local and global controllability for nonlinear systems a technique to study local and global controllability properties for a wide class of nonlinear systems is presented in addition to an extensive study of systems on r2 we propose as an application of our method a new criterion for global controllability of systems with polynomial drift term defined on rn in the case of linear systems the criterion reduces to the classical kalman condition a study of local controllability at the equilibrium point of the drift term of systems defined on r2 enables us not only to rederive a local controllability result derived by hermes 4 5 but also to extend this result when no assumptions are made on the boundedness of the controls

symmetric linear systems an application of algebraic systems theory dynamical systems which contain several identical subsystems occur in a variety of applications ranging from command and control systems and discretization of partial differential equations to the stability augmentation of pairs of helicopters lifting a large mass linear models for such systems display certain obvious symmetries in this paper we discuss how these symmetries can be incorporated into a mathematical model that utilizes the modern theory of algebraic systems such systems are inherently related to the representation theory of algebras over fields we will show that any control scheme which respects the dynamical structure either implicitly or explicitly uses the underlying algebra

new characterisations of positive realness and static output feedback control of discrete time systems this article is concerned with the problems of positive real analysis and control synthesis for discrete time systems new linear matrix inequality lmi characterisations of positive realness are derived which enable one to check the positive realness by using parameter dependent lyapunov function the relationship between the proposed characterisations and the existing ones are clarified which shows that our new results are of less conservatism for characterising the positive realness of discrete time systems with polytopic uncertainty in addition sufficient conditions for static output feedback positive real controller design are given in terms of solutions to a set of linear matrix inequalities numerical examples are included for illustration

nilpotent bases for distributions and control systems abstract let v m be the lie algebra infinite dimensional of real analytic vector fields on the n dimensional manifold m necessary conditions that a real analytic k dimensional distibution on m have a local basis which generates a nilpotent subalgebra of v m are derived two methods for sufficient conditions are given the first depending on the existence of a solution to a system of partial differential equations the second using darboux s theorem to give a computable test for an n 1 dimensional distribution a nonlinear control system in which the control variables appear linearly can be transformed into an orbit equivalent system whose describing vector fields generate a nilpotent algebra if the distribution generated by the original describing vector fields admits a nilpotent basis when this is the case local analysis of the control system is greatly simplified

quantitative analysis for controllability of symmetric control systems this paper is concerned with the controllability of systems possessing symmetries in particular we aim to give a lower bound for the number of functioning modules needed to ensure the controllability of the entire symmetric system our concern is the characteristics derived from the symmetry of the systems and not from the numerical information nor from the sparsity of the connections among the modules if structurally independent modules are connected only one functioning module would suffice to ensure the controllability for symmetric systems however it is shown that we need more than one functioning module for the entire system to be controllable we treat systems of general symmetry and show the lower bound based on group representation theory

behaviors of susceptible infected epidemics on scale free networks with identical infectivity in this paper we propose a susceptible infected model with identical infectivity in which at every time step each node can only contact a constant number of neighbors we implemented this model on scale free networks and found that the infected population grows in an exponential form with the time scale proportional to the spreading rate furthermore by numerical simulation we demonstrated that the targeted immunization of the present model is much less efficient than that of the standard susceptible infected model finally we investigate a fast spreading strategy when only local information is available different from the extensively studied path finding strategy the strategy preferring small degree nodes is more efficient than that preferring large degree nodes our results indicate the existence of an essential relationship between network traffic and network epidemic on scale free networks

brief analysis of exclusively kinetic two link underactuated mechanical systems analysis of exclusively kinetic two link underactuated mechanical systems is undertaken in this paper it is first shown that such systems are not full state feedback linearizable around any equilibrium point also the equilibrium points for which the system is small time locally controllable stlc is at most a one dimensional submanifold a concept less restrictive than stlc termed the small time local output controllability stloc is introduced the satisfaction of which guarantees that a chosen configuration output can be controlled at its desired value it is shown that the class of systems considered is stloc if the inertial coupling between the input and output is nonzero also in such a case the system is nonminimum phase an example section illustrates all the results presented

