control of singularly perturbed hybrid stochastic systems we study a class of optimal stochastic control problems involving two different time scales the fast mode of the system is represented by deterministic state equations whereas the slow mode of the system corresponds to a jump disturbance process under a fundamental ergodicity property for a class of infinitesimal control systems associated with the fast mode we show that there exists a limit problem which provides a good approximation to the optimal control of the perturbed system both the finite and infinite discounted horizon cases are considered we show how an approximate optimal control law can be constructed from the solution of the limit control problem in the particular case where the infinitesimal control systems possess the so called turnpike property i e characterized by the existence of global attractors the limit control problem can be given an interpretation related to a decomposition approach

on existence of limit occupational measures set of a controlled stochastic differential equation we establish that under certain conditions the set of occupational measures as well as the set of mathematical expectations of occupational measures generated by the admissible controls and the corresponding solutions of a controlled stochastic differential equation csde converge with the time horizon tending to infinity to a set called limit occupational measures set loms and we show that this limit set coincides with the set of stationary marginal distributions of the csde we also demonstrate the applicability of our results for averaging of singularly perturbed csde

on the reachable set of inflated singularly perturbed differential equations singularly perturbed differential equations with slow and fast subsystems are under consideration it is well known that the invariant probability measures of the unperturbed fast subsystems produce a limiting system for the slow subsystem unfortunately the limiting system is non smooth in general and might be too big since it also generates trajectories that are not related to the singularly perturbed system however if the flows produced by the unperturbed fast subsystems are chain transitive an inflation of the singularly perturbed system can be used in order to approximate all trajectories of the limiting system moreover it turns out that the reachable sets of the limiting system are contained in the reachable sets of the slightly inflated singularly perturbed system

nonsmooth ica contrast minimization using a riemannian nelder mead method this brief concerns the design and application of a riemannian nelder mead algorithm to minimize a hartley entropy based contrast function to reliably estimate the sources from their mixtures despite its nondifferentiability the contrast function is endowed with attractive properties such as discriminacy and hence warrants an effort to be effectively handled by a derivative free optimizer aside from tailoring the nelder mead technique to the constraint set namely oblique manifold the source separation results attained in an empirical study with quasi correlated synthetic signals and digital images are presented which favor the proposed method on a comparative basis

singularly perturbed control systems with one dimensional fast dynamics the order reduction approach to singularly perturbed control systems suggests employing as a variational limit the differential algebraic system obtained when the small parameter is set to be zero it is known that the method is valid only under restrictive convergence conditions on the fast dynamics we verify in this paper that when the fast state variable is one dimensional the order reduction method is valid in general this is true however when appropriate relaxation is allowed in the reduced order system we also indicate how to extract near optimal solutions to the original system from optimal solutions of the order reduction one along the traditional reasoning of separating time scales examples are displayed showing that without allowing the relaxation the order reduction may not provide the correct limit

solutions to hybrid inclusions via set and graphical convergence with stability theory applications motivated by questions in stability theory for hybrid dynamical systems we establish some fundamental properties of the set of solutions to such systems using the notion of a hybrid time domain and general results on set and graphical convergence we establish under weak regularity and local boundedness assumptions that the set of solutions is sequentially compact and upper semicontinuous with respect to initial conditions and system perturbations the general facts are then used to establish several results for the behavior of hybrid systems that have asymptotically stable compact sets these results parallel what is already known for differential inclusions and difference inclusions for example the basin of attraction for a compact attractor is relatively open the attractivity is uniform from compact subsets of the basin of attraction and asymptotic stability is robust with respect to small perturbations

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

on a representation of the limit occupational measures set of a control system with applications to singularly perturbed control systems a representation of the limit occupational measures set of a control system in terms of the vector function defining the system s dynamics is established applications in averaging of singularly perturbed control systems are demonstrated

singular perturbation of a finite horizon problem with state space constraints we study the singular perturbation of optimal control problems for nonlinear systems with constraints on the fast state variables and a cost functional either of bolza type or involving the exit time of the system from a given domain under a controllability assumption on the fast variables we show that these variables become controls in the limit problem our method consists of passing to the limit in the associated hamilton jacobi bellman hjb equations by means of some tools in the theory of viscosity solutions

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

multiscale singularly perturbed control systems limit occupational measures sets and averaging an averaging technique for nonlinear multiscale singularly perturbed control systems is developed issues concerning the existence and structure of limit occupational measures sets generated by such systems are discussed general results are illustrated with special cases

containment control for coupled harmonic oscillators with multiple leaders under directed topology this paper investigates the problem of containment control for coupled harmonic oscillators with multiple leaders under directed topology using tools from matrix graph and stability theories necessary and sufficient conditions are obtained for coupled harmonic oscillators under continuous time and sampled data based protocols respectively when the continuous time protocol is used it is proved that every follower will ultimately converge to the convex hull spanned by the leaders if and only if there exists at least one leader that has a directed path to that follower at any time when the sampled data based protocol is used it is shown that the containment can be achieved if and only if 1 an appropriate sampling period is chosen and 2 for every follower there exists at least one leader that has a directed path to that follower at any time and we also give the containment conditions for coupled harmonic oscillators under undirected topology as a special case finally numerical simulations are

