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

structural controllability of switched linear systems this paper studies the structural controllability of a class of uncertain switched linear systems where the parameters of subsystems state matrices are either unknown or zero the structural controllability is a generalization of the traditional controllability concept for dynamical systems and purely based on the interconnection relation between the state variables and inputs through non zero elements in the state matrices in order to illustrate such a relationship two kinds of graphic representations of switched linear systems are proposed based on which graph theory based necessary and sufficient characterizations of the structural controllability for switched linear systems are presented finally the paper concludes with discussions on the results and future work

exponential convergence of recursive least squares with exponential forgetting factor this paper demonstrates that provided the system input is persistently exciting the recursive least squares estimation algorithm with exponential forgetting factor is exponentially convergent further it is shown that the incorporation of the exponential forgetting factor is necessary to attain this convergence and that the persistence of excitation is virtually necessary the result holds for stable finite dimensional linear time invariant systems but has its chief implications to the robustness of the parameter estimator when these conditions fail

sensor location and classification for disturbance rejection by measurement feedback in this paper a new necessary and sufficient condition is proposed for the solvability of the disturbance rejection by measurement feedback drmf problem involving linear structured systems the associated system graph can be used to easily check whether or not the condition holds in relation to the drmf problem two issues related to the available sensor set have been investigated sensor number and location when the drmf problem is not solvable with the given sensor set how many sensors are needed and where should they be located to make the drmf problem solvable sensor classification when the drmf problem is solvable with the given sensor set what is the impact of the failure of a sensor on the solvability based on the new condition a lower bound can be determined for the number of sensors required moreover measuring state variables outside a given subset is found to be of no use to solve the drmf problem it is sufficient to measure state variables sufficiently close to the disturbances in the associated system graph sensor classification is used to distinguish between essential sensors i e sensors for which failure leads to unsolvability and useless sensors that have no impact on solvability partial classification results are provided for the general case and a complete characterization of essential and useless sensors is provided for the single disturbance case

a measure of the tracking capability of recursive stochastic algorithms with constant gains a criterion is given for measuring the tracking capability of recursive algorithms when applied to slowly time varying systems the optimal gain for a given disturbance is also calculated this criterion is seen to have some connection with the fisher information matrix and allows us to select a priori the best algorithm for identifying a given unknown parameter which may be subject to smooth unknown disturbances examples of applications are given in the areas of identification theory and data communication theory

identification of time varying systems in reproducing kernel hilbert spaces we consider a class of linear systems in state space form whose parameters evolve in time according to a continuous time gauss markov process our problem is to identify the system from a finite set of noisy output measurements we derive a connection between this problem and tikhonov regularization in reproducing kernel hilbert spaces relying upon this result conditions that ensure the existence of the maximum a posteriori estimate of the parameter trajectory are provided and an identification algorithm is worked out simulated data are used to test the goodness of the proposed approach

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 categorical semantics for fuzzy predicate logic the object of this study is to look at categorical approaches to many valued logic both propositional and predicate to see how different logical properties result from different parts of the situation in particular the relationship between the categorical fabric i introduced at linz in 2004 and the fuzzy logics studied by hajek 2003 5 esteva et al 2003 1 and hajek 1998 4 comes from restricting the kind of structures used for truth values we see how the structure of the various kinds of algebras shows up in the categorical logic giving a variant on natural deduction for these logics quantification typically needs more completeness than is present in the algebras used in hajek 1998 4 hence the need for safe interpretations the categorical setting gives a predicate logic without variables the language in the more traditional sense comes from a structure built on a particular freely generated cartesian category formulas have a clear meaning in that more restricted context interpretation of the language in other categorical fabrics is given by application of a product preserving functor traditional completeness results relate to this kind of interpretation completeness can also be understood as showing that the derivable truths in the general fabric are the necessary truths those which are true in all of the possible worlds

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 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

bounds on achievable performance in the identification and adaptive control of time varying systems treats the identification and adaptive control of time varying linear systems for linear systems with a gauss markov parameter process a global lower bound on the mean square error is obtained which is valid for any causal parameter estimator a similar lower bound is obtained for any causal one step ahead predictor these bounds are applied to the adaptive control of time varying systems to obtain a lower bound on closed loop mean square performance for any causal control law for a specific control law mean square stability is established and through simulations it is seen that the performance nearly meets the theoretical lower bound

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

categorical approaches to non commutative fuzzy logic in this paper we consider what it means for a logic to be non commutative how to generate examples of structures with a non commutative operation which have enough nice properties to serve as the truth values for a logic inference in the propositional logic is gotten from the categorical properties products coproducts monoidal and closed structures adjoint functors of the categories of truth values we then show how to extend this view of propositional logic to a predicate logic using categories of propositions about a type a with functors giving change of type and adjoints giving quantifiers in the case where the semantics takes place in set l goguen s category of l fuzzy sets the categories of predicates about a can be represented as internal category objects with the quantifiers as internal functors

