almost invariant subspaces an approach to high gain feedback design part ii almost conditionally invariant subspaces in part i of this paper almost controlled invariant subspaces were studied in this part we will consider their duals the almost conditionally invariant subspaces these concepts give immediately by dualization of the almost disturbance decoupling control by state feedback the solution of the almost disturbance decoupled estimation problem finally we consider the problem of approximate disturbance decoupling by measurement feedback and it is shown that this problem is solvable to any arbitrary degree of accuracy if and only if 1 almost disturbance decoupling by state feedback and 2 almost disturbance decoupled estimation of the to be controlled output are both possible

generating directional residuals with dynamic parity relations abstract it is shown how diagnostic residuals which exhibit directional properties at all times in response to an arbitrary mix of input and output faults can be generated using dynamic parity relations the parity relations are applied directly to the observables of the monitored plant the design relies on the plant s dynamic input output model this residual generator can be made computationally polynomial moving average by including the invariant zero polynomial of the fault system in the specified fault responses the polynomial design yields moving average noise transfers as well white noise transfer and disturbance decoupling are achieved by extending the response specification the parity relation approach is compared with the traditional detection filter design and is shown to be more straightforward and have milder existence conditions if subjected to the same specification the two approaches yield identical residual generators

invariant subspaces for lpv systems and their applications the aim of this paper is to extend the notion of invariant subspaces known in the geometric control theory of the linear time invariant systems to the linear parameter varying lpv systems by introducing the concept of parameter varying invariant subspaces for lpv systems affine in their parameters algorithms are given to compute many parameter varying subspaces relevant in the solution of state feedback and observer design problems

brief paper leader following consensus of second order agents with multiple time varying delays in this paper a leader following consensus problem of second order multi agent systems with fixed and switching topologies as well as non uniform time varying delays is considered for the case of fixed topology a necessary and sufficient condition is obtained for the case of switching topology a sufficient condition is obtained under the assumption that the total period over which the leader is globally reachable is sufficiently large we not only prove that a consensus is reachable asymptotically but also give an estimation of the convergence rate an example with simulation is presented to illustrate the theoretical results

a descriptor approach to robust leader following output consensus of uncertain multi agent systems with delay in this technical note a descriptor approach to leader following output consensus of multi agent systems with both stationary and dynamic leaders is given in the presence of transmission delay and model uncertainty the proposed method can deal with stable and unstable agents described by general linear models to this end a new proportional derivative integral pid consensus protocol for the closed loop multi agent system is proposed under a directed graph applying this consensus protocol to the multi agent system leads to a time delay closed loop equation of neutral type to deal with the resulting neutral system a descriptor model transformation is used to derive delay dependent sufficient conditions for the existence of the consensus protocol in terms of certain linear matrix inequalities lmi the application of the proposed method is illustrated in a teleoperation system simulation results are given to show the effectiveness of the proposed approach

variational approach and euler s integrating factors for environmental studies abstract we are promoting the use of variational principles as some generalizing idea that allows us to create consistent approximations of mathematical models in this paper we formulate a computing technology to solve direct and inverse problems of atmospheric dynamics and chemistry for the implementation we use functional decomposition methods splitting techniques and integrating factors designed as the solutions of some adjoint problems one of the main purposes of the paper is to relate the theory of approximation with the concept of eulerian integrating factors that plays the fundamental role in the theory of differential equations we demonstrate the utility and versatility of the concept applying it to solve the systems of differential equations of convection diffusion with dominant convection and stiff systems of kinetic equations to identify the prospects of our approach we briefly introduce how to use integrating factors in the case of unstructured grids

detection filter design spectral theory and algorithms a new formulation of the detection filter problem is generated by assignment of the closed loop eigenstructure under certain constraints detection filters which are actually a specific class of observers fix the output error direction of the system so that it can be associated with a particular failure mode and its known design failure direction the derivation of detection filters from an eigensystem assignment approach permits a very transparent theory the detection filter gains and closed loop eigenvectors are obtained from a set of simultaneous equations necessary and sufficient conditions for the solution of these algebraic equations are determined which produce a complete theory for detection filters

a geometric approach to the synthesis of failure detection filters a geometric formulation of beard s failure detection filter problem is stated using the concepts of c a invariant and unobservability subspaces the notions of output separable and mutually detectable families of subspaces introduced by beard are also clarified it is shown that mutual detectability is a necessary and sufficient condition for the existence of a detection filter with arbitrarily assignable spectrum moreover it is shown that the failure detection falter problem has a computationally simple solution when the failure events satisfy some mild restrictions finally the complete duality between a generalization of beard s detection filter problem and the restricted control decoupling problem is illustrated