range based ica using a nonsmooth quasi newton optimizer for electroencephalographic source localization in focal epilepsy independent component analysis ica aims at separating a multivariate signal into independent nongaussian signals by optimizing a contrast function with no knowledge on the mixing mechanism despite the availability of a constellation of contrast functions a hartley entropy based ica contrast endowed with the discriminacy property makes it an appealing choice as it guarantees the absence of mixing local optima fueled by an outstanding source separation performance of this contrast function in practical instances a succession of optimization techniques has recently been adopted to solve the ica problem nevertheless the nondifferentiability of the considered contrast restricts the choice of the optimizer to the class of derivative free methods on the contrary this letter concerns a riemannian quasi newton scheme involving an explicit expression for the gradient to optimize the contrast function that is differentiable almost everywhere furthermore the inexact line search insisting on the weak wolfe condition and a terminating criterion befitting the partly smooth function optimization have been generalized to manifold settings leaving the previous results intact the investigations with diversified images and the electroencephalographic eeg data acquired from 45 focal epileptic subjects demonstrate the efficacy of our approach in terms of computational savings and reliable eeg source localization respectively additional experimental results are available in the online supplement

singularly perturbed ordinary differential equations with dynamic limits coupled slow and fast motions generated by ordinary differential equations are examined the qualitative limit behaviour of the trajectories as the small parameter tends to zero is sought after invariant measures of the parametrised fast flow are employed to describe the limit behaviour rather than algebraic equations which are used in the standard reduced order approach in the case of a unique invariant measure for each parameter the limit of the slow motion is governed by a chattering type equation without the uniqueness the limit of the slow motion solves a differential inclusion the fast flow in turn converges in a statistical sense to the direct integral respectively the set valued direct integral of the invariant measures

designing fully distributed consensus protocols for linear multi agent systems with directed graphs this technical note addresses the distributed consensus protocol design problem for multi agent systems with general linear dynamics and directed communication graphs existing works usually design consensus protocols using the smallest real part of the nonzero eigenvalues of the laplacian matrix associated with the communication graph which however is global information in this technical note based on only the agent dynamics and the relative states of neighboring agents a distributed adaptive consensus protocol is designed to achieve leader follower consensus in the presence of a leader with a zero input for any communication graph containing a directed spanning tree with the leader as the root node the proposed adaptive protocol is independent of any global information of the communication graph and thereby is fully distributed extensions to the case with multiple leaders are further studied

an averaging method for singularly perturbed systems of semilinear differential inclusions with analytic semigroups we consider a system of two semilinear parabolic inclusions depending on a small parameter e 0 which is present both in front of the derivative in one of the two inclusions and in the nonlinear terms to model high frequency inputs the aim is to provide conditions in order to guarantee for e 0 sufficiently small the existence of periodic solutions and in order to study their behaviour as e tends to zero our assumptions permit the definition of upper semicontinuous convex valued compact vector operators whose fixed points represent the sought after periodic solutions the existence of fixed points is shown by using topological degree theory arguments

controllability and stabilization of one dimensional systems near bifurcation points abstract bifurcation theory deals with the change of qualitative behavior in a parameter dependent family of differential equations for one dimensional equations the possible bifurcation scenarios are well understood if the family of differential equations can be controlled by admissible controls with compact range the question arises whether the systems are controllable near a bifurcation point and whether stabilization around unstable bifurcation branches via bounded feedback is possible in this paper we show that controllability for parametrized families of one dimensional control systems can be characterized in terms of two parameters the original bifurcation parameter and the size of the control range these results are used to construct nonsmooth stabilizing feedbacks and to describe the set of initial values from which stabilization is possible furthermore robustness properties of the stabilizing feedback are discussed

a unified framework for quadratic measures of independence this paper proposes a unified framework for several available measures of independence by generalizing the concept of information theoretic learning itl the key component of itl is the use of inner product between two density functions as a measure of similarity between two random variables we show that by generalizing the inner product using a symmetric strictly positive definite kernel and by choosing appropriate kernels it is possible to reproduce a number of popular measures of independence this unified framework also allows the design of new strictly positive definite kernels and corresponding measures of independence following this framework we explore a new measure of independence and apply it in the context of linear independent component analysis ica an attractive property of the proposed method is that it does not involve any free parameter and we demonstrate that it performs equally well compared to the existing methods for ica

on the risk of using renyi s entropy for blind source separation recently some researchers have suggested renyi s entropy in its general form as a blind source separation bss objective function this was motivated by two arguments 1 shannon s entropy which is known to be a suitable criterion for bss is a particular case of renyi s entropy and 2 some practical advantages can be obtained by choosing another specific value for the renyi exponent yielding to e g quadratic entropy unfortunately by doing so there is no longer guarantee that optimizing this generalized criterion would lead to recovering the original sources in this paper we show that renyi s entropy in its exact form i e out of any consideration about its practical estimation or computation might lead to not recovering the sources depending on the source densities and on renyi s exponent value this is illustrated on specific examples we also compare our conclusions with previous works involving renyi s entropies for blind deconvolution

