balanced truncation for temporal and spatial lpv interconnected systems based on the full block s procedure abstractthis paper presents a technique for model order reduction of exponentially stable temporal and spatial lpv linear parameter varying interconnected systems represented in linear fractiona

lmi relaxation to riccati equations in structured control in this paper we discuss structured control methods for large scale interconnected systems based on a relaxation of riccati equations we derive some linear matrix inequality lmi conditions for sub optimal controllers in which information structure can be imposed in particular we derive controllers by solving low dimensional lmis which are decentralized except for the sharing information between neighbours as determined by the plant interconnection also we optimize a performance bound for each of the derived controllers

distributed control of spatially invariant systems we consider distributed parameter systems where the underlying dynamics are spatially invariant and where the controls and measurements are spatially distributed these systems arise in many applications such as the control of vehicular platoons flow control microelectromechanical systems mems smart structures and systems described by partial differential equations with constant coefficients and distributed controls and measurements for fully actuated distributed control problems involving quadratic criteria such as linear quadratic regulator lqr h sub 2 and h sub spl infin optimal controllers can be obtained by solving a parameterized family of standard finite dimensional problems we show that optimal controllers have an inherent degree of decentralization and this provides a practical distributed controller architecture we also prove a general result that applies to partially distributed control and a variety of performance criteria stating that optimal controllers inherit the spatial invariance structure of the plant connections of this work to that on systems over rings and systems with dynamical symmetries are discussed

construction of optimal order nonlinear solvers using inverse interpolation abstract there is a vast literature on finding simple roots of nonlinear equations by iterative methods these methods can be classified by order by the information used or by efficiency there are very few optimal methods that is methods of order 2 m requiring m 1 function evaluations per iteration here we give a general way to construct such methods by using inverse interpolation and any optimal two point method the presented optimal multipoint methods are tested on numerical examples and compared to existing methods of the same order of convergence

a robust control approach to perfect reconstruction of digital signals in this paper we present a deterministic worst case approach for reconstructing discrete valued signals that have been filtered via dispersive and noisy systems ldquochannelsrdquo this approach which is explored based on robust control ideas and makes no assumption on the noise distribution or structure other than a requirement that its magnitude be bounded can serve as a complement to existing approaches that attempt to reconstruct discrete valued signals by optimizing probabilistic criteria the particular problems touched upon are i necessary and sufficient conditions for causal possibly delayed perfect reconstruction under deterministic magnitude bounded noise for single input single output siso and multi input multi output mimo channels ii perfect reconstruction based on decision feedback df structures and iii necessary and sufficient conditions for perfect reconstruction with df structures in the presence of uncertainties in the channel the l1 control theory emerges as the natural key player for analysis and synthesis of perfect reconstructing strategies in this framework

subspace identification of circulant systems this article concerns the identification of a class of large scale systems called circulant systems circulant systems have a special property that allows them to be decomposed into simpler subsystems through a state transformation this property has been used in literature for control design and here we show how it can be used for system identification the approach that is proposed here will both reduce the complexity of the problem as well as provide models which have a circulant structure that can be exploited for control design a novel identification algorithm for circulant systems based on subspace identification is presented the algorithm is then tested in simulation on an academic example of circulant system and on a realistic finite element model of a vibrating plate

a scaled small gain theorem with applications to spatially interconnected systems in this note a new result that extends the scaled small gain theorem is presented as is well known the scaled small gain theorem gives necessary and sufficient conditions for robust stability of a nominal linear time invariant system in feedback with structured operators of norm less than or equal to unity we propose alternative linear matrix inequality conditions that give necessary and sufficient conditions for robust stability against the class of structured unitary operators invertible operators of exactly unit norm it is shown that this result besides being a less conservative version of the scaled small gain theorem has connections to several recent results on the control of spatially interconnected systems and serves to unify and quantify the conservatism of those results

on continuity properties of the two block l1 optimal design abstract this paper investigates continuity properties of the two block l 1 optimization resulting from the optimal design of bibo stability robustness for discrete time systems in the presence of coprime factor perturbations in general the two block l 1 optimal design might lack continuity properties since it might have no finite dimensional solution however this paper shows that for a suitable given truncated order the two block l 1 suboptimal design is continuous as a map from the plant to the suboptimal closed loop solution if the plant has no zeros on the unit circle and has a unique suboptimal solution furthermore if the set of plants is compactness we show that there exists a uniform bound on the degree of suboptimal solution for all plants in the set such that their deviation of suboptimal value from the optimal one have the same bound and the two block l 1 suboptimal design is uniformly continuous in particular in the case in which the plant has nonunique solution a procedure is also developed on how to choose a solution that preserves continuity the results enable the stability of robust l 1 adaptive scheme to hold in the presence of coprime factor perturbations