distributed containment control with multiple stationary or dynamic leaders in fixed and switching directed networks in this paper we study the problem of distributed containment control of a group of mobile autonomous agents with multiple stationary or dynamic leaders under both fixed and switching directed network topologies first when the leaders are stationary and all followers share an inertial coordinate frame we present necessary and sufficient conditions on the fixed or switching directed network topology such that all followers will ultimately converge to the stationary convex hull formed by the stationary leaders for arbitrary initial states in a space of any finite dimension when the directed network topology is fixed we partition the nonsymmetric laplacian matrix and explore its properties to derive the convergence results when the directed network topology is switching the commonly adopted decoupling technique based on the kronecker product in a high dimensional space can no longer be applied and we hence present an important coordinate transformation technique to derive the convergence results the proposed coordinate transformation technique also has potential applications in other high dimensional distributed control scenarios and might be used to simplify the analysis of a high dimensional system to that of a one dimensional system when the decoupling technique based on the kronecker product cannot be applied second when the leaders are dynamic and all followers share an inertial coordinate frame we propose a distributed tracking control algorithm without velocity measurements when the directed network topology is fixed we derive conditions on the network topology and the control gain to guarantee that all followers will ultimately converge to the dynamic convex hull formed by the dynamic leaders for arbitrary initial states in a space of any finite dimension when the directed network topology is switching we derive conditions on the network topology and the control gain such that all followers will ultimately converge to the minimal hyperrectangle that contains the dynamic leaders and each of its hyperplanes is normal to one axis of the inertial coordinate frame in any high dimensional space we also show via some counterexamples that it is in general impossible to find distribute containment control algorithms without velocity measurements to guarantee that all followers will ultimately converge to the convex hull formed by the dynamic leaders under a switching network topology in a high dimensional space simulation results are presented as a proof of concept

containment control of leader following multi agent systems with markovian switching network topologies and measurement noises this paper investigates the distributed containment tracking control problem for first order agents with multiple dynamic leaders under directed markovian switching network topologies the control input of each agent can only use its local state and the states of its neighbors corrupted by white noises firstly when the dynamic leaders velocities have some special forms which include the stationary leaders as a special case some necessary and sufficient conditions are presented for the containment tracking in the asymptotic unbiased mean square sense secondly for more general leaders velocities necessary and sufficient conditions are provided for the containment tracking with bounded errors in the mean square sense finally a simulation example is given to illustrate the performance of the proposed control scheme

inversion based residual generation for robust detection and isolation of faults by means of estimation of the inverse dynamics in linear dynamical systems in this article the idea of inversion based direct input reconstruction for robust detection separation and estimation of multiple simultaneous faults in the presence of persistent disturbances which proved to be non separable by conventional decoupling methods in linear dynamical systems is presented in particular it is shown how in a specific filtering structure a residual generator relying on the inverse representation of the system by means of estimation of the inverse dynamics can be designed providing robust fault decoupling in the development of the method three solution approaches are contrasted with each other in the first approach the traditional h filter providing the classical disturbance attenuated non decoupling solution is presented then in a novel solution an h detection filter on the inverse system is designed providing detection residuals by exact fault decoupling the estimation of the inverse dynamics is obtained by means of the optimal filter thus ensuring h disturban

flocking of multi agent systems with multiple groups in this paper we consider the flocking problem of multi agent systems with multiple groups first some algorithms using local information are designed to divide the agents into any pre assigned number of groups in fixed and switching heterogeneous networks respectively based on algebraic graph theory and barbalat s lemma convergence criteria are established to ensure velocity alignment and cohesion of each subgroup as well as collision avoidance between any agents in the whole group second an algorithm for homogeneous networks is studied simulation examples are finally presented to verify the effectiveness of our theoretical results

a time domain approach to robust fault detection of linear time varying systems this paper gives the optimal solutions to several robust fault detection problems such as 2 and problems for linear time varying systems in a time domain which extends the previous results on linear time invariant systems in a frequency domain it is shown that all three problems have the same optimal detection filter and the filter is a simple observer obtained by solving a standard differential riccati equation finally an example is given to illustrate our results