singular perturbations of nonlinear degenerate parabolic pdes a general convergence result the main result of the paper is a general convergence theorem for the viscosity solutions of singular perturbation problems for fully nonlinear degenerate parabolic pdes partial differential equations with highly oscillating initial data it substantially generalizes some results obtained previously in 2 under the only assumptions that the hamiltonian is ergodic and stabilizing in a suitable sense the solutions are proved to converge in a relaxed sense to the solution of a limit cauchy problem with appropriate effective hamiltonian and initial data in its formulation our convergence result is analogous to the stability property of barles and perthame it should thus reveal a useful tool for studying general singular perturbation problems by viscosity solutions techniques a detailed exposition of ergodicity and stabilization is given with many examples applications to homogenization and averaging are also discussed

singular perturbations in infinite dimensional control systems in this paper we consider a singularly perturbed control system involving differential inclusions in banach spaces with slow and fast solutions using the averaging approach we obtain sufficient conditions for the hausdorff convergence of the set of slow solutions in the supremum norm we present applications of the theorem to prove convergence of the fast solutions in terms of invariant measures and convergence of equi lipschitz solutions

averaging method for one sided lipschitz differential inclusions with generalized solutions we investigate the convergence of the solution set for singularly perturbed differential inclusions using an averaging technique the limits of the fast solutions are considered as generalized solutions i e radon probability measures of the degenerate system exploiting in addition the one sided lipschitz condition we prove the existence of a limit of the solution set in an appropriate topology

convergence of the value functions of discounted infinite horizon optimal control problems with low discount rates for autonomous nonlinear smooth optimal control systems on n dimensional manifolds we investigate the relationship between the discounted and the average yield optimal value of infinite horizon problems it is shown that the value functions of discounted problems converge to the value function of the average yield problem as the discount rate tends to zero if there exist approximately optimal solutions satisfying some periodicity conditions in general the discounted value functions cannot be expected to converge which is shown by a counterexample a connection to geometric control theory is then made to establish a result of uniform convergence on compact subsets of the interior of control sets if optimal trajectories do not leave a compact subset of the interior of these control sets

a new reduction technique for a class of singularly perturbed optimal control problems we consider a class of singularly perturbed optimal control problems which may not be approximated by the reduced problems constructed via the formal replacement of the fast variables by the states of equilibrium of the fast subsystem considered with frozen slow variables and controls we construct a reduced optimal control problem which provides a true approximation for the problems under consideration and write down the necessary and sufficient optimality conditions for this reduced problem

averaging problem for weakly coupled nonexpansive control systems this paper investigates the limit behavior of a singularly perturbed control system with two state variables which are weakly coupled the main novelty of our averaging approach lies in the fact that the limit dynamic may depend the initial condition of the fast system while in the literature this problem has been usually addressed under conditions that ensure that the limit dynamic is independent to this initial condition our study is based on a suitable nonexpansivity condition on the fast system which generalized dissipativity or stability properties of the fast dynamics

uniqueness of constrained viscosity solutions in hybrid control systems we study constrained viscosity solutions with an unbounded growth for a class of first order hamilton jacobi bellman equations arising in hybrid control systems to deal with the boundary constraint and rapid growth of the solutions we construct a particular set of test functions and under very mild conditions establish a comparison theorem which gives the estimate of distance between the subsolution and the supersolution the comparison theorem implies uniqueness of the constrained viscosity solution if its existence is ensured and under some additional assumptions we give an existence result by showing that the value function is a constrained viscosity solution we then apply the obtained uniqueness results to an optimal scheduling problem and finally to stochastic manufacturing systems

on representation formulas for long run averaging optimal control problem we investigate an optimal control problem with an averaging cost the asymp totic behavior of the values is a classical problem in ergodic control to study the long run averaging we consider bothce aro and abel means a main result of the paper says that there is at most one possible accumulation point in the uniform convergence topology of the values when the time horizon of thece aro means converges to infinity or the discount factor of the abel means converges to zero this unique accumulation point is explicitly described by representation formulas involving probability measures on the state and control spaces as a byproduct we obtain the existence of a limit value whenever thece aro or abel values are equicon tinuous our approach allows to generalise several results in ergodic control and in particular it allows to cope with cases where the limit value is not constant with respect to the initial condition

distributed containment tracking of multiple stochastic nonlinear systems this paper investigates distributed containment tracking for multiple stochastic nonlinear systems with multiple dynamic leaders under directed network topology the control input of each agent can only use its local state and the states of its neighbors with the backstepping design method distributed tracking controllers are designed by using stochastic analysis and graph theory it is shown that the followers outputs will exponentially converge to the convex hull spanned by the dynamic leaders s outputs with tunable tracking errors while all the states of the closed loop system remain bounded in probability a numerical example is provided to illustrate the effectiveness of the theoretical results

spherical mesh adaptive direct search for separating quasi uncorrelated sources by range based independent component analysis it is seemingly paradoxical to the classical definition of the independent component analysis ica that in reality the true sources are often not strictly uncorrelated with this in mind this letter concerns a framework to extract quasi uncorrelated sources with finite supports by optimizing a range based contrast function under unit norm constraints to handle the inherent scaling indeterminacy of ica but without orthogonality constraints albeit the appealing contrast properties of the range based function e g the absence of mixing local optima the function is not differentiable everywhere unfortunately there is a dearth of literature on derivative free optimizers that effectively handle such a nonsmooth yet promising contrast function this is the compelling reason for the design of a nonsmooth optimization algorithm on a manifold of matrices having unit norm columns with the following objectives to ascertain convergence to a clarke stationary point of the contrast function and adhere to the necessary unit norm constraints more naturally the proposed nonsmooth optimization algorithm crucially relies on the design and analysis of an extension of the mesh adaptive direct search mads method to handle locally lipschitz objective functions defined on the sphere the applicability of the algorithm in the ica domain is demonstrated with simulations involving natural face aerial and texture images

