that the coefficients in the equations are classified into independent physical parameters and dimensionless constants for such a structured descriptor system the generic structure at infinity is characterized in terms of an independent assignment or weighted matroid intersection problem this leads to necessary and sufficient conditions for the generic solvability of the exact matching problem for a singular descriptor system and for the generic solvability of the disturbance decoupling problem for a nonsingular descriptor system the obtained conditions can be checked by efficient matroid theoretic algorithms

simultaneous decoupling and disturbance rejection a structural approach abstract the combined problem of disturbance rejection and decoupling for linear systems is considered new necessary and sufficient conditions are derived for the existence of a state feedback controller that rejects the disturbances and simultaneously decouples the closed loop system these conditions are simple intuitively appealing and are expressed in terms of system structural invariants such as infinite zero orders then we consider the disturbance rejection with simultaneous decoupling problem for structured linear systems necessary and sufficient conditions for the generic solvability of this problem are provided they are expressed in terms of input output path length comparisons on the system associated graph

on the fixed controllable subspace in linear structured systems in this paper we consider interconnected networks that are described by means of structured linear systems with state and control variables we represent these systems whose matrices contain fixed zeros and free parameters by means of directed graphs and study questions concerning controllability and the controllable subspace we show in this paper that the controllable subspace can have a part that will be present for almost all values of the free parameters it actually is a subspace of the controllable subspace and will be referred to as the fixed controllable subspace the subspace can then be seen as a kind of robustly controllable part of the system indeed it is a subspace in the state space with the generic property that states in it can be steered in an arbitrary way we derive a characterization of the fixed controllable subspace using the graph representation the obtained characterization makes use of well known algorithms from optimization and networks theory to get some more insight in the components in the fixed part we also give a representation of the structured linear systems by means of bipartite graphs using the dulmage mendelsohn decomposition we are able to decompose our structured systems in such a way that in some special cases the fixed controllable subspace can be obtained directly from the decomposition

hidden convexity in some nonconvex quadratically constrained quadratic programming we consider the problem of minimizing an indefinite quadratic objective function subject to twosided indefinite quadratic constraints under a suitable simultaneous diagonalization assumption which trivially holds for trust region type problems we prove that the original problem is equivalent to a convex minimization problem with simple linear constraints we then consider a special problem of minimizing a concave quadratic function subject to finitely many convex quadratic constraints which is also shown to be equivalent to a minimax convex problem in both cases we derive the explicit nonlinear transformations which allow for recovering the optimal solution of the nonconvex problems via their equivalent convex counterparts special cases and applications are also discussed we outline interior point polynomial time algorithms for the solution of the equivalent convex programs

convexifiability of continuous and discrete nonnegative quadratic programs for gap free duality abstract in this paper we show that a convexifiability property of nonconvex quadratic programs with nonnegative variables and quadratic constraints guarantees zero duality gap between the quadratic programs and their semi lagrangian duals more importantly we establish that this convexifiability is hidden in classes of nonnegative homogeneous quadratic programs and discrete quadratic programs such as mixed integer quadratic programs revealing zero duality gaps as an application we prove that robust counterparts of uncertain mixed integer quadratic programs with objective data uncertainty enjoy zero duality gaps under suitable conditions various sufficient conditions for convexifiability are also given

a framework for structural input output and control configuration selection in large scale systems this paper addresses problems on the structural design of large scale control systems an efficient and unified framework is proposed to select the minimum number of manipulated measured variables to achieve structural controllability observability of the system and to select the minimum number of feedback interconnections between measured and manipulated variables such that the closed loop system has no structural fixed modes global solutions are computed using polynomial complexity algorithms in the number of the state variables of the system finally graph theoretic characterizations are proposed which allow a characterization of all possible solutions

structural minimum controllability problem for switched linear continuous time systems abstract this paper addresses a structural design problem in control systems and explicitly takes into consideration the possible application to large scale systems more precisely we aim to determine and characterize the minimum number of manipulated state variables ensuring structural controllability of switched linear continuous time systems towards this goal we provide a new necessary and sufficient condition that leverages both graph theoretic and algebraic properties required to ensure feasibility of the solutions with this new condition we show that a solution can be determined by an efficient procedure i e polynomial in the number of state variables in addition we also discuss the switching signal properties that ensure structural controllability and the computational complexity of determining these sequences in particular we show that determining the minimum number of modes that a switching signal requires to ensure structural controllability is np hard

algorithms for leader selection in stochastically forced consensus networks we are interested in assigning a pre specified number of nodes as leaders in order to minimize the mean square deviation from consensus in stochastically forced networks this problem arises in several applications including control of vehicular formations and localization in sensor networks for networks with leaders subject to noise we show that the boolean constraints which indicate whether a node is a leader are the only source of nonconvexity by relaxing these constraints to their convex hull we obtain a lower bound on the global optimal value we also use a simple but efficient greedy algorithm to identify leaders and to compute an upper bound for networks with leaders that perfectly follow their desired trajectories we identify an additional source of nonconvexity in the form of a rank constraint removal of the rank constraint and relaxation of the boolean constraints yields a semidefinite program for which we develop a customized algorithm well suited for large networks several examples ranging from regular lattices to random graphs are provided to illustrate the effectiveness of the developed algorithms