containment control for second order multi agent systems with time varying delays abstract this paper considers the containment control problem for second order multi agent systems with time varying delays both the containment control problem with multiple stationary leaders and the problem with multiple dynamic leaders are investigated sufficient conditions on the communication digraph the feedback gains and the allowed upper bound of the delays to ensure containment control are given in the case that the leaders are stationary the lyapunov razumikhin function method is used in the case that the leaders are dynamic the lyapunov krasovskii functional method and the linear matrix inequality lmi method are jointly used a novel discretized lyapunov functional method is introduced to utilize the upper bound of the derivative of the delays no matter how large it is which leads to a better result on the allowed upper bound of the delays to ensure containment control finally numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results

event based leader following consensus of multi agent systems with input time delay the event based control strategy is an effective methodology for tackling the distributed control of multi agent systems with limited on board resources this technical note focuses on event based leader following consensus for multi agent systems described by general linear models and subject to input time delay between controller and actuator for each agent the controller updates are event based and only triggered at its own event times a necessary condition and two sufficient conditions on leader following consensus are presented respectively it is shown that continuous communication between neighboring agents can be avoided and the zeno behavior of triggering time sequences is excluded a numerical example is presented to illustrate the effectiveness of the obtained theoretical results

solution of the static state feedback decoupling problem for linear systems with two outputs we give for linear systems with two outputs a necessary and sufficient condition for the solvability of the restricted decoupling problem rdp in terms of some structural invariants a geometric characterization is also given which provides the least dynamical extension needed when rdp is not solvable

observer based fault detection and isolation filter design for linear time invariant systems in this paper we consider a model based fault detection and isolation problem for linear time invariant dynamic systems subject to faults and disturbances we use a state observer scheme that cancels the system dynamics and defines a residual vector signal that is sensitive only to faults and disturbances we then design a stable fault detection and isolation filter such that the norm of the transfer matrix function from disturbances to the residual is minimised for fault detection subject to the constraint that the transfer matrix function from faults to residual is equal to a pre assigned diagonal transfer matrix for isolation of possibly simultaneous occurring faults our solution is given in the form of linear matrix inequalities using state space techniques as well as a model matching problem using matrix factorisation techniques a numerical example is given to illustrate the efficiency of the fault detection and isolation filter

the role of the dissipation matrix in singular optimal control the optimal cost in the regular stationary linear quadratic optimal control problem is given by the maximal solution of an algebraic riccati equation this solution minimizes the rank of a certain matrix which we call the dissipation matrix the rank minimization problem is also meaningful in the singular case does it provide the optimal cost for the singular control problem this question was posed by j c willems in 1971 the answer is yes

leader following consensus of multi agent systems under fixed and switching topologies the leader following consensus problem of higher order multi agent systems is considered in the system the dynamics of each agent and the leader is a linear system the control of each agent using local information is designed and detailed analysis of the leader following consensus is presented for both fixed and switching interaction topologies which describe the information exchange between the multi agent systems the design technique is based on algebraic graph theory riccati inequality and lyapunov inequality simulations indicate the capabilities of the algorithms

decoupling by restricted static state feedback the general case in this paper we tackle the general block decoupling problem for linear constant dynamical systems c a b with m inputs and p outputs with restricted static state feedback in other words with control laws of type u gfx gv we give a necessary and sufficient condition of existence for such laws which generalizes the one previously given in 2 for the simple case k p leq m where k denotes the number of blocks to be decoupled

a game theoretic approach to a finite time disturbance attenuation problem a disturbance attenuation problem over a finite time interval is considered by a game theoretic approach where the control restricted to a function of the measurement history plays against adversaries composed of the process and measurement disturbances and the initial state a zero sum game formulated as a quadratic cost criterion subject to linear time varying dynamics and measurements is solved by a calculus of variation technique by first maximizing the quadratic cost criterion with respect to the process disturbance and initial state a full information game between the control and the measurement residual subject to the estimator dynamics results the resulting solution produces an n dimensional compensator which expresses the controller as a linear combination of the measurement history a disturbance attenuation problem is solved based on the results of the game problem for time invariant systems it is shown that under certain conditions the time varying controller becomes time invariant on the infinite time interval the resulting controller satisfies an h sub infinity norm bound

observer based residual generation for fault diagnosis for non affine non linear polynomial systems this paper proposes an observer based residual generator obrg for diagnosing faults in a continuous non affine system with polynomial non linearities up to any finite degree where the fault and an unknown input affect both the system and part of the output firstly given certain assumptions and the use of defined extended vectors a parameterized polynomial system is considerred for which a compact set of sufficient conditions is given for the existence of a candidate obrg conditions for error stability by a lyapunov method and detectability are given the calculation steps in the design of the obrg are shown to involve the solution of three linear equations with parameterizations and the calculation of a set of constant matrices for detectability of faults a result is then given establishing that the design holds for a much wider class of systems the residual design is applied to a real three tank system