hamilton jacobi equations with state constraints in the present paper we consider hamilton jacobi equations of the form h x u vu 0 x e q where q is a bounded open subset of rn h is a given continuous real valued function of x s p e q x r x rn and vu is the gradient of the unknown function u we are interested in particular solutions of the above equation which are required to be supersolutions in a suitable weak sense of the same equation up to the boundary of q this requirement plays the role of a boundary condition the main motivation for this kind of solution comes from deterministic optimal control and differential games problems with constraints on the state of the system as well from related questions in constrained geodesics

distributed containment control for multiple unknown second order nonlinear systems with application to networked lagrangian systems in this paper we consider the distributed containment control problem for multiagent systems with unknown nonlinear dynamics more specifically we focus on multiple second order nonlinear systems and networked lagrangian systems we first study the distributed containment control problem for multiple second order nonlinear systems with multiple dynamic leaders in the presence of unknown nonlinearities and external disturbances under a general directed graph that characterizes the interaction among the leaders and the followers a distributed adaptive control algorithm with an adaptive gain design based on the approximation capability of neural networks is proposed we present a necessary and sufficient condition on the directed graph such that the containment error can be reduced as small as desired as a byproduct the leaderless consensus problem is solved with asymptotical convergence because relative velocity measurements between neighbors are generally more difficult to obtain than relative position measurements we then propose a distributed containment control algorithm without using neighbors velocity information a two step lyapunov based method is used to study the convergence of the closed loop system next we apply the ideas to deal with the containment control problem for networked unknown lagrangian systems under a general directed graph all the proposed algorithms are distributed and can be implemented using only local measurements in the absence of communication finally simulation examples are provided to show the effectiveness of the proposed control algorithms

robust finite time containment control for high order multi agent systems with matched uncertainties under directed communication graphs abstractin this paper we study the robust finite time containment control problem for a class of high order uncertain nonlinear multi agent systems modelled as high order integrator systems with bounded matched uncertainties when relative state information between neighbouring agents is available an observer based distributed controller is proposed for each follower using the sliding mode control technique which solves the finite time containment control problem under general directed communication graphs when only relative output information is available robust exact differentiators and high order sliding mode controllers are employed together with the distributed finite time observers it is shown that robust finite time containment control can still be achieved in this situation an application in the coordination of multiple non holonomic mobile robots is used as an example to illustrate the effectiveness of the proposed control strategies

singular perturbation of optimal control problems on multidomains the goal of this paper is to study a singular perturbation problem in the framework of optimal control on multi domains we consider an optimal control problem in which the controlled system contains a fast and a slow variables this problem is reformulated as an hamilton jacobi bellman hjb equation the main difficulty comes from the fact that the fast variable lives in a multi domain the geometric singularity of the multi domains leads to the discontinuity of the hamiltonian under a controllability assumption on the fast variables the limit equation as the velocity of the fast variable goes to infinity is obtained via a pde approache and by means of the tools of the control theory

independent component analysis by entropy bound minimization a novel differential entropy estimator is introduced where the maximum entropy bound is used to approximate the entropy given the observations and is computed using a numerical procedure thus resulting in accurate estimates for the entropy we show that such an estimator exists for a wide class of measuring functions and provide a number of design examples to demonstrate its flexible nature we then derive a novel independent component analysis ica algorithm that uses the entropy estimate thus obtained ica by entropy bound minimization ica ebm the algorithm adopts a line search procedure and initially uses updates that constrain the demixing matrix to be orthogonal for robust performance we demonstrate the superior performance of ica ebm and its ability to match sources that come from a wide range of distributions using simulated and real world data

viscosity solutions methods for singular perturbations in deterministic and stochastic control viscosity solutions methods are used to pass to the limit in some penalization problems for first order and second order degenerate parabolic hamilton jacobi bellman equations this characterizes the limit of the value functions of singularly perturbed optimal control problems for deterministic systems and for controlled degenerate diffusions the results apply to cases where the usual order reduction method does not give the correct limit and to systems with fast state variables depending nonlinearly on the control some connections with ergodic control and periodic homogenization are discussed

the lyapunov spectrum of families of time varying matrices for l families of time varying matrices centered at an unperturbed matrix the lyapunov spectrum contains the floquet spectrum obtained by considering periodically varying piecewise constant matrices on the other hand it is contained in the morse spectrum of an associated flow on a vector bundle a closer analysis of the floquet spectrum based on geometric control theory in projective space and in particular on control sets is performed introducing a real parameter p 0 which indicates the size of the li perturbation we study when the floquet spectrum the morse spectrum and hence the lyapunov spectrum all coincide this holds if an inner pair condition is satisfied for all up to at most countably many p values

on square roots of m matrices abstract the question of the existence and uniqueness of an m matrix which is a square root of an m matrix is discussed the results are then used to derive some new necessary and sufficient conditions for a real matrix with nonpositive off diagonal elements to be an m matrix

