survey paper static output feedback a survey this paper reviews the static output feedback problem in the control of linear time invariant lti systems it includes analytical and computational methods and presents in a unified fashion the knowledge gained in the decades of research into this important open problem the paper shows that although many approaches and techniques exist to approach different versions of the problem no efficient algorithmic solutions are available

an elementary proof for a compact imbedding result in generalized electromagnetic theory propriete de plongement compact et certaines de ses consequences on etudie la validite du plongement suivant r 9 g e q 1 d q g l 2 q loc g

distributed static output feedback control for state synchronization in networks of identical lti systems this paper studies state synchronization of multi agent systems with disturbances using distributed static output feedback opfb control the bounded l 2 gain synchronization problem using distributed static opfb is defined and solved the availability of only output measurements restricts the local controls design while the communication graph topology restricts global information flow among the agents it is shown here that these two types of restriction can be dealt with in a symmetric manner and lead to two similar conditions guaranteeing the existence of bounded l 2 gain static opfb one condition is on the output measurement matrix on a local scale and the other on the graph laplacian matrix on a global scale under additional conditions a distributed two player zero sum game using static opfb is also solved and leads to distributed nash equilibrium on the communication graph as a special case the static opfb globally optimal control is given a new class of digraphs satisfying the above condition on the graph laplacian is studied the synchronizing region for distributed static opfb control is exposed and found to be conical different than the infinite right half plane synchronizing region for distributed state feedback

distributed l 2 gain output feedback control of homogeneous and heterogeneous systems the importance of static output feedback opfb design for aircraft control process control and elsewhere has been well documented since the 1960s since full state measurements are not usually available in practical systems this problem is compounded in the case of multi agent systems mas where each agent has its own state variable and measured outputs therefore this paper addresses the l 2 gain opfb synchronization of linear mas subject to external disturbances both homogeneous and heterogeneous mas are considered for homogeneous mas it is shown that the l 2 gain static opfb synchronization problem of mas can be cast into the l 2 gain static opfb problem for a set of decoupled systems that depend on the graph topology a modified riccati equation is introduced which gives the opfb gain and the coupling gain of the proposed static opfb control protocol for heterogeneous mas it is shown that the l 2 gain synchronization problem can be cast into the l 2 gain static opfb problem of a set of decoupled systems plus a coupling condition on their dynamic compensators that depends on the graph topology a certain novel gain matrix is introduced in the dynamics of the control protocol to improve the performance

coordination of multi agent systems on interacting physical and communication topologies abstract a new framework is given for coordination of multi agent systems that are interconnected by a physical coupling digraph the edges of this graph represent physical couplings between agents that are fixed due to dynamical interactions on top of the physical graph distributed control protocols are designed where the allowed communications between agents for control purposes are prescribed by a second fixed communication digraph the physical and communication digraphs are generally different and the combination of these two graphs forms a cyber physical system the interactions between physical and communication graphs are the focus of this paper we consider different interactions between two graphs including the case when their pinned laplacian commutes the case of the communication graph with diagonalizable pinned laplacian and the case of two general graphs moreover within each graph the relations between the agents can be either collaborative or antagonistic to capture this the theory of bipartite consensus is used coordination protocols for different cases are designed that are distributed with respect to the communication graph and overcome the detrimental effects of the signed physical graph the proposed control methods are illustrated by simulation examples

optimal design for synchronization of cooperative systems state feedback observer and output feedback this technical note studies synchronization of identical general linear systems on a digraph containing a spanning tree a leader node or command generator is considered which generates the desired tracking trajectory a framework for cooperative tracking control is proposed including full state feedback control observer design and dynamic output feedback control the classical system theory notion of duality is extended to networked systems it is shown that unbounded synchronization regions that achieve synchronization on arbitrary digraphs containing a spanning tree can be guaranteed by using linear quadratic regulator based optimal control and observer design methods at each node

a contraction approach to the hierarchical analysis and design of networked systems this brief is concerned with the stability of continuous time networked systems using contraction theory a result is established on the network structure and the properties of the individual component subsystems and their couplings to ensure the overall contractivity of the entire network specifically it is shown that a contraction property on a reduced order matrix that quantifies the interconnection structure coupled with contractivity expansion estimates on the individual component subsystems suffices to ensure that trajectories of the overall system converge towards each other

brief paper synchronization in networks of identical linear systems the paper investigates the synchronization of a network of identical linear state space models under a possibly time varying and directed interconnection structure the main result is the construction of a dynamic output feedback coupling that achieves synchronization if the decoupled systems have no exponentially unstable mode and if the communication graph is uniformly connected the result can be interpreted as a generalization of classical consensus algorithms stronger conditions are shown to be sufficient but to some extent also necessary to ensure synchronization with the diffusive static output coupling often considered in the literature

disconnected synchronized regions of complex dynamical networks this technical note addresses the synchronized region problem which is converted to a more convenient matrix stability problem for complex dynamical networks for any natural number n the existence of a network with n disconnected synchronized regions is theoretically proved and numerically demonstrated this shows the intrinsic complexity of the network synchronization problem convexity characteristic of stability for relevant matrix pencils is further discussed a smooth chua s circuit network is finally discussed as an example for illustration