generalized positiveness of spatially interconnected systems over quadratically constrained frequency domains abstract generalized positiveness is investigated in this paper for a spatially interconnected system sis results of 7 are corrected and extended to a more general frequency domain and to more complicated requirements on the frequency response of a sis based on an equivalent characterization of the interested frequency domain a linear matrix inequality lmi based sufficient condition is derived for the generalized positiveness of a sis over a frequency domain described by several matrix valued quadratic functions moreover using the separability property of convex sets situations have also been clarified under which this sufficient condition becomes also necessary

a comparison between lqr control for a long string of siso systems and lqr control of the infinite spatially invariant version in this paper we consider a long string of siso systems which in the limit becomes a scalar infinite spatially invariant system we compare the lqr control for long but finite strings with the lqr control for the corresponding infinite strings we give analytical and numerical examples where these are quite different and we investigate the cause in addition we obtain sufficient conditions for the lqr solutions to be similar as the length of the string increases

on slowly time varying systems abstract a characterization of stabilizing controllers for slowly time varying systems based on input output descriptions of the plant and the controller is presented this approach generalizes standard results on slowly time varying systems with finite dimensional state space representation and allows both the plant and the controller to be infinite dimensional the controller design will be based on frozen time versions of the plant obtained at equally spaced instances in time

a robust direct adaptive controller this paper proposes a new direct adaptive control algorithm which is robust with respect to additive and multiplicative plant unmodeled dynamics the algorithm is designed based on the reduced order plant which is assumed to be minimum phase and of known order and relative degree but is analyzed with respect to the overall plant which due to the unmodeled dynamics may be nonminimum phase and of unknown order and relative degree it is shown that if the unmodeled dynamics are sufficiently small in the low frequency range then the algorithm guarantees boundedness of all signals in the adaptive loop and small residual tracking errors for any bounded initial conditions in the absence of unmodeled dynamics the residual tracking error is shown to be zero

on the control and estimation over relative sensing networks in this note we consider certain structural aspects of estimation and control over relative sensing networks rsns in this venue using tools from basic algebraic graph theory namely the incidence matrix and cut and cycle spaces of a connect graph we examine transformations among relative sensing topologies for a networked system these transformations are parameterized for noise free as well as noisy networks and their utility in the context of network centric robust control and control reconfigurations is explored

a family of three point methods of optimal order for solving nonlinear equations a family of three point iterative methods for solving nonlinear equations is constructed using a suitable parametric function and two arbitrary real parameters it is proved that these methods have the convergence order eight requiring only four function evaluations per iteration in this way it is demonstrated that the proposed class of methods supports the kung traub hypothesis 1974 3 on the upper bound 2 n of the order of multipoint methods based on n 1 function evaluations consequently this class of root solvers possesses very high computational efficiency numerical examples are included to demonstrate exceptional convergence speed with only few function evaluations

a family of high order multistep methods with vanished phase lag and its derivatives for the numerical solution of the schrodinger equation many simulation algorithms chemical reaction systems differential systems arising from the modelling of transient behaviour in the process industries etc contain the numerical solution of systems of differential equations for the efficient solution of the above mentioned problems linear multistep methods or runge kutta single step methods are used for the simulation of chemical procedures the radial schrodinger equation is used frequently in the present paper we will study a class of linear multistep methods more specifically the purpose of this paper is to develop an efficient algorithm for the approximate solution of the radial schrodinger equation and related problems this algorithm belongs in the category of the multistep methods in order to produce an efficient multistep method the phase lag property and its derivatives are used hence the main result of this paper is the development of an efficient multistep method for the numerical solution of systems of ordinary differential equations with oscillating or periodical solutions the reason of their efficiency as the analysis proved is that the phase lag and its derivatives are eliminated another reason of the efficiency of the new obtained methods is that they have high algebraic order

brief paper unification of independent and sequential procedures for decentralized controller design this paper is concerned with decentralized control problems there are two typical procedures to design decentralized controllers independent and sequential design procedures as the concepts and the techniques in these two approaches are too different from each other there have been no attempts to unify these approaches this paper proposes an iterative independent design procedure for decentralized control systems which is a unified approach to these conventional approaches

sparse solution of the lyapunov equation for large scale interconnected systems we consider the problem of computing an approximate banded solution of the continuous time lyapunov equation a x x a t p where the coefficient matrices a and p are large symmetric banded matrices the sparsity pattern of a describes the interconnection structure of a large scale interconnected system recently it has been shown that the entries of the solution x are spatially localized or decaying away from a banded pattern we show that the decay of the entries of x is faster if the condition number of a is smaller by exploiting the decay of entries of x we develop two computationally efficient methods for approximating x by a banded matrix for a well conditioned and sparse banded a the computational and memory complexities of the methods scale linearly with the state dimension we perform extensive numerical experiments that confirm this and that demonstrate the effectiveness of the developed methods the methods proposed in this paper can be generalized to sparsity patterns of a and p that are more general than banded matrices the results of this paper open the possibility for developing computationally efficient methods for approximating the solution of the large scale riccati equation by a sparse matrix

on the kalman yakubovich popov lemma the purpose of this note is to present a new elementary proof for the multivariable k y p lemma a minimum of linear algebra and finite dimensional convexity theory is used