multi vehicle consensus with a time varying reference state in this paper we study the consensus problem in multi vehicle systems where the information states of all vehicles approach a time varying reference state under the condition that only a portion of the vehicles e g the unique team leader have access to the reference state and the portion of the vehicles might not have a directed path to all of the other vehicles in the team we first analyze a consensus algorithm with a constant reference state using graph theoretical tools we then propose consensus algorithms with a time varying reference state and show necessary and sufficient conditions under which consensus is reached on the time varying reference state the time varying reference state can be an exogenous signal or evolve according to a nonlinear model these consensus algorithms are also extended to achieve relative state deviations among the vehicles an application example to multi vehicle formation control is given as a proof of concept

fast and robust fixed point algorithms for independent component analysis independent component analysis ica is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible we use a combination of two different approaches for linear ica comon s information theoretic approach and the projection pursuit approach using maximum entropy approximations of differential entropy we introduce a family of new contrast functions for ica these contrast functions enable both the estimation of the whole decomposition by minimizing mutual information and estimation of individual independent components as projection pursuit directions the statistical properties of the estimators based on such contrast functions are analyzed under the assumption of the linear mixture model and it is shown how to choose contrast functions that are robust and or of minimum variance finally we introduce simple fixed point algorithms for practical optimization of the contrast functions

limit behavior and genericity for nonlinear control systems abstract for nonlinear control systems of the form x0 x mi 1ui t xi x with constrained control range u r m the limit behavior of the trajectories is analyzed the limit sets are closely related to regions of the state space where the system is controllable in particular under a rank condition on the linear span of the derived vectorfields on a limit set this limit set is contained in the interior of a control set this result is a mathematical basis for the control of complicated behavior it also allows the characterization of morse sets of a differential equation as intersections of topologically transitive sets of control systems topological genericity theorems classify the possible limit behavior of a control system for open and dense sets in u m where u is the space of admissible control functions and m is the state space the methods are a combination of control theoretic arguments and chain transitivity for the control flow on u m the results are applied to the lorenz equations showing that its strange attractor is contained in a region of controllability in which its dynamics can be altered e g to yield periodic motions

a minimum range approach to blind extraction of bounded sources in spite of the numerous approaches that have been derived for solving the independent component analysis ica problem it is still interesting to develop new methods when among other reasons specific a priori knowledge may help to further improve the separation performances in this paper the minimum range approach to blind extraction of bounded source is investigated the relationship with other existing well known criteria is established it is proved that the minimum range approach is a contrast and that the criterion is discriminant in the sense that it is free of spurious maxima the practical issues are also discussed and a range measure estimation is proposed based on the order statistics an algorithm for contrast maximization over the group of special orthogonal matrices is proposed simulation results illustrate the performances of the algorithm when using the proposed range estimation criterion

singular perturbations in manufacturing an asymptotic analysis for a large class of stochastic optimization problems arising in manufacturing is presented a typical example of the problems considered in this paper is a production planning problem with random capacity and demand in this example it is assumed that the capacity of the system fluctuates faster than the other quantities the general model considered here also has a fast controlled markov process in its state description by using the difference in the time scales of different quantities the problem is simplified by averaging out the fast process then asymptotically optimal strategies are constructed from the optimal solutions of the limiting problems the proofs of these results use the theory of viscosity solutions to dynamic programming equations however the formal construction of the asymptotically optimal strategies does not require knowledge of this theory

brief paper distributed discrete time coordinated tracking with a time varying reference state and limited communication this paper studies a distributed discrete time coordinated tracking problem where a team of vehicles communicating with their local neighbors at discrete time instants tracks a time varying reference state available to only a subset of the team members we propose a pd like discrete time consensus algorithm to address the problem under a fixed communication graph we then study the condition on the communication graph the sampling period and the control gain to ensure stability and give the quantitative bound of the tracking errors it is shown that the ultimate bound of the tracking errors is proportional to the sampling period the benefit of the proposed pd like discrete time consensus algorithm is also demonstrated through comparison with an existing p like discrete time consensus algorithm simulation results are presented as a proof of concept

modeling the shape of the scene a holistic representation of the spatial envelope in this paper we propose a computational model of the recognition of real world scenes that bypasses the segmentation and the processing of individual objects or regions the procedure is based on a very low dimensional representation of the scene that we term the spatial envelope we propose a set of perceptual dimensions naturalness openness roughness expansion ruggedness that represent the dominant spatial structure of a scene then we show that these dimensions may be reliably estimated using spectral and coarsely localized information the model generates a multidimensional space in which scenes sharing membership in semantic categories e g streets highways coasts are projected closed together the performance of the spatial envelope model shows that specific information about object shape or identity is not a requirement for scene categorization and that modeling a holistic representation of the scene informs about its probable semantic category