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

reduction and non linear controllability of symmetric distributed systems this paper considers the reduction problem for distributed control systems in particular we consider controllability of systems containing multiple instances of diffeomorphic components where the overall system dynamics is invariant with respect to a discrete group action a subclass of such systems are systems with a set of identical components where the overall system dynamics are invariant with respect to physically interchanging these components the main result is a proposition which shows that for an equivalence class of symmetric systems of this type controllability of the entire class of systems can be determined by analysing the member of the equivalence class with the smallest state space the reduction methods developed are illustrated by considering the controllability of a team of mobile robots and a platoon of underwater vehicles

lie brackets and local controllability a sufficient condition for scalar input systems we develop a general formalism based on exponential lie series which can be used to study control variations we apply the formalism to prove a result conjectured by h hermes that gives a sufficient condition for small time local controllability for single input systems

controllability of a class of underactuated mechanical systems with symmetry in this paper we develop results based on geometric mechanics to study the controllability of a class of controlled under actuated left invariant mechanical systems on lie groups we exploit the invariance of the controlled nonlinear dynamics to the group action symmetry to derive a set of reduced dynamics for the system we first present sufficient conditions for the controllability of the reduced dynamics we prove conditions boundedness of coadjoint orbits and existence of a radially unbounded lyapunov function under which the drift vector field of the reduced system is weakly positively poisson stable wpps the wpps nature of the drift vector field along with the lie algebra rank condition is used to show controllability of the reduced system we then extend these results to the unreduced dynamics considering separately the cases when the symmetry group is compact and noncompact in the noncompact case under further assumptions of equilibrium controllability sufficient conditions for controllability of the unreduced dynamics are derived jetpuck hovercraft and underwater vehicles are used as mechanical systems to motivate our work and illustrate our theoretical results

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

configuration controllability of mechanical systems underactuated by one control we investigate local configuration controllability for mechanical control systems within the affine connection formalism we rely on previous results on controllability and series expansions for the evolution of mechanical systems starting from rest extending the work by lewis for the single input case we are able to characterize local configuration controllability for systems with n degrees of freedom and n 1 input forces

weak small controls and approximations associated with controllable affine control systems abstract in this paper is shown that solutions associated with an extended affine control system can be obtained as a limit process using solutions for a parameterized affine control system and weak small controls

controllability of linear systems on generalized heisenberg groups this paper is devoted to the study of global controllability of linear systems on higher dimensional heisenberg groups hn necessary conditions and sufficient ones are provided they are compared to the known necessary and sufficient conditions on h1 stated in dath and jouan 2016 controllability of linear systems on low dimensional nilpotent and solvable lie groups journal of dynamical and control systems 22 2 207 225 the notion of decoupled systems is introduced in order to get examples and counter examples and more precise controllability criteria are stated for them

multiplier design for extended strict positive realness and its applications given a stable square plant g 1 s based on linear matrix inequality lmi method necessary and sufficient conditions are presented for the existence of a stable multiplier g 2 s such that g 1 s g 2 s is extended strictly positive real espr furthemore for uncertain plants the corresponding problems are considered and solved an application to the study of dichotomy for pendulum like systems is also presented examples are given to illustrate the results

all controllers for the general h control problem lmi existence conditions and state space formulas this paper presents all controllers for the general h control problem with no assumptions on the plant matrices necessary and sufficient conditions for the existence of an h controller of any order are given in terms of three linear matrix inequalities lmis our existence conditions are equivalent to scherer s results but with a more elementary derivation furthermore we provide the set of all h controllers explicitly parametrized in the state space using the positive definite solutions to the lmis even under standard assumptions full rank etc our controller parametrization has an advantage over the q parametrization the freedom q a real rational stable transfer matrix with the h norm bounded above by a specified number is replaced by a constant matrix l of fixed dimension with a norm bound and the solutions x y to the lmis the inequality formulation converts the existence conditions to a convex feasibility problem and also the free matrix l and the pair x y define a finite dimensional design space as opposed to the infinite dimensional space associated with the q parametrization