indirect adaptive control for interconnected systems an indirect adaptive controller for interconnected systems is introduced each subsystem is subject to bounded disturbances and to possibly unbounded interconnections with other subsystems a variable dead zone is incorporated into a gradient estimation scheme to limit the effects of the interconnections and disturbances an adaptive state feedback control law is described which stabilizes the interconnected system forcing the input and output signals of each subsystem to remain bounded

distributed control of a class of flexible mechanical systems with global constraint in this paper the constrained problem is investigated for both flexible string model and euler bernoulli beam model with the tip payload based on an infinite dimensional generalisation of a distributed control method the control objectives are to develop the control law so that the motion of flexible mechanical systems can track a desired reference signal and ensure that the string or beam remain in a constrained space we prove that with the proposed control the tracking error is exponentially stable without violation of the constraint the proof of convergence is based on an integral barrier lyapunov function iblf and extensive simulations are provided to illustrate the performance of the control system

a new eighth order iterative method for solving nonlinear equations abstract in this paper we present an improvement of the fourth order newton type method for solving a nonlinear equation the new newton type method is shown to converge of the order eight per iteration the new method requires three evaluations of the function and one evaluation of its first derivative and therefore the new method has the efficiency index of 8 4 which is better than the well known newton type methods of lower order we shall examine the effectiveness of the new eighth order newton type method by approximating the simple root of a given nonlinear equation numerical comparisons are made with several other existing methods to show the performance of the presented method

a family of optimal sixteenth order multipoint methods with a linear fraction plus a trivariate polynomial as the fourth step weighting function a new family of four step optimal multipoint iterative methods of order sixteen for solving nonlinear equations are developed along with their convergence properties numerical experiments with comparison to some existing methods are demonstrated to support the underlying theory

subspace algorithms for identifying separable in denominator 2d systems with deterministic stochastic inputs abstractin this paper we present an algorithm for identifying two dimensional 2d causal recursive and separable in denominator crsd state space models in the roesser form with deterministic stochastic inputs the algorithm implements the n4sid po moesp and cca methods which are well known in the literature on 1d system identification but here we do so for the 2d crsd roesser model the algorithm solves the 2d system identification problem by maintaining the constraint structure imposed by the problem i e toeplitz and hankel and computes the horizontal and vertical system orders system parameter matrices and covariance matrices of a 2d crsd roesser model from a computational point of view the algorithm has been presented in a unified framework where the user can select which of the three methods to use furthermore the identification task is divided into three main parts 1 computing the deterministic horizontal model parameters 2 computing the deterministic vertical model parameters

structure preserving model reduction for spatially interconnected systems with experimental validation on an actuated beam abstracta technique for model reduction of exponentially stable spatially interconnected systems is presented where the order of the reduced model is determined by the number of truncated small generalised singular values of the structured solutions to a pair of lyapunov inequalities for parameter invariant spatially interconnected systems the technique is based on solving a pair of lyapunov inequalities in continuous time and space domain with a rank constraint using log det and cone complementarity methods an improved error bound can be obtained the approach is extended to spatially parameter varying systems and a balanced truncation approach using parameter dependent gramians is proposed to reduce the conservatism caused by the use of constant gramians this is done by considering two important operators which can be used to represent multidimensional systems temporal and spatial linear parameter varying interconnected systems the results are illustrated with their application to an experi

robust h sub spl infin filtering for uncertain2 d continuous systems this paper considers the problem of robust h sub spl infin filtering for uncertain two dimensional 2 d continuous systems described by the roesser state space model the parameter uncertainties are assumed to be norm bounded in both the state and measurement equations the purpose is the design of a 2 d continuous filter such that for all admissible uncertainties the error system is asymptotically stable and the h sub spl infin norm of the transfer function from the noise signal to the estimation error is below a prespecified level a sufficient condition for the existence of such filters is obtained in terms of a set of linear matrix inequalities lmis when these lmis are feasible an explicit expression of a desired h sub spl infin filter is given finally a simulation example is provided to demonstrate the effectiveness of the proposed method

a semilocal convergence analysis for directional newton methods a semilocal convergence analysis for directional newton methods in n variables is provided in this study using weaker hypotheses than in the elegant related work by y levin and a ben israel and introducing the center lipschitz condition we provide under the same computational cost as in levin and ben israel a semilocal convergence analysis with the following advantages weaker convergence conditions larger convergence domain finer error estimates on the distances involved and an at least as precise information on the location of the zero of the function a numerical example where our results apply to solve an equation but not the ones in levin and ben israel is also provided in this study

distributed control design for systems interconnected over an arbitrary graph we consider the problem of synthesizing a distributed dynamic output feedback controller achieving h sub spl infin performance for a system composed of different interconnected sub units when the topology of the underlying graph is arbitrary first using tools inspired by dissipativity theory we derive sufficient conditions in the form of finite dimensional linear matrix inequalities when the interconnections are assumed to be ideal these inequalities are coupled in a way that reflects the spatial structure of the problem and can be exploited to design distributed synthesis algorithms we then investigate the case of lossy interconnection links and derive similar results for systems whose interconnection relations can be captured by a class of integral quadratic constraints that includes constant delays