output feedback protocols without controller interaction for consensus of homogeneous multi agent systems a unified robust control view abstract this paper investigates the consensus problem of homogeneous linear multi agent systems using output feedback an observer type protocol is formulated which only requires the relative output information of neighbours and does not require information exchange between controllers it is shown that the protocol bridges some existing ones of the same nature a robust control approach is presented for consensus protocol design which requires one to solve a riccati equation and a linear matrix inequality dual results are also discussed by virtue of low and high gain techniques it is shown that certain solvability conditions are to be satisfied to achieve consensus for agents that are not exponentially unstable or are minimum phase leading to a unified point of view for some existing results a numerical example is provided to illustrate the advantages of the proposed design method

brief paper an internal model principle is necessary and sufficient for linear output synchronization output synchronization of a network of heterogeneous linear state space models under time varying and directed interconnection structures is investigated it is shown that assuming stabilizability and detectability of the individual systems and imposing very mild connectedness assumptions on the interconnection structure an internal model requirement is necessary and sufficient for synchronizability of the network to polynomially bounded trajectories the resulting dynamic feedback couplings can be interpreted as a generalization of existing methods for identical linear systems

pinning control of scale free dynamical networks abstract recently it has been demonstrated that many large complex networks display a scale free feature that is their connectivity distributions have the power law form in the present work control of a scale free dynamical network by applying local feedback injections to a fraction of network nodes is investigated the specifically and randomly pinning schemes are considered the specifically pinning of the most highly connected nodes is shown to require a significantly smaller number of local controllers as compared to the randomly pinning scheme the method is applied to an array of chua s oscillators as an example

brief paper parameterization of all stabilizing h static state feedback gains application to output feedback design this paper presents a simplified parameterization of all h static state feedback controllers in terms of a single algebraic riccati equation and a free parameter matrix as a special case necessary and sufficient conditions for the existence of an static output feedback gain are given an efficient computational algorithm is given and its correctness proven no initial stabilizing output feedback gain is needed the technique is used to design an h lateral directional command augmentation system for the f 16 aircraft

convergent dynamics a tribute to boris pavlovich demidovich we review and pay tribute to a result on convergent systems by the russian mathematician boris pavlovich demidovich in a sense demidovich s approach forms a prelude to a field which is now called incremental stability of dynamical systems developments on incremental stability are reviewed from a historical perspective

cooperative optimal control for multi agent systems on directed graph topologies this note brings together stability and optimality theory to design distributed cooperative control protocols that guarantee consensus and are globally optimal with respect to a positive semi definite quadratic performance criterion a common problem in cooperative optimal control is that global optimization problems generally require global information which is not available to distributed controllers optimal control for multi agent systems is complicated by the fact that the communication graph topology interplays with the agent system dynamics in the note we use an inverse optimality approach together with partial stability to consider the cooperative consensus and pinning control agents with identical linear time invariant dynamics are considered communication graphs are assumed directed and having fixed topology structured quadratic performance indices are derived that capture the topology of the graph which allows for global optimal control that is implemented using local distributed protocols a new class of digraphs is defined that admits a distributed solution to the global optimal control problem namely those with simple graph laplacian matrices

clean positive operator valued measures in quantum mechanics the statistics of the outcomes of a measuring apparatus is described by a positive operator valued measure povm a quantum channel transforms povms into povms generally irreversibly thus losing some of the information retrieved from the measurement this poses the problem of which povms are undisturbed i e they are not irreversibly connected to another povm we will call such povms clean in a sense the clean povms would be perfect since they would not have any additional extrinsical noise quite unexpectedly it turns out that such a cleanness property is largely unrelated to the convex structure of povms and there are clean povms that are not extremal and vice versa in this article we solve the cleannes classification problem for number n of outcomes n d d dimension of the hilbert space and we provide a set of either necessary or sufficient conditions for n d along with an iff condition for the case of informationally complete povms for n d2

controllability of complex networks via pinning we study the problem of controlling a general complex network toward an assigned synchronous evolution by means of a pinning control strategy we define the pinning controllability of the network in terms of the spectral properties of an extended network topology the roles of the control and coupling gains as well as of the number of pinned nodes are also discussed

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

discrete time local value iteration adaptive dynamic programming admissibility and termination analysis in this paper a novel local value iteration adaptive dynamic programming adp algorithm is developed to solve infinite horizon optimal control problems for discrete time nonlinear systems the focuses of this paper are to study admissibility properties and the termination criteria of discrete time local value iteration adp algorithms in the discrete time local value iteration adp algorithm the iterative value functions and the iterative control laws are both updated in a given subset of the state space in each iteration instead of the whole state space for the first time admissibility properties of iterative control laws are analyzed for the local value iteration adp algorithm new termination criteria are established which terminate the iterative local adp algorithm with an admissible approximate optimal control law finally simulation results are given to illustrate the performance of the developed algorithm

extremal covariant quantum operations and positive operator valued measures we consider the convex sets of qo s quantum operations and povm s positive operator valued measures which are covariant under a general finite dimensional unitary representation of a group we derive necessary and sufficient conditions for extremality and give general bounds for ranks of the extremal povm s and qo s results are illustrated on the basis of simple examples