h_ infty controller design using an alternative to youla parameterization all h controllers of a siso lti system are parameterized thanks to the relation between bounded real lemma and positive real lemma this new parameterization shares the same features with youla parameterization namely on the convexity of h norm constraints for the closed loop transfer functions however it can deal with low order controllers and can be extended easily for the systems with polytopic uncertainty the effectiveness of the proposed method is shown via an academic example

application of a multiplier method to uncertain lur e like systems abstract this paper investigates the conditions under which an abstract matrix multiplier method can be applied to determine guaranteeing cost controls for systems containing nonlinear uncertain elements via linear matrix inequalities lmis quadratically constrained uncertainties and nonlinearities are considered which comprehend the cases of norm bounded positive real and sector bounded uncertainties nonlinearities both the discrete time and the continuous time cases are discussed necessary and sufficient conditions are formulated in the case of unstructured uncertainty the conditions are sufficient in the structured case the cost guaranteeing controls can be determined by solving lmis numerical examples illustrate the effectiveness of the proposed method

complex networks constructed from irrational number sequences in this paper we construct d r networks from sequences of different irrational numbers in detail segment an irrational number sequence of length m into groups of d digits which represent the nodes while two consecutive groups overlap by r digits r 0 1 d 1 and the undirected edges indicate the adjacency between two consecutive groups 3 r and 4 r networks are respectively constructed from 14 different irrational numbers and their topological properties are examined by observation we find that network topologies change with different values of d r and even sequence length m instead of the types of irrational numbers although they share some similar features with traditional random graphs we make a further investigation to explain these interesting phenomena and propose the identical degree random graph model the results presented in this paper provide some insight into distributions of irrational number digits that may help better understanding of the nature of irrational numbers

solution to the positive real control problem for linear time invariant systems in this paper we study the problem of synthesizing an internally stabilizing linear time invariant controller for a linear time invariant plant such that a given closed loop transfer function is extended strictly positive real necessary and sufficient conditions for the existence of a controller are obtained state space formulas for the controller design are given in terms of solutions to algebraic riccati equations or inequalities the order of the constructed controller does not exceed that of the plant

local controllability of nonlinear systems abstract the local controllability of control systems with an arbitrary number of controls is considered first on an open set and then at a given point necessary conditions are derived concerning the lie algebra t generated by the input vector fields and applied to gradient systems the main results are a geometric sufficient condition for local controllability at a point and an equivalent condition based on the computation of lie brackets assuming t to be n 1 dimensional

explicit controller formulas for lmi based h synthesis the set of h controllers with closed loop performance c can be implicitly parametrized by the solutions r s of a system of linear matrix inequalities lmi the matrices r and s play a role analogous to that of the riccati solutions x and y in classical riccati based h control useful applications include lmi based h synthesis mixed h 2h design and h design with a pole placement constraint this paper is concerned with the reliable computation of h controllers given a solution r s of the characteristic system of lmis explicit formulas are derived for both the regular and singular cases remarkably these formulas are extensions of the usual central controller formulas where the lmi solutions r and s replace the riccati solutions x and y simple and numerically appealing new formulas for discrete time h controllers are also derived

on the relation between local controllability and stabilizability for a class of nonlinear systems the problem of local stabilizability of locally controllable nonlinear systems is considered it is well known that contrary to the linear case local controllability does not necessarily imply stabilizability a class of nonlinear systems for which local controllability implies local asymptotic stabilizability using continuous static state feedback is described as for this class of systems the well known hermes controllability condition is necessary and sufficient for local controllability

local controllability along a reference trajectory abstract local controllability along a reference trajectory of analytic and smooth affine single input control systems without any a priori bounds on the control is considered and a geometric proof of a version of the hermes conjecture is given

qualitative analysis and decentralized controller synthesis for a class of large scale systems with symmetrically interconnected subsystems abstract a number of large scale interconnected systems often encountered in practice are composed of subsystems with similar dynamics interconnected in a symmetrical fashion and the synthesis of controllers for such systems must exploit the special structural properties in order to avoid overly conservative designs and to take advantage of the possible beneficial effects of the interconnections an analysis of some important qualitative properties of such symmetrically interconnected systems focussing on the spectrum characterization controllability and observability and the solutions of the algebraic riccati equation and the matrix lyapunov equation is conducted in this paper and procedures for constructing the solutions to the analysis problems at the overall system level from the computationally simple subsystem level solutons are developed a decentralized controller design procedure is presented as an illustration of the utilization of the available structural information in addressing synthesis problems numerical examples are included to demonstrate the superiority of the presented designs over the use of existing approaches which do not take full advantage of the structural knowledge in these large scale systems