structure of hierarchical linear systems with cyclic symmetry abstract in this paper we analyze the structure of hierarchical linear systems that are invariant under actions of finite cyclic groups in particular we consider n n 1 n 2 n m identical d dimensional linear systems grouped into m hierarchies such that in each level of hierarchy the partitioned subsystems are invariant under the action of cyclic groups we prove that the equivalence classes of all possible partitions of such hierarchical systems have one one correspondence with the decomposition of n th order abelian groups into cyclic groups of prime power order

brief a controller perturbation technique for transferring closed loop stability between systems this brief paper presents a perturbation technique with which a controller stabilizing one plant may be modified so that it stabilizes a second related plant the proposed technique produces an internally stable loop for a broad class of linear systems without requiring any further calculations on the part of the designer four seemingly different examples are described in terms of this result

an analysis of a new family of eighth order optimal methods a new family of eighth order optimal methods is developed and analyzed numerical experiments show that our family of methods perform well and in many cases some members are superior to other eighth order optimal methods it is shown how to choose the parameters to widen the basin of attraction

multi agent compositional stability exploiting system symmetries this paper considers nonlinear symmetric control systems by exploiting the symmetric structure of the system stability results are derived that are independent of the number of components in the system this work contributes to the fields of research directed toward compositionality and composability of large scale system in that a system can be built up by adding components while maintaining system stability the modeling framework developed in this paper is a generalization of many existing results which focus on interconnected systems with specific dynamics the main utility of the stability result is one of scalability or compositionality if the system is stable for a given number of components under appropriate conditions stability is then guaranteed for a larger system composed of the same type of components which are interconnected in a manner consistent with the smaller system the results are general and applicable to a wide class of problems the examples in this paper focus on the formation control problems for multi agent robotic systems

on a general class of optimal order multipoint methods for solving nonlinear equations abstract we develop a class of n point iterative methods with optimal 2 n order of convergence for solving nonlinear equations newton s second order and ostrowski s fourth order methods are special cases corresponding to n 1 and n 2 eighth and sixteenth order methods that correspond to n 3 and n 4 of the class are special cases of the eighth and sixteenth order methods proposed by sharma et al 25 the methodology is based on employing the previously obtained n 1 step scheme and modifying the n th step by using rational hermite interpolation unlike that of existing higher order techniques the proposed technique is attractive since it leads to a simple implementation local convergence analysis is provided to show that the iterations are locally well defined and convergent theoretical results are verified through numerical experimentations the performance is also compared with already established methods in literature it is observed that new algorithms are more accurate than existing counterparts and very effective in high precision computations

on a general class of multipoint root finding methods of high computational efficiency a general class of n point iterative methods for solving nonlinear equations is constructed by combining methods of newton s type and an arbitrary two point method of the fourth order of convergence it is proved that these methods have the convergence order 2 n requiring only n 1 function evaluations per iteration in this way it is demonstrated that the proposed class of methods supports the kung traub hypothesis 1974 on the upper bound 2 n of the order of multipoint methods based on n 1 function evaluations consequently this class possess as high as possible computational efficiency in the sense of the kung traub hypothesis numerical examples are included to demonstrate exceptional convergence speed with only few function evaluations

high order closed newton cotes trigonometrically fitted formulae for the numerical solution of the schrodinger equation abstract in this paper we investigate the connection between closed newton cotes formulae trigonometrically fitted methods symplectic integrators and efficient integration of the schrodinger equation the study of multistep symplectic integrators is very poor although in the last decades several one step symplectic integrators have been produced based on symplectic geometry see the relevant literature and the references here in this paper we study the closed newton cotes formulae and we write them as symplectic multilayer structures based on the closed newton cotes formulae we also develop trigonometrically fitted symplectic methods an error analysis for the one dimensional schrodinger equation of the new developed methods and a comparison with previous developed methods is also given we apply the new symplectic schemes to the well known radial schrodinger equation in order to investigate the efficiency of the proposed method to these type of problems

local global double algebras for slow h sup infinity adaptation ii optimization of stable plants for pt i see ibid vol 36 no 2 p 130 42 1991 the authors presently establish an explicit formula linking global and local sensitivity for systems with stable plants in which local sensitivity is a lipschitz continuous function of data frequency domain estimates of time domain sensitivity norms which become accurate as rates of time variation approach zero are obtained notions of adaptive versus nonadaptive robust control are introduced it is shown that adaptive control can achieve better sensitivity than optimal nonadaptive control it is demonstrated that in general h sup infinity optimal interpolants do not depend lipschitz continuously on data however delta suboptimal interpolants of the aak central maximal entropy type are shown to satisfy a tractable lipschitz condition