eigenfactor solution of the matrix riccati equation a continuous square root algorithm this paper introduces a new algorithm for solving the matrix riccati equation differential equations for the eigenvalues and eigenvectors of the solution matrix are developed in which their derivatives are expressed in terms of the eigenvalues and eigenvectors themselves and not as functions of the solution matrix the solution of these equations yields then the time behavior of the eigenvalues and eigenvectors of the solution matrix a reconstruction of the matrix itself at any desired time is immediately obtained through a trivial similarity transformation this algorithm serves two purposes first being a square root solution it entails all the advantages of square root algorithms such as nonnegative definiteness and accuracy secondly it furnishes the eigenvalues and eigenvectors of the solution matrix continuously without resorting to the complicated route of solving the equation directly and then decomposing the solution matrix into its eigenvalues and eigenvectors the algorithm which handles cases of distinct as well as multiple eigenvalues is tested on several examples through these examples it is seen that the algorithm is indeed more accurate than the ordinary one moreover it is seen that the algorithm works in cases where the ordinary algorithm fails and even in cases where the closed form solution cannot be computed as a result of numerical difficulties

enhancement of robustness in observer based fault detection a prerequisite for the feasibility of the technique of observer based fault detection and isolation fdi in dynamic systems is a satisfactory robustness with respect to modelling uncertainties this paper surveys the most relevant methods to increase the robustness in both the stage of residual generation and residual evaluation among these methods are the generalized observer scheme the robust parity space check the unknown input and h observer scheme the decorrelation filter and the concept of adaptive threshold selection it is pointed out that the unknown input observer concept which provides perfect decoupling from the modelling errors or its optimal approximation with the aid of h techniques constitutes a general framework of robust residual generation that generalizes and unifies numerous other approaches among them the parity space and detection filter approach it is further shown that this fdi method can even be applied to a certain class of nonlinear systems

a geometric approach to nonlinear fault detection and isolation we present a differential geometric approach to the problem of fault detection and isolation for nonlinear systems a necessary condition for the problem to be solvable is derived in terms of an unobservability distribution which is computable by means of suitable algorithms the existence and regularity of such a distribution implies the existence of changes of coordinates in the state and in the output space which induce an observable quotient subsystem unaffected by all fault signals but one for this subsystem a fault detection filter is designed

a game theoretic fault detection filter the fault detection process is approximated with a disturbance attenuation problem the solution to this problem for both linear time varying and time invariant systems leads to a game theoretic filter which bounds the transmission of all exogenous signals except the fault to be detected in the limit when the disturbance attenuation bound is brought to zero a complete transmission block is achieved by embedding the nuisance inputs into an unobservable invariant subspace since this is the same invariant subspace structure seen in some types of detection filters we can claim that the asymptotic game filter is itself a detection filter one can also make use of this subspace structure to reduce the order of the limiting game theoretic filter by factoring this invariant subspace out of the state space the resulting lower dimensional filter will then be sensitive only to the failure to be detected a pair of examples given at the end of the paper demonstrate the effectiveness of the filter for time invariant and time varying problems in both full order and reduced order forms

fault detection in a mixed h sub 2 h sub spl infin setting in this note we study the problem of fault detection in linear time invariant lti systems which are simultaneously effected by two classes of unknown inputs noises having fixed spectral densities and unknown finite energy disturbances this problem is formulated as a mixed h sub 2 h sub spl infin filtering problem necessary and sufficient conditions for local optimality are presented moreover it is shown that suboptimal solutions can be computed by solving a convex minimization problem with a set of linear matrix inequality lmi constrains a numerical example is given to illustrate the advantage of the mixed h sub 2 h sub spl infin approach as compared to existing techniques which are based on optimization of h sub 2 and h sub spl infin criteria

delay dependent robust stabilization of uncertain state delayed systems this paper concerns a problem of robust stabilization of uncertain state delayed systems a new delay dependent stabilization condition using a memoryless controller is formulated in terms of matrix inequalities an algorithm involving convex optimization is proposed to design a controller guaranteeing a suboptimal maximal delay such that the system can be stabilized for all admissible uncertainties