brief paper criteria for dichotomy and gradient like behavior of a class of nonlinear systems with multiple equilibria this paper considers global properties of a class of nonlinear systems with infinite equilibria time domain and frequency domain criteria for dichotomy and gradient like behavior are established similar to the sector condition in absolute stability problems the bounded derivative condition of nonlinear functions can be used to reduce the conservativeness of the given criteria compared with the frequency domain conditions the time domain inequalities can be solved easily by linear matrix inequality lmi toolbox and used to discuss controller design problems several examples are given to illustrate the effectiveness of the results

local controllability for families of diffeomorphisms abstract we study groups and semigroups which are generated by analytic families of diffeomorphisms the central notion is that of local controllability of a family of diffeomorphisms at a given point of the state manifold which generalizes the familiar notion of local controllability of control systems with continuous as well as discrete time lie theory methods are used we systematically exploit the so called fast switching variations and properties of the jet spaces of curves on the state manifold

robustness analysis and synthesis of siso systems under both plant and controller perturbations abstract in this paper we consider the robustness analysis and synthesis problem for a class of control systems under both plant and controller perturbations necessary and sufficient conditions are given for robust stability of siso systems subject to additive norm bounded perturbations linear matrix inequality lmi based controller design method is presented robust stability of systems with both plant and controller perturbations and stability analysis of a class of multilinear disc polynomials are unified in the same framework and can be solved by computing the largest norm of a second order matrix along the imaginary axis

symmetries and conservation laws for hamiltonian systems with inputs and outputs a generalization of noether s theorem the definition of symmetries and conservation laws for autonomous i e without external cases hamiltonian systems are generalized to hamiltonian systems with inputs and outputs it is shown that a symmetry implies the existence of a conservation law and vice versa thereby generalizing noether s theorem for autonomous hamiltonian systems

reduction of some classical non holonomic systems with symmetry two types of nonholonomic systems with symmetry are treated i the configuration space is a total space of a g principal bundle and the constraints are given by a connection ii the configuration space is g itself and the constraints are given by left invariant forms the proofs are based on the method of quasicoordinates in passing a derivation of the maurer cartan equations for lie groups is obtained simple examples are given to illustrate the algorithmical character of the main results

low order controllability and kinematic reductions for affine connection control systems controllability and kinematic modeling notions are investigated for a class of mechanical control systems first low order controllability results are given for the class of mechanical control systems second a precise connection is made between those mechanical systems which are dynamic i e have forces as inputs and those which are kinematic i e have velocities as inputs interestingly and surprisingly these two subjects are characterized and linked by a certain intrinsic vector valued quadratic form that can be associated to an affine connection control system

nonholonomic mechanical systems with symmetry this work develops the geometry and dynamics of mechanical systems with nonholonomic constraints and symmetry from the perspective of lagrangian mechanics and with a view to control theoretical applications the basic methodology is that of geometric mechanics applied to the formulation of lagrange d alembert generalizing the use of connections and momentum maps associated with a given symmetry group to this case we begin by formulating the mechanics of nonholonomic systems using an ehresmann connection to model the constraints and show how the curvature of this connection enters into lagrange s equations unlike the situation with standard configuration space constraints the presence of symmetries in the nonholonomic case may or may not lead to conservation laws however the momentum map determined by the symmetry group still satisfies a useful differential equation that decouples from the group variables this momentum equation which plays an important role in control problems involves parallel transport operators and is computed explicitly in coordinates an alternative description using a body reference frame relates part of the momentum equation to the components of the euler poincar e equations along those symmetry directions consistent with the constraints one of the purposes of this paper is to derive this evolution equation for the momentum and to distinguish geometrically and mechanically the cases where it is conserved and those where it is not an example of the former is a ball or vertical disk rolling on a flat plane and an example of the latter is the snakeboard a modified version of the skateboard which uses momentum coupling for locomotion generation we construct a synthesis of the mechanical connection and the ehresmann connection defining the constraints obtaining an important new object we call the nonholonomic connection when the nonholonomic connection is a principal connection for the given symmetry group we show how to perform lagrangian reduction in the presence of nonholonomic constraints generalizing previous results which only held in special cases several detailed examples are given to illustrate the theory september 1994 revised march 1995 revised june 1995