design of optimal controllers for spatially invariant systems with finite communication speed we consider the problem of designing optimal distributed controllers whose impulse response has limited propagation speed we introduce a state space framework in which all spatially invariant systems with this property can be characterized after establishing the closure of such systems under linear fractional transformations we formulate the h 2 optimal control problem using the model matching framework we demonstrate that even though the optimal control problem is non convex with respect to some state space design parameters a variety of numerical optimization algorithms can be employed to relax the original problem thereby rendering suboptimal controllers in particular for the case in which every subsystem has scalar input disturbance scalar measurement and scalar actuation signal we investigate the application of the steiglitz mcbride gauss newton and newton iterative schemes to the optimal distributed controller design problem we apply this framework to examples previously considered in the literature to demonstrate that by designing structured controllers with infinite impulse response superior performance can be achieved compared to finite impulse response structured controllers of the same temporal degree

gain scheduling via linear fractional transformations abstract a linear finite dimensional plant with rational state space parameter dependence is controlled using a parameter dependent controller the parameters are known to take on values in a unit ball and are known in real time the goal of control is to stabilize the parameter dependent closed loop system and provide disturbance error attenuation as measured in induced l 2 norms the approach taken uses the optimally scaled small gain theorem and solves the control synthesis problem by reformulating the existence conditions into a finite dimensional convex optimization

an extended numerov type method for the numerical solution of the schrodinger equation abstract a new method which is based on the new property of phase lag for computing eigenvalues of schrodinger equations with potentials is developed in this paper we investigate two cases 1 i the specific case in which the potential v x is an even function with respect to x it is assumed also that the wavefunctions tend to zero for x 2 ii the general case for positive and negative eigenvalues and for the well known cases of the morse potential and of the woods saxon or optical potential numerical and theoretical results show that this new method is more efficient compared with previously derived methods

distributed control of systems over discrete groups this paper discusses distributed controller design and analysis for distributed systems with arbitrary discrete symmetry groups we show how recent results for designing controllers for spatially interconnected systems based on semidefinite programming are applicable to a much larger class of interconnection topologies we also show how to exploit the structure of the symmetry group to produce a hierarchy of decreasingly conservative analysis and synthesis conditions

explicit solutions to separable problems in optimal cooperative control this paper presents explicit state space solutions for a class of networked cooperative control problems we consider the optimal control problem for a class of systems with dynamics defined at the vertices of a directed acyclic graph and dynamic propagation along the edges of the graph the controller is also constrained to use information flowing along the edges of the graph with the additional assumption of transitive closure such problems have linear optimal controllers we show that under the factorization condition that every disturbance non sink takes state feedback these problems separate into several independent subproblems and hence they can be explicitly solved this technique generalizes and unifies several existing approaches for optimal decentralized control and it further provides the optimal controller for many cases in which the optimal control was previously unknown the optimal solutions are expressed in terms of a series of riccati equations whose sizes are bounded by the system order the separated problems highlight the structure of the optimal controller we demonstrate our approach on a salvo guidance problem for a team of networked missiles

a family of trigonometrically fitted partitioned runge kutta symplectic methods abstract we are presenting a family of trigonometrically fitted partitioned runge kutta symplectic methods of fourth order with six stages the solution of the one dimensional time independent schrodinger equation is considered by trigonometrically fitted symplectic integrators the schrodinger equation is first transformed into a hamiltonian canonical equation numerical results are obtained for the one dimensional harmonic oscillator and the exponential potential

on the stability and robust stability of networked dynamic systems some necessary and sufficient conditions are derived for the stability of a networked system with linear time invariant dynamics connections among its subsystems are fixed but arbitrary and every subsystem can have different dynamics based on these results some necessary or sufficient conditions are further obtained for both its stability and robust stability which essentially depend only on parameter matrices of each individual subsystem and the subsystem connection matrix this characteristic makes them attractive in the analysis and synthesis of a large scale networked system

a new method for the numerical solution of fourth order bvp s with oscillating solutions abstract a new finite difference scheme with minimal phase lag for the numerical solution of fourth order differential equations is developed in this paper numerical and theoretical results show that this new approach is more efficient compared with previously derived methods

a family of optimal three point methods for solving nonlinear equations using two parametric functions abstract using an interactive approach which combines symbolic computation and taylor s series a wide family of three point iterative methods for solving nonlinear equations is constructed these methods use two suitable parametric functions at the second and third step and reach the eighth order of convergence consuming only four function evaluations per iteration this means that the proposed family supports the kung traub hypothesis 1974 on the upper bound 2 m of the order of multipoint methods based on m 1 function evaluations providing very high computational efficiency different methods are obtained by taking specific parametric functions the presented numerical examples demonstrate exceptional convergence speed with only few function evaluations

optimal rejection of persistent and bounded disturbances continuity properties and adaptation continuity properties of the problem of optimal rejection of bounded persistent disturbances otherwise known as l sup 1 optimal control are furnished for discrete time single input single output systems it is shown that for any plant with no zeros on the unit circle the l sup 1 optimal design is continuous as a map from the plant to the optimal closed loop solution if the plant has a unique optimal solution in the case of nonuniqueness a superoptimal criterion is proposed that will always lead to a unique solution however it still fails to supply continuity a characterization of a general class of adaptive controllers in the presence of bounded disturbances is given using this characterization an adaptive robust scheme based on the l sup 1 design methodology is proposed and it is shown to be globally convergent