brief paper observability analysis and sensor location study for structured linear systems in descriptor form with unknown inputs this paper deals with the state and input right hand side observability and the sensor location problem to ensure this property for structured linear systems in the descriptor form the proposed method is based on a graph theoretic approach it is applicable to a large class of descriptor systems including regular and nonregular systems even if they are underdetermined overdetermined or square after defining a bipartite graph which represents such systems we deduce some graphic necessary and sufficient conditions to achieve the right hand side observability of the state and the input next we propose a sensor placement procedure to recover this property more precisely we provide the minimal number of the sensors required and either their pertinent location or a necessary and sufficient condition to check if a given sensor configuration is adequate or not to ensure state and input right hand side observability our approach uses algorithms with polynomial complexity orders and assumes only the knowledge of the system s structure and so is suited for large scale systems

optimal actuator sensor location for active noise regulator and tracking control problems in this paper we investigate the problem of finding the optimal location of sensors and actuators to achieve reduction of the noise field in an acoustic cavity we offer two control strategies the first is based on linear quadratic tracking where the offending noise is tracked and the second considers the formulation of the harmonic control strategy as a periodic static output feedback control problem the first method which is based on full state information is suitable for optimal location of actuators while the second strategy can extend the results to finding optimal location of sensors as well as actuators for both methods we consider the optimization of an appropriate quadratic performance criterion with respect to the location of the actuators and or the sensors numerical examples are presented to compare the effectiveness of each control strategy and also the effect of optimal placement of actuators and sensors

complete characterizations of stable farkas lemma and cone convex programming duality we establish necessary and sufficient conditions for a stable farkas lemma we then derive necessary and sufficient conditions for a stable duality of a cone convex optimization problem where strong duality holds for each linear perturbation of a given convex objective function as an application we obtain stable duality results for convex semi definite programs and convex second order cone programs

structurally fixed modes a notion of structurally fixed modes is introduced in the framework of decentralized control systems to identify the modes that cannot be shifted by decentralized feedback regardless of the numerical values of system parameters in this way a qualitative characterization of decentralized fixed modes is provided which is suitable for delineating decentrally stabilizable systems the characterization leads naturally to the notion of fixed modes with respect to arbitrary feedback structure constraints

minimum structural controllability problems of complex networks abstract controllability of complex networks has been one of the attractive research areas for both network and control community and has yielded many promising and significant results in minimum inputs and minimum driver vertices however few studies have been devoted to studying the minimum controlled vertex set through which control over the network with arbitrary structure can be achieved in this paper we prove that the minimum driver vertices driven by different inputs are not sufficient to ensure the full control of the network when the associated graph contains the inaccessible strongly connected component which has perfect matching and propose an algorithm to identify a minimum controlled vertex set for network with arbitrary structure using convenient graph and mathematical tools and the simulation results show that the controllability of network is correlated to the number of inaccessible strongly connected components which have perfect matching and these results promote us to better understand the relationship between the network s structural characteristics and its control

some convex programs without a duality gap an important issue in convex programming concerns duality gap various conditions have been developed over the years that guarantee no duality gap including one developed by rockafellar network flows and monotropic programming wiley interscience new york 1984 involving separable objective function and affine constraints we show that this sufficient condition can be further relaxed to allow the constraint functions to be separable we also refine a sufficient condition involving weakly analytic functions by allowing them to be extended real valued

selection mechanisms based on the maximin fitness function to solve multi objective optimization problems in this paper we study three selection mechanisms based on the maximin fitness function and we propose another one these selection mechanisms give rise to the following moeas mc moea md moea mh moea and mah moea we validated them using standard test functions taken from the specialized literature having from three up to ten objective functions we compare these four moeas among them and also with respect to moea d which is based on decomposition and to sms emoa which is based on the hypervolume indicator our preliminary results indicate that md moea and mah moea are promising alternatives for solving mops with either low or high dimensionality

a geometric characterization of strong duality in nonconvex quadratic programming with linear and nonconvex quadratic constraints we first establish a relaxed version of dines theorem associated to quadratic minimization problems with finitely many linear equality and a single nonconvex quadratic inequality constraints the case of unbounded optimal valued is also discussed then we characterize geometrically the strong duality and some relationships with the conditions employed in finsler theorem are established furthermore necessary and sufficient optimality conditions with or without the slater assumption are derived our results can be used to situations where none of the results appearing elsewhere are applicable in addition a revisited theorem due to frank and wolfe along with that due to eaves is established for asymptotically linear sets

brief paper graph theoretic characterization of fixed modes in frequency domain we examine a characterization of fixed modes in a frequency domain framework based on the graphical representation of systems with multiple poles we present a graph theoretic characterization of the characteristic polynomials of closed loop systems under arbitrary structural constraints based on this characterization fixed modes are characterized using the weight products of 1 factors of the weighted directed graphs associated with closed loop systems it is also shown that the well known characterization of fixed modes in terms of transmission zeros can be derived from the proposed graph theoretic characterization

alternative theorems for quadratic inequality systems and global quadratic optimization we establish alternative theorems for quadratic inequality systems consequently we obtain lagrange multiplier characterizations of global optimality for classes of nonconvex quadratic optimization problems we present a generalization of dine s theorem to a system of two homogeneous quadratic functions with a regular cone the class of regular cones are cones k for which k cup k is a subspace as a consequence we establish a generalization of the powerful s lemma which paves the way to obtain a complete characterization of global optimality for a general quadratic optimization model problem involving a system of equality constraints in addition to a single quadratic inequality constraint we then present an alternative theorem for a system of three nonhomogeneous inequalities by way of establishing the convexity of the joint range of three homogeneous quadratic functions using a regular cone this yields lagrange multiplier characterizations of global optimality for classes of trust region type problems with two inequality constraints finally we establish an alternative theorem for systems involving an arbitrary finite number of quadratic inequalities involving z matrices which are matrices with nonpositive off diagonal elements and present necessary and sufficient conditions for global optimality for classes of nonconvex inequality constrained quadratic optimization problems