the π sequence as a complex network abstract in this paper a new topological approach for studying a sufficiently long random number sequence is proposed by segmenting the sequence into groups of digits which represent the node identities while the undirected edges symbolize the adjacency between them a network is constructed for analysis in particular the network constructed from a sequence is examined in detail and its properties are contrasted with the erdos renyi er random graph model based on the observation that there are more nodes with even degrees than the adjacent odd counterparts in the constructed network a new random graph model named random eulerian re model and its extension are finally proposed and analyzed

preservation of controllability observability in expanded systems the result contributed by the article is that controllability observability of an original continuous time lti dynamic system can always be simultaneously preserved in expanded systems within the inclusion principle when using block structured complementary matrices this new structure offers more degrees of freedom for the selection of specific complementary matrices than well known used cases such as aggregations and restrictions which enable such preservation only in certain special cases a complete unrestricted transmission of these qualitative properties from the original controllable observable system to its expansion is a basic requirement on the expansion contraction process mainly when controllers observers are designed in expanded systems to be consequently contracted for implementation in initially given systems an original system composed of two overlapped subsystems is adopted as a general prototype ease a numerical example is supplied

structural and functional clusters of complex brain networks recent research using the complex network approach has revealed a rich and complicated network topology in the cortical connectivity of mammalian brains it is of importance to understand the implications of such complex network structures in the functional organization of the brain activities here we study this problem from the viewpoint of dynamical complex networks we investigate synchronization dynamics on the corticocortical network of the cat by modeling each node cortical area of the network with a sub network of interacting excitable neurons we find that the network displays clustered synchronization behavior and the dynamical clusters coincide with the topological community structures observed in the anatomical network our results provide insights into the relationship between the global organization and the functional specialization of the brain cortex

a convex parameterization of robustly stabilizing controllers this paper treats synthesis of robust controllers for linear time invariant systems uncertain real parameters are assumed to appear linearly in the closed loop characteristic polynomial the main contribution is to give a convex parameterization of all controllers that simultaneously stabilize the system for all possible parameter combinations with the new parameterization certain robust performance problems can be stated in terms of quasi convex optimization

the complexity of deciding controllability abstract it is shown that the problem of deciding whether a control system is small time locally controllable or not is np hard this is an extension of a recent paper by sontag to single input systems and to bounded controls

local equilibrium controllability of multibody systems controlled via shape change we study local equilibrium controllability of shape controlled multibody systems the multibody systems are defined on a trivial principal fiber bundle by a lagrangian that characterizes the base body motion and shape dynamics a potential dependent on an advected parameter e g uniform gravitational potential is considered this potential breaks base body symmetries but a symmetry subgroup is assumed to exist symmetric product formulas are derived and important properties are obtained for symmetric products of horizontal shape control vector fields and a potential vector field that is dependent on an advected parameter based on these properties sufficient conditions for local equilibrium controllability and local fiber equilibrium controllability are developed these results are applied to two classes of shape controlled multibody systems in a uniform gravitational field multibody attitude systems and neutrally buoyant multibody underwater vehicles

mean field theory for scale free random networks random networks with complex topology are common in nature describing systems as diverse as the world wide web or social and business networks recently it has been demonstrated that most large networks for which topological information is available display scale free features here we study the scaling properties of the recently introduced scale free model that can account for the observed power law distribution of the connectivities we develop a mean eld method to predict the growth dynamics of the individual vertices and use this to calculate analytically the connectivity distribution and the scaling exponents the mean eld method can be used to address the properties of two variants of the scale free model that do not display power law scaling c 1999 elsevier science b v all rights reserved