consensus of multiple nonholonomic chained form systems abstract consensus problems of multiple nonholonomic systems are considered in this paper this problem is simplified into consensus problems of two subsystems based on the cascaded structure of nonholonomic chained form systems continuous and hybrid distributed controllers have been constructed for these two subsystems respectively based on the theory of cascaded systems consensus of multiple nonholonomic chained form systems can be realized using the methodology proposed in this paper no matter whether the group reference signal is persistently exciting or not different to previous assumptions on group reference such as persistent excitation or converging to nonzero constant the condition on the group reference signal have been further relaxed in this paper simulation results using matlab have illustrated the effectiveness of the results presented in this paper

bibo stability robustness in the presence of coprime factor perturbations a necessary and sufficient condition for robustly stabilizing a family of plants described by perturbations of fixed coprime factors of a plant is given the computation of the largest stability margin is discussed via solving a nonsquare l sup 1 optimal control problem an algorithm for obtaining lower approximations of the minimum value of the optimization problem mu sub 0 is proposed this together with the standard algorithm which provides upper approximations allows mu sub 0 to be computed within any degree of accuracy

extension of parrott s theorem to nondefinite scalings in this paper the matrix version of parrott s theorem is extended to encompass nondefinite scalings this extension can be used to relax the causality requirements for many linear matrix inequality based synthesis problems

supervisory control of uncertain linear time varying systems we consider the problem of adaptively stabilizing linear plants with unknown time varying parameters in the presence of noise disturbances and unmodeled dynamics using the supervisory control framework which employs multiple candidate controllers and an estimator based switching logic to select the active controller at every instant of time time varying uncertain linear plants can be stabilized by supervisory control provided that the plant s parameter varies slowly enough in terms of mixed dwell time switching and average dwell time switching the noise and disturbances are bounded and small enough in terms of l infinity norms and the unmodeled dynamics are small enough in the input to state stability sense this work extends previously reported works on supervisory control of linear time invariant systems with constant unknown parameters to the case of linear time varying uncertain systems a numerical example is included and limitations of the approach are discussed

control of heterogeneous groups of systems interconnected through directed and switching topologies this note presents a technique to synthesize distributed controllers for the control of heterogeneous systems interconnected through switching directed interaction topologies groups of subsystems are defined with undirected interaction within but directed interconnections between each other this allows to construct a virtual symmetric interconnection matrix representation of the graph topology the symmetry guarantees the existence of a diagonalizing transformation which renders both analysis and synthesis problems particularly simple structural constraints on multipliers are used to reduce the complexity of the resulting coupled matrix inequalities to be of the order of a single subsystem times the number of groups the problem can then be essentially solved by linear fractional transformation lft based linear parameter varying lpv gain scheduling synthesis methods in which the possibly time varying eigenvalues of the interconnection matrix act as the scheduling variables of the transformed problem

a higher accuracy finite difference method for an elliptic equation of order four the elliptic equation 1 with boundary value conditions either 2 or 3 is solved by an o h4 convergent finite difference method combined with an implicit iterative method the method is tested by examples of boundary value problems with use of the enclosed mathematica module solve bhpeq the module solve bhpeq gives options either it implements the o h4 convergent nine mesh points scheme or the o h2 convergent standard five points scheme when the finite difference approximation of eq 1 is considered

a new family of eighth order iterative methods for solving nonlinear equations a family of eighth order iterative methods with four evaluations for the solution of nonlinear equations is presented kung and traub conjectured that an iteration method without memory based on n evaluations could achieve optimal convergence order 2 n 1 the new family of eighth order methods agrees with the conjecture of kung traub for the case n 4 therefore this family of methods has efficiency index equal to 1 682 numerical comparisons are made with several other existing methods to show the performance of the presented methods

runge kutta interpolants with minimal phase lag abstract we develop the basic theory for the construction of explicit scaled runge kutta methods srk for the integration of first order differential equations having an oscillatory solution based on this theory and on the theory of runge kutta methods with minimal phase lag we construct an embedded runge kutta 10 12 method and an explicit scaled runge kutta method numerical results indicate the efficiency of the new algorithms

robust adaptive control a slowly varying systems approach in this paper we characterize a class of indirect adaptive controllers that can stabilize a time invariant system subjected to both parametric and l to l bounded unstructured uncertainty pertaining to this class of controllers a particular indirect adaptive scheme is proposed and an a priori computable upper bound on the size of the unstructured uncertainty for which stability is ensured is provided