the morse spectrum of linear flows on vector bundles for a linear flow on a vector bundle e s a spectrum can be defined in the following way for a chain recurrent component m on the projective bundle pe consider the exponential growth rates associated with finite time e t chains in m and define the morse spectrum mo m over m as the limits of these growth rates as e 0 and t the morse spectrum mo of is then the union over all componentsm pe this spectrum is a synthesis of the topological approach of selgrade and salamon zehnder with the spectral concepts based on exponential growth rates such as the oseledec spectrum or the dichotomy spectrum of sacker sell it turns out that mo contains all lyapunov exponents of for arbitrary initial values and the mo m are closed intervals whose boundary points are actually lyapunov exponents using the fact that is cohomologous to a subflow of a smooth linear flow on a trivial bundle one can prove integral representations of all morse and all lyapunov exponents via smooth ergodic theory a comparison with other spectral concepts shows that in general the morse spectrum is contained in the topological spectrum and the dichotomy spectrum but the spectral sets agree if the induced flow on the base space is chain recurrent however even in this case the associated subbundle decompositions of e may be finer for the morse spectrum than for the dynamical spectrum if one can show that the closure of the floquet spectrum i e the lyapunov spectrum based on periodic trajectories in pe agrees with the morse spectrum then one obtains equality for the floquet the entire oseledec the lyapunov and the morse spectrum we present an example flows induced by c vector fields with hyperbolic chain recurrent components on the projective bundle where this fact can be shown using a version of bowen s shadowing lemma

nonsmooth optimization via quasi newton methods we investigate the behavior of quasi newton algorithms applied to minimize a nonsmooth function f not necessarily convex we introduce an inex act line search that generates a sequence of nested intervals containing a set of points of nonzero measure that satisfy the armijo and wolfe conditions if f is absolutely continuous along the line furthermore the line search is guaranteed to terminate if f is semi algebraic it seems quite difficult to establish a convergence theorem for quasi newton methods applied to such general classes of functions so we give a care ful analysis of a special but illuminating case the euclidean norm in one variable using the inexact line search and in two variables assuming that the line search is exact in practice we find that when f is locally lipschitz and semi algebraic with bounded sublevel sets the bfgs broyden fletcher goldfarb shanno method with the inexact line search almost always generates sequences whose cluster points are clarke stationary and with function values converging r linearly to a clarke station ary value we give references documenting the successful use of bfgs in a variety of nonsmooth applications particularly the design of low order controllers for linear dynamical systems we conclude with a challenging open question

descent algorithms on oblique manifold for source adaptive ica contrast a riemannian manifold optimization strategy is proposed to facilitate the relaxation of the orthonormality constraint in a more natural way in the course of performing independent component analysis ica that employs a mutual information based source adaptive contrast function despite the extensive development of manifold techniques catering to the orthonormality constraint only a limited number of works have been dedicated to oblique manifold ob algorithms to intrinsically handle the normality constraint which has been empirically shown to be superior to other riemannian and euclidean approaches imposing the normality constraint implicitly in line with the ica definition essentially guarantees a substantial improvement in the solution accuracy by way of increased degrees of freedom while searching for an optimal unmixing ica matrix in contrast with the orthonormality constraint designs of the steepest descent conjugate gradient with hager zhang or a hybrid update parameter quasi newton and cost effective quasi newton methods intended for ob are presented in this paper their performance is validated using natural images and systematically compared with the popular state of the art approaches in order to assess the performance effects of the choice of algorithm and the use of a riemannian rather than euclidean framework we surmount the computational challenge associated with the direct estimation of the source densities using the improved fast gauss transform in the evaluation of the contrast function and its gradient the proposed ob schemes may find applications in the offline image signal analysis wherein on one hand the computational overhead can be tolerated and on the other the solution quality holds paramount interest

optimal control with state space constraint i optimal control of piecewise deterministic processes with state space constraint is studied under appropriate assumptions it is shown that the optimal value function is the only viscosity solution on the open domain which is also a supersolution on the closed domain finally the uniform continuity of the value function is obtained under a condition on the deterministic drift

cluster consensus control of generic linear multi agent systems under directed topology with acyclic partition this paper investigates the cluster consensus control for generic linear multi agent systems mass under directed interaction topology via distributed feedback controller focus of this paper is particularly on addressing the following problem which is of both theoretical and practical interests but have not been considered in the existing literature under what kind of interaction among the clusters can the cluster consensus control be achieved regardless of the magnitudes of the coupling strengths among the agents directed acyclic interaction topology among the clusters is proved to have this property as opposed to the algebraic conditions provided in the existing literature conditions for guaranteeing the cluster consensus control in this paper are presented in terms of purely the graphic topology conditions and thus are very easy to be verified

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

applications of singular perturbation techniques to control problems this paper discusses typical applications of singular perturbation techniques to control problems in the last fifteen years the first three sections are devoted to the standard model and its time scale stability and controllability properties the next two sections deal with linear quadratic optimal control and one with cheap near singular control then the composite control and trajectory optimization are considered in two sections and stochastic control in one section the last section returns to the problem of modeling this time in the context of large scale systems the bibliography contains more than 250 titles

independent component analysis based on nonparametric density estimation in this paper we introduce a novel independent component analysis ica algorithm which is truly blind to the particular underlying distribution of the mixed signals using a nonparametric kernel density estimation technique the algorithm performs simultaneously the estimation of the unknown probability density functions of the source signals and the estimation of the unmixing matrix following the proposed approach the blind signal separation framework can be posed as a nonlinear optimization problem where a closed form expression of the cost function is available and only the elements of the unmixing matrix appear as unknowns we conducted a series of monte carlo simulations involving linear mixtures of various source signals with different statistical characteristics and sample sizes the new algorithm not only consistently outperformed all state of the art ica methods but also demonstrated the following properties 1 only a flexible model capable of learning the source statistics can consistently achieve an accurate separation of all the mixed signals 2 adopting a suitably designed optimization framework it is possible to derive a flexible ica algorithm that matches the stability and convergence properties of conventional algorithms 3 a nonparametric approach does not necessarily require large sample sizes in order to outperform methods with fixed or partially adaptive contrast functions