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

nonasymptotic results for finite memory wls filters a nonasymptotic analysis of properties of weighted least squares wls adaptive filters used for identification of time varying systems is presented it is shown that the problem of mean square boundedness of wls estimates is closely related to the problem of invertibility in the mean sense of the corresponding regression matrix necessary and sufficient conditions are discussed for such invertibility to hold based on that a number of results are derived paralleling those already obtained for least mean square lms filters and the problem of statistical robustness of the wls estimator is briefly discussed

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

efficient bounded influence regression estimation abstract the least squares estimator for in the classical linear regression model is strongly efficient under certain conditions however in the presence of heavy tailed errors and or anomalous data the least squares efficiency can be markedly reduced in this article we propose an estimator that limits the influence of any small subset of the data and show that it satisfies a first order condition for strong efficiency subject to the constraint we then show that the estimator is asymptotically normal the article concludes with an outline of an algorithm for computing a bounded influence regression estimator and with an example comparing least squares robust regression as developed by huber and the estimator proposed in this article

monoidal closed categories weak topoi and generalized logics abstract a weak topos can be considered as the categorical foundation of fuzzy set theory prominent examples of weak topoi are the category met1 the category of sheaves and the category cm set of complete m valued sets over a locally involutory monoid m

the generic number of invariant zeros of a structured linear system in this paper we consider a structured linear system represented by means of a directed graph we present a graph theoretic method to compute the generic number of invariant zeros of the corresponding rosenbrock matrix the method is based on a fundamental decomposition of the directed graph representing the structured system the generic number of invariant zeros is important in generic versions of problems involving controllability and pole placement

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

structural invertibility of transfer functions in this note we study certain properties of a transfer function in terms of the structure of the state space representation a b c specifically the rank of the transfer function and the degree of a decoupled system which can be obtained by applying a left decoupler are characterized in terms of the structure of a b c

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

persistence of excitation properties for time varying autoregressive systems it is well known that a crucial property for the effective identification of time varying systems is that the data carry continual information on the parameters to be estimated as a matter of fact only in this case can the identification algorithm rely on fresh information in forming a reliable estimate of the current value of these parameters this concept has been formalized in the system identification literature under the name of persistence of excitation in this paper the persistence of excitation property is studied for a class of time varying systems that includes the standard autoregressive model as a particular case and conditions for it to hold are derived

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

normal forms and truth tables for fuzzy logics in this paper we examine and compare de morgan kleene and boolean disjunctive and conjunctive normal forms and consider their role in fuzzy settings in particular we show that there are normal forms and truth tables for classical fuzzy propositional logic and interval valued fuzzy propositional logic that are completely analogous to those for boolean propositional logic thus determining logical equivalence of two expressions in fuzzy propositional logic is a finite problem and similarly for the interval valued case turksen s work on interval valued fuzzy sets is examined in light of these results

convergence analysis of the least squares identification algorithm with a variable forgetting factor the time varying linear systems abstract this paper studies the convergence of the least squares identification algorithm with a variable forgetting factor the evolution of the parameter estimator with respect to initial conditions actual parameter changes and stochastic perturbations is analysed bounds on the deterministic and stochastic parts of their estimator error are found and their relation to a persistent excitation condition is discussed this relation explains the possibility of having bursting phenomena during the identification process special attention is paid to the consistency of these results with the classical ones obtained for the ordinary least squares algorithm when the forgetting factor tends to unity

estimating time varying parameters by the kalman filter based algorithm stability and convergence convergence and stability properties of the kalman filter based parameter estimator are established for linear stochastic time varying regression models the main features are both the variances and sample path averages of the parameter tracking error are shown to be bounded the regression vector includes both stochastic and deterministic signals and no assumptions of stationarity or independence are requires and the unknown parameters are only assumed to have bounded variations in an average sense

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

the averaged overdetermined and generalized lms algorithm this paper provides and exploits one possible formal framework in which to compare and contrast the two most important families of adaptive algorithms the least mean square lms family and the recursive least squares rls family existing and well known algorithms belonging to any of these two families like the lms algorithm and the rls algorithm have a natural position within the proposed formal framework the proposed formal framework also includes among others the lms overdetermined recursive instrumental variable oriv algorithm and the generalized lms glms algorithm which is an instrumental variable iv enable lms algorithm furthermore this formal framework allows a straightforward derivation of new algorithms with enhanced properties respect to the existing ones specifically the oriv algorithm is exported to the lms family resulting in the derivation of the averaged overdetermined and generalized lms aoglms algorithm an overdetermined lms algorithm able to work with an iv the proposed aoglms algorithm overcomes as we analytically show here the limitations of glms and possesses a much lower computational burden than lms oriv being in this way a better alternative to both algorithms simulations verify the analysis