adaptive control of spatially invariant systems a slowly varying approach we present a general class of adaptive controllers for spatially invariant systems based on certainty equivalence approach at each step the plant is estimated via the distributed projection algorithm as presented in sarwar that guarantees to result in a gradually varying spatiotemporal estimated plant for large enough time given an instance in space and time the estimated plant is thought of as a linear spatially invariant system with the defining operators fixed at that time and space instance the spatiotemporal local controllers assumed to exist are designed to stabilize the corresponding frozen linear spatially invariant systems we show that as long as the rates of spatiotemporal variations of the estimated plant and the spatiotemporal controller eventually become sufficiently small a globally stable adaptive scheme can be guaranteed

design issues in adaptive control an integrated approach to the design of practical adaptive control algorithms is presented many existing ideas are brought together and the effect of various design parameters available to a user is explored the theory is extended by showing how the problem of stabilizability of the estimated model can be overcome by running parallel estimators it is shown how asymptotic tracking of deterministic set points can be achieved in the presence of unmodeled dynamics

identification of spatiotemporally invariant systems for control adaptation we present a distributed projection algorithm for system identification of spatiotemporally invariant systems with the ultimate purpose of utilizing it in an indirect adaptive control scheme each subsystem communicates only with its immediate neighbors to share its current estimate along with a cumulative improvement index on the basis of the cumulative improvement index the best estimate available is picked in order to carry out the next iteration for small estimation error the scheme switches over to a smart averaging routine the proposed algorithm guarantees to bring the local estimates arbitrarily close to one another developing a local consensus which makes it amenable to control by the application of indirect distributed adaptive control schemes it is also shown through simulations that the proposed algorithm has a clear advantage over the standard projection algorithm our proposed algorithm is also suitable for addressing the estimation problem in distributed networks that arise in a variety of applications such as environment monitoring target localization and potential sensor network problems

the complex structured singular value a tutorial introduction to the complex structured singular value is presented with an emphasis on the mathematical aspects of the based methods discussed here have been useful for analysing the performance and robustness properties of linear feedback systems several tests for robust stability and performance with computable bounds for transfer functions and their state space realizations are compared and a simple synthesis problem is studied uncertain systems are represented using linear fractional transformations lfts which naturally unify the frequency domain and state space methods

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

decomposition based distributed control for continuous time multi agent systems in this technical note we consider the problem of designing distributed controller for a continuous time system composed of a number of identical dynamically coupled subsystems the underlying mathematical derivation is based on kronecker product and a special similarity transformation constructed from interconnection pattern matrix that decomposes the system into modal subsystems this along with the result of extended linear matrix inequality lmi formulation for continuous time systems makes it possible to derive explicit expressions for computing the parameters of distributed controllers for both static state feedback and dynamic output feedback cases the main contribution of the technical note is the solution of distributed control problem for continuous time systems under h stability and h2 stability performances by solving a set of lmis with noncommon lyapunov variables the effectiveness of this method is demonstrated by means of a satellite formation example

semistability theory for spatially distributed systems abstract the concepts of semistability and exponential semistability are well developed for finite dimensional systems with nonisolated equilibrium points where asymptotic or exponential stability is not possible definitions of semistability and exponential semistability have recently been formulated for networks with time delays this paper further extends the semistability theory to continuous and discrete spatially distributed systems this requires the definition of the notions of exact and approximate semicontrollability and semiobservability and discrete approximate semicontrollability and semiobservability also introduced is the property of weak semistability necessary and sufficient conditions are given for exponential semistability and weak semistability and sufficient conditions are given for semistability

static output feedback stabilization of interconnected systems abstract this paper is concerned with the celebrated static output feedback control problem sofp subject to linear constraints on control input k e g bounds on control magnitude zeros in some elements of k etc these constraints typically arise in the control of resource limited systems interconnected to each other where the local control for each system makes use of its own and neighboring systems outputs only and its magnitude is bounded this control problem can be approached by a spectral norm minimization technique q snm whose preliminary version was previously introduced with little mathematical justification but shown to be promising for the regular sofp without control constraints this paper mathematically justifies q snm by showing its explicit relationship with spectral radius and extends q snm to accommodate various linear control constraints this paper also discusses the practical application of q snm to vehicle formation control which demonstrates the merit of q snm

distributed lpv state feedback control under control input saturation developed in this note is a scheduled state feedback controller synthesis method for discrete time linear parameter varying lpv systems subjected to control input saturation constraints the static state feedback gain is scheduled with an exact replica of the parameter matrix the saturation effect is modeled by introducing time varying parameters as functions of the control inputs which are also used to schedule the controller the synthesis method is then specialized to distributed state feedback by imposing a particular structure on the feedback gain matrix an explicit formula is also derived for the computation of the distributed control input from a nonlinear equation the viability of the proposed method is tested in a simulation environment for a ramp meter traffic flow control problem

three step iterative methods with eighth order convergence for solving nonlinear equations a family of eighth order iterative methods for the solution of nonlinear equations is presented the new family of eighth order methods is based on king s fourth order methods and the family of sixth order iteration methods developed by chun et al per iteration the new methods require three evaluations of the function and one evaluation of its first derivative therefore this family of methods has the efficiency index which equals 1 682 kung and traub conjectured that a multipoint iteration without memory based on n evaluations could achieve optimal convergence order 2 n 1 thus we provide a new example which agrees with the conjecture of kung traub for n 4 numerical comparisons are made to show the performance of the presented methods

