recovering the initial state of an infinite dimensional system using observers let a be the generator of a strongly continuous semigroup t on the hilbert space x and let c be a linear operator from d a to another hilbert space y possibly unbounded with respect to x not necessarily admissible we consider the problem of estimating the initial state z 0 d a with respect to the norm of x from the output function y t ct tz 0 given for all t in a bounded interval 0 t we introduce the concepts of estimatability and backward estimatability for a c in a more general way than currently available in the literature we introduce forward and backward observers and we provide an iterative algorithm for estimating z 0 from y this algorithm generalizes various algorithms proposed recently for specific classes of systems and it is an attractive alternative to methods based on inverting the gramian our results lead also to a very general formulation of russell s principle i e estimatability and backward estimatability imply exact observability this general formulation of the principle does not require t to be invertible we illustrate our estimation algorithms on systems described by wave and schrodinger equations and we provide results from numerical simulations

controlled symmetries and passive walking in this note we investigate the relationship between nonlinear control and passive walking in bipedal locomotion for the general case of an n degree of freedom biped in three dimensional space we introduce the notion of controlled symmetry to capture the effect of the control input on the invariance of the system lagrangian under group action we then show the existence of a controlled symmetry for general bipeds under the action of so 3 taking into account not only the kinetic energy but also the potential energy and impact dynamics we use this result to show the existence of a nonlinear control law that reproduces so called passive gaits independent of the particular ground slope our contribution in this note is two fold first our result contains the first rigorous proof of the existence of so called passivity mimicking control laws that explicitly accounts for the impact dynamics second whereas previous papers have studied only planar bipeds with and without knees our result is completely general our results can be viewed as direct extensions of several previous results such as passivity based control virtual gravity and virtual passive dynamic walking from the planar case to general n degrees of freedom dof robots in three dimensional space

incremental stochastic subgradient algorithms for convex optimization this paper studies the effect of stochastic errors on two constrained incremental subgradient algorithms the incremental subgradient algorithms are viewed as decentralized network optimization algorithms as applied to minimize a sum of functions when each component function is known only to a particular agent of a distributed network first the standard