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

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

controllability of switched bilinear systems the controllability of switched bilinear systems sblss is considered three kinds of controllabilities including weak controllability approximate controllability and global controllability are investigated one by one sets of easily verifiable sufficient conditions are obtained for each case which are applicable to a large class of switched bilinear systems

smith mcmillan factorizations at infinity of rational matrix functions and their control interpretation in this paper the smith mcmillan factorizations at infinity of a transfer function are studied the non uniqueness of these factorizations is characterized via a multiplicative group of bicausal isomorphisms control interpretations are given in terms of system equivalence under some groups of transformations a characterization of the stabilizer of morse group at a b c is given for irreducible systems

handling the valuation of the predicates in a fuzzy model given a fuzzy model and therefore a graded valuation of the predicates several handlings of such a valuation are possible for example we can change the set of truth values modify the scale cut the predicates and identify truth values in this exploratory paper we analyze some of the properties preserved under these handlings to do this we refer to an approach to fuzzy semantics in which the valuation structures can vary freely inside a given type

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

on the category set jcpos category set jcpos of lattice valued subsets of sets is introduced and studied we prove that it is topological over setxjcpos and show its natural coalgebraic subcategory

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

exact distribution and moments for the rls estimate in a time varying ar 1 process abstract the recursive least squares rls identification algorithm with a forgetting factor is often used to estimate time varying parameters in stochastic systems however it is hard to say anything about the distribution of the parameter estimates since they are nonlinear functions of the observations in this paper we present a way to compute the exact distribution and moments of the weighted least squares wls estimator in a time varying gaussian ar 1 process the rls estimate follows as special case of the wls estimator

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

output feedback disturbance decoupling graph interpretation for structured systems abstract in this paper we consider first the output feedback disturbance decoupling problem for linear systems we derive a set of new necessary or sufficient conditions for the solvability of this problem these conditions are expressed in terms of system structural invariants such as infinite zero orders and essential orders then we consider the output feedback disturbance decoupling problem for structured linear systems necessary or 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

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

bounded error identification of time varying parameters by rls techniques the performance of the recursive least squares algorithm with constant forgetting factor in the identification of time varying parameters is studied in a stochastic framework it is shown that the mean square tracking error keeps bounded if and only if the so called covariance matrix of the algorithm is l sup 1 bounded then a feasibility range for the forgetting factor is worked out in correspondence of which the covariance matrix and therefore the tracking error keeps bounded

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

brief paper design of switching sequences for controllability realization of switched linear systems in this paper we study the problem of designing switching sequences for controllability of switched linear systems each controllable state set of designed switching sequences coincides with the controllable subspace both aperiodic and periodic switching sequences are considered for the aperiodic case a new approach is proposed to construct switching sequences and the number of switchings involved in each designed switching sequence is shown to be upper bounded by d d d 1 1 here d is the dimension of the controllable subspace d email protected i 1 m where a i b i are subsystems for the periodic case we show that the controllable subspace can be realized within d switching periods

stability and stabilizability of switched linear systems a survey of recent results during the past several years there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems this paper aims to briefly survey recent results in this field first the stability analysis for switched systems is reviewed we focus on the stability analysis for switched linear systems under arbitrary switching and we highlight necessary and sufficient conditions for asymptotic stability after a brief review of the stability analysis under restricted switching and the multiple lyapunov function theory the switching stabilization problem is studied and a variety of switching stabilization methods found in the literature are outlined then the switching stabilizability problem is investigated that is under what condition it is possible to stabilize a switched system by properly designing switching control laws note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature a necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here

weak convergence and asymptotic properties of adaptive filters with constant gains the basic adaptive filtering algorithm x n 1 epsilon x n epsilon epsilon y n y n x n epsilon psi n is analyzed using the theory of weak convergence apart from some very special cases the analysis is hard when done for each fixed epsilon 0 but the weak convergence techniques are set up to provide much information for small epsilon the relevant facts from the theory are given define x epsilon cdot by x epsilon t x n epsilon on n epsilon n epsilon epsilon then weak distributional convergence of x epsilon cdot and of x epsilon cdot t epsilon is proved under very weak assumptions where t epsilon rightarrow infty as epsilon rightarrow 0 the normalized errors x n epsilon theta sqrt epsilon are analyzed where theta is a stable point for the mean algorithm the asymptotic properties of a projection algorithm are developed where the x n epsilon are truncated at each iteration if they fall outside of a given set

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

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

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

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

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

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