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

distributed control design for spatially interconnected systems this paper deals with analysis synthesis and implementation of distributed controllers designed for spatially interconnected systems we develop a state space framework for posing problems of this type and focus on systems whose model is spatially discrete in this paper analysis and synthesis results are developed for this class of systems using the l sub 2 induced norm as the performance criterion the results are stated in terms of linear matrix inequalities and are thus readily amenable to computation a special implementation of the resulting controllers is presented which is particularly attractive for distributed operation of the controller several examples are provided to further illustrate the application of the results

eighth order methods with high efficiency index for solving nonlinear equations in this paper we derive a new family of eighth order methods for solving simple roots of nonlinear equations by using weight function methods per iteration these methods require three evaluations of the function and one evaluation of its first derivative which implies that the efficiency indexes are 1 682 numerical comparisons are made to show the performance of the derived methods as shown in the illustration examples

a convex characterization of gain scheduled h sub spl infin controllers an important class of linear time varying systems consists of plants where the state space matrices are fixed functions of some time varying physical parameters spl theta small gain techniques can be applied to such systems to derive robust time invariant controllers yet this approach is often overly conservative when the parameters spl theta undergo large variations during system operation in general higher performance can be achieved by control laws that incorporate available measurements of spl theta and therefore adjust to the current plant dynamics this paper discusses extensions of h sub spl infin synthesis techniques to allow for controller dependence on time varying but measured parameters when this dependence is linear fractional the existence of such gain scheduled h sub spl infin controllers is fully characterized in terms of linear matrix inequalities the underlying synthesis problem is therefore a convex program for which efficient optimization techniques are available the formalism and derivation techniques developed here apply to both the continuous and discrete time problems existence conditions for robust time invariant controllers are recovered as a special case and extensions to gain scheduling in the face of parametric uncertainty are discussed in particular simple heuristics are proposed to compute such controllers

boundedness of multidimensional filters over a prescribed frequency domain signal processing often requires the magnitude of a filter simultaneously upper and lower bounded on some specified frequency domains in this paper on the basis of the structure of the span of a multivariate matrix polynomial a sufficient condition is derived for the boundedness of a multidimensional multiple input multiple output mimo infinite impulse response iir filter over a cuboid frequency domain this condition is expressed through a linear matrix inequality lmi and can be proved to be less conservative than a condition derived from an upper bound of matrix structured singular value moreover using parameter dependent lmis and the linear fractional transformation structure of the filter two necessary and sufficient conditions are also obtained for this boundedness verification problem which are again expressed by lmis furthermore lmi based conditions are derived for filter output matrix and direct transmission matrix which are applicable to filter design numerical examples are included to illustrate the efficiency and characteristics of the derived theoretical results

three step iterative methods with optimal eighth order convergence in this paper based on ostrowski s method a new family of eighth order methods for solving nonlinear equations is derived in terms of computational cost each iteration of these methods requires three evaluations of the function and one evaluation of its first derivative so that their efficiency indices are 1 682 which is optimal according to kung and traub s conjecture numerical comparisons are made to show the performance of the new family

coordinated one step optimal distributed state prediction for a networked dynamical system a new recursive one step state prediction procedure is derived for a networked dynamic system under the coordination of a collaboration unit that provides optimal update gains for each individual subsystem utilizing merely system parameters this predictor estimates plant s local states based only on local system output measurements this estimator can be easily realized in a distributed way and can also be simply scaled to systems with a large amount of subsystems provided it has enough communication and storage capacities it is proved that when prediction error variances are adopted in performance comparisons the optimal gain matrix is usually unique recursive and explicit expressions are derived for both this optimal gain matrix and the covariance matrix of the corresponding prediction errors the optimal gain matrix for every subsystem in this distributed recursive predictor has been shown to be equal to that of the well known kalman filter utilizing only local system output measurements which makes it possible to robustify this state predictor using a sensitivity penalization approach numerical simulation results illustrate that prediction accuracy of the suggested procedure may sometimes be as good as that of the lumped kalman filter

edge agreement graph theoretic performance bounds and passivity analysis this work explores the properties of the edge variant of the graph laplacian in the context of the edge agreement problem we show that the edge laplacian and its corresponding agreement protocol provides a useful perspective on the well known node agreement or the consensus algorithm specifically the dynamics induced by the edge laplacian facilitates a better understanding of the role of certain subgraphs e g cycles and spanning trees in the original agreement problem using the edge laplacian we proceed to examine graph theoretic characterizations of the h2 and h performance for the agreement protocol these results are subsequently applied in the contexts of optimal sensor placement for consensus based applications finally the edge laplacian is employed to provide new insights into the nonlinear extension of linear agreement to agents with passive dynamics