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

self adjoint differential equations for classical orthogonal polynomials this paper deals with spectral type differential equations of the self adjoint differential operator 2r order l 2r y x 1 x dr dxr x r x dry x dxr rny x if x is the weight function and x is a second degree polynomial function then the corresponding classical orthogonal polynomials qn x n 0 are shown to satisfy this differential equation when rn is given by rn r 1k 0 n k 1 n k 1 2 where 1 and 2 are the leading coefficients of the two polynomial functions associated with the classical orthogonal polynomials moreover the singular eigenvalue problem associated with this differential equation is shown to have qn x and rn as eigenfunctions and eigenvalues respectively any linear combination of such self adjoint operators has qn x as eigenfunctions and the corresponding linear combination of rn as eigenvalues

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

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

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

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

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

e structure for q r maclane homology of a ringr is the hochschild homology of the so called cubical construction q r which is a chain algebra if we take a commutative ring r the dixmier product onq r is no longer commutative the main result of this paper is that it is commutative up to higher homotopies i e that it is an e1 algebra the e1 operad which acts onq r is constructed by using the analogue of theq complex in the context of finite sets for the precise notation of an operad action on these complexes the definition of an e1 monoidal functor is introduced

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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