bipartite containment tracking of signed networks abstract this paper considers a class of bipartite containment tracking problems for leader following networks associated with signed digraphs it admits multiple leaders which can be not only stationary but also dynamically changing via interactions between them and their neighbored leaders it is shown that the followers can converge to the convex hull containing each leader s trajectory as well as its symmetric trajectory which is the same as it in modulus but different in sign in particular if the adjacency weight matrix of the digraph is not signed but nonnegative then the leader following network achieves the traditional containment tracking simulation tests are performed to illustrate the observed bipartite containment tracking performances of signed networks

leader follower containment control over directed random graphs the leader follower consensus problem for multi agent systems over directed random graphs is investigated motivated by the fact that inter agent communication can be subject to random failure when agents perform tasks in a complex environment a directed random graph is used to model the random loss of communication between agents where the connection of the directed edge in the graph is assumed to be probabilistic and evolves according to a two state markov model in the leader follower network the leaders maintain a constant desired state and the followers update their states by communicating with local neighbors over the random communication network based on convex properties and a stochastic version of lasalle s invariance principle almost sure convergence of the followers states to the convex hull spanned by the leaders states is established for the leader follower random network a numerical simulation is provided to demonstrate the developed result

duality in linear programming problems related to deterministic long run average problems of optimal control it has been established recently that under mild conditions deterministic long run average problems of optimal control are asymptotically equivalent to infinite dimensional linear programming problems lpps and that these lpps can be approximated by finite dimensional lpps in this paper we introduce the corresponding infinite and finite dimensional dual problems and study duality relationships we also investigate the possibility of using solutions of finite dimensional lpps and their duals for numerical construction of the optimal controls in periodic optimization problems the construction is illustrated with a numerical example

exit time problems in optimal control and vanishing viscosity method the authors study the connections between deterministic exit time control problems and possibly discontinuous viscosity solutions of a first order hamilton jacobi hj equation up to the boundary this equation admits a maximum and a minimum solution that are the value functions associated to stopping time problems on the boundary when these solutions are equal they can be obtained through the vanishing viscosity method finally when the hj equation has a continuous solution it is proved to be the value function for the first exit time of the domain it is also the vanishing viscosity limit arising in particular in some large deviations problems

containment control of multi agent systems in a noisy communication environment the containment problem of first order and second order integral multi agent systems with communication noises is investigated in this paper motivated by the previous work a time varying gain a t is introduced to attenuate the noise effect it is proved that the proposed protocol can solve the mean square containment problem if the following conditions hold 1 the communication topology graph has a spanning forest whose roots are leaders of the multi agent system 2 0 a t dt 3 lim t a t 0 moreover if a t is uniformly continuous these conditions are necessary for ensuring the mean square containment in addition the proposed protocol is also extended to allow the case where each agent has its own gain a i t it is proved that the mean square containment problem can still be solved if all agent dependent gains are infinitesimals of the same order as time goes to infinity finally two simulation examples are provided to demonstrate the effectiveness of the proposed protocols

suboptimization of singularly perturbed control systems a technique different from the boundary layer method is developed to deal with singularly perturbed optimal control problems the technique is applicable in particular in the case when the optima

three dimensional formation merging control under directed and switching topologies this paper concentrates on the formation merging control problem for a leader follower network the objective is to control a team of agents called followers such that they are merged with another team of agents called leaders to form a single globally rigid formation a method based on graph laplacian is introduced to address this problem each follower selects its interaction neighbors and interaction weights according to the given target configuration the graph modeling the interaction topology of all the agents is directed and time varying first by assuming that the synchronized velocity of the leaders is known to all the followers a necessary and sufficient condition is derived to ensure uniform asymptotic formation merging second we relax this assumption and consider that the velocity of the leaders is known to only a subset of followers for which the same necessary and sufficient condition is obtained with the help of an internal model for velocity synchronization

analysis for a class of singularly perturbed hybrid systems via averaging a class of singularly perturbed hybrid dynamical systems is analyzed the fast states are restricted to a compact set a priori the continuous time boundary layer dynamics produce solutions that are assumed to generate a well defined average vector field for the slow dynamics this average the projection of the jump map in the direction of the slow states and flow and jump sets from the original dynamics define the reduced or average hybrid dynamical system assumptions about the average system lead to conclusions about the original higher dimensional system for example forward pre completeness for the average system leads to a result on closeness of solutions between the original and average system on compact time domains in addition global asymptotic stability for the average system implies semiglobal practical asymptotic stability for the original system we give examples to illustrate the averaging concept and to relate it to classical singular perturbation results as well as to other singular perturbation results that have appeared recently for hybrid systems we also use an example to show that our results can be used as an analysis tool to design hybrid feedbacks for continuous time plants implemented by fast but continuous actuators

distributed adaptive containment control of uncertain nonlinear multi agent systems in strict feedback form abstract this paper presents a distributed containment control approach for uncertain nonlinear strict feedback systems with multiple dynamic leaders under a directed graph topology where the leaders are neighbors of only a subset of the followers the strict feedback followers with nonparametric uncertainties are considered and the local adaptive dynamic surface controller for each follower is designed using only neighbors information to guarantee that all followers converge to the dynamic convex hull spanned by the dynamic leaders where the derivatives of leader signals are not available to implement controllers i e the position information of leaders is only required the function approximation technique using neural networks is employed to estimate nonlinear uncertainty terms derived from the controller design procedure for the followers it is shown that the containment control errors converge to an adjustable neighborhood of the origin

containment control in mobile networks in this paper the problem of driving a collection of mobile robots to a given target destination is studied in particular we are interested in achieving this transfer in an orderly manner so as to ensure that the agents remain in the convex polytope spanned by the leader agents while the remaining agents only employ local interaction rules to this aim we exploit the theory of partial difference equations and propose hybrid control schemes based on stop go rules for the leader agents non zenoness liveness and convergence of the resulting system are also analyzed

long time behavior of stochastic multimolecular reaction model abstract in the paper we focus on asymptotic behavior of a stochastic multimolecular reaction model our main goal is not only to prove the permanence of the reaction but also to estimate the polynomial convergence rate of the transition probability to an invariant probability measure our result gives a precise characterization of the rate with which the different powers of a test function converges in terms of the exponent the rate of convergence is proved to be bounded above by any polynomial decay

periodic near optimal control we consider the infinite time optimal control problem of minimizing an average cost functional for nonlinear singularly perturbed systems in particular we are interested in the existence of near optimal trajectories which are periodic for this purpose we investigate nonlinear control systems with three time scales and construct a limiting system for the slowest motion by an iterated averaging procedure we furthermore show that global tools invariant control sets and local tools lie algebra ranks of vector fields are preserved under singular perturbations the existence of periodic near optimal trajectories is verified under the condition that the fast subsystem and an unperturbed slow subsystem are controllable and that a standard lie algebra rank condition for local accessibility holds

averaging method for discontinuous mayer s problem of singularly perturbed control systems abstract in the present paper we prove that the optimal cost of a mayer s problem for a control system with singular perturbation does converge to the optimal cost of a mayer s problem associated with control system obtained by averaging the main novelty of our result lies on the fact that we did not require any continuity assumption on the final cost

controllability of product systems abstract for nonlinear continuous time control systems we introduce the notion of controllability with selectable time which is a little bit stronger than the usual controllability notion for a large class of nonlinear systems on compact manifolds controllability with selectable time is equivalent to controllability together with strong accessibility it turns out that the controllability of products of independent control systems is related to this new controllability notion the main result states that a smooth control affine product system is controllable if and only if all factors are controllable and at most one factor is not controllable with selectable time provided the accessibility algebra of the product system has full rank

some properties of viscosity solutions of hamilton jacobi equations abstract recently m g crandall and p l lions introduced the notion of viscosity solutions of scalar nonlinear first order partial differential equations viscosity solutions need not be differentiable anywhere and thus are not sensitive to the classical problem of the crossing of characteristics the value of this concept is established by the fact that very general existence uniqueness and continuous dependence results hold for viscosity solutions of many problems arising in fields of application the notion of a viscosity solution admits several equivalent formulations here we look more closely at two of these equivalent criteria and exhibit their virtues by both proving several new facts and reproving various known results in a simpler manner moreover by forsaking technical generality we hereby provide a more congenial introduction to this subject than the original paper author

containment control of single integrator network with limited communication data rate this technical note investigates distributed containment control for a single integrator continuous time multi agent system with a limited communication data rate network topology is a directed communication graph the containment control with quantized communication for each follower is designed using only its neighbour s quantized information so that all followers move into the convex hull spanned by the leaders necessary and sufficient criteria which guarantee achievement of containment consensus are given if the communication data rates are unfixed or fixed under a given bound on communication data rate an algorithm is established to achieve the containment consensus finally all the theoretical results are illustrated by numerical simulations

suboptimal control of singularly perturbed systems and periodic optimization a traditional approach to singularly perturbed optimal control problems is based on an approximation of these problems by reduced problems which are obtained via the formal replacement of the fast variables by the states of equilibrium of the fast subsystems considered with frozen slow variables and controls it is shown that such an approximation is valid if and only if certain families of periodic optimization problems admit steady state solutions it is also shown how the solutions of these problems can be used to construct suboptimal controls for singularly perturbed problems when approximation by reduced problems is not possible

on singular perturbations for differential inclusions on the infinite interval abstract we consider a differential inclusion subject to a singular perturbation i e part of the derivatives are multiplied by a small parameter 0 we show that under some stability and structural assumptions every solution of the singularly perturbed inclusion comes close to a solution of the degenerate inclusion obtained for 0 when tends to 0 the goal of the present paper is to provide a new result of tikhonov type on the time interval 0

dynamic leaders containment control of high order multi agent systems with state time delay an lmi approach abstractthis paper addresses the containment control of a multi agent system with dynamic leaders while considering the state time delay and time varying input disturbances the agents dynamics are assumed to be high order integrals and an unkown state time delay with a known upper bound is considered in order to deal with dynamic leaders and time varying input disturbances an appropriate distributed pip type based control protocol is proposed in this study thereafter utilising the lyapunov krasovskii stability theorem and based on lmi linear matrix inequality approach two theorems are proved which guarantee asymptotically stability of the multi agent system with fixed and switching networks in addition to stability assurance the gains of the proposed protocol are achieved through solving the lmi finally some numerical examples are given to demonstrate the validity of the theoretical results