optimal stochastic fault detection filter a fault detection and identification algorithm called optimal stochastic fault detection filter is determined the objective of the filter is to detect a single fault called the target fault and block other faults called the nuisance faults in the presence of the process and sensor noises the filter is derived by maximizing the transmission from the target fault to the projected output error while minimizing the transmission from the nuisance faults therefore the residual is affected primarily by the target fault and minimally by the nuisance faults the transmission from the process and sensor noises is also minimized so that the filter is robust with respect to these disturbances it is shown that the filter recovers the geometric structure of the unknown input observer in the limit where the weighting on the nuisance fault transmission goes to infinity further the asymptotic behavior of the filter near the limit is determined by using a perturbation method filter designs can be obtained for both time invariant and time varying systems

the generalized eigenstructure problem in linear system theory the algebraic theory of linear time invariant systems has been studied in large detail during the past few decades and numerous computational algorithms have been developed to solve problems arising in this context in this paper the numerical aspects of a certain class of such algorithms dealing with what the author calls generalized eigenstructure problems are discussed some new and or modified algorithms are presented both the nmnerical stability of the algorithms and the conditioning of the problems they solve are analyzed using numerical criteria

on the approximation of fault directions for mutual detectability an invariant zero approach this note is concerned with the approximation of fault directions in relation to mutual detectability in detection filter problems as an efficient system representation for analysis of detection order we utilize the observer canonical form by which we show that the invariant zero and the detection order can be analytically calculated by a set of polynomials associated with fault directions noting that this approach clearly shows the condition for the detection order to be plural we propose a fault direction approximation method which increases its detection order for obtaining a mutually detectable system regarding the resulting degradation of fault isolation performance as a disturbance we present its quantitative analysis and propose a method of selecting a threshold in order to guarantee proper fault isolation

discrete analytical methods for the implementation of variational principles in environmental applications a new method of constructing numerical schemes on the base of a variational principle for models including convection diffusion operators is proposed an original element is the use of analytical solutions of local adjoint problems formulated for the operators of convection diffusion within the framework of the splitting technique this results in numerical schemes which are absolutely stable monotonic transportive and differentiable with respect to the state functions and parameters of the model artificial numerical diffusion is avoided due to the analytical solutions the variational technique provides strong consistency between the numerical schemes of the main and adjoint problems a theoretical study of the new class of schemes is given the quality of the numerical approximations is demonstrated by an example of the non linear burgers equation these new schemes enhance our variational methodology of environmental modelling as one of the environmental applications an inverse problem of risk assessment for lake baikal is presented

an analysis of a uniformly accurate difference method for a singular perturbation problem it will be proven that an exponential tridiagonal difference scheme when applied with a uniform mesh of size h to euxx b x ux f x for o o b and f smooth e in 0 1 and u o and u i given is uniformly second order accurate i e the maximum of the errors at the grid points is bounded by ch2 with the constant c independent of h and e this scheme was derived by el mistikawy and werle by a c patching of a pair of piecewise constant coefficient approximate differential equations across a common grid point the behavior of the approximate solution in between the grid points will be analyzed and some numerical results will also be given

a controller degree bound for h 0e control problems of the second kind this paper is a continuation of our work on mathcal h infty optimal control problems which may be embedded in the linear fractional configuration of fig 1 in two previous articles 19 20 a controller degree bound was established for problems in which both p 12 s and p 21 s are square problems of the first kind if the mcmillan degree of p s is n it was shown that there exist mathcal h infty optimal controllers with mcmillan degree no greater than n 1 here we switch our attention to problems of the second kind that is we allow p 12 s to have more rows than columns with p 21 s square or alternatively we allow p 21 s to have more columns than rows with p 12 s square our main result shows that the degree bound derived previously for problems of the first kind carries over to problems of the second kind without change in addition to the controller degree bound our analysis suggests a number of modifications which are easily made to cur

brief generic solvability of the failure detection and identification problem necessary and sufficient conditions for the generic solvability of the extended fundamental problem in residual generation efprg massoumnia et al 1989 ieee trans automat control 34 316 321 in the case of simultaneous actuator and sensor failures are presented in the process of deriving these conditions the generic forms of supremal controllability and infimal unobservability subspaces of lti systems having diagonal state space matrices are obtained

failure detection and identification using the geometric concept of an unobservability subspace a solution is given to the problem of detecting and identifying control system component failures in linear time invariant systems conditions are developed for the existence of a causal linear time invariant processor that can detect and uniquely identify a component failure first for the case where components can fail simultaneously and then for the case where they fail only one at a time explicit design algorithms are provided when these conditions are satisfied in addition to time domain solvability conditions frequency domain interpretations of the results are given and connections are drawn with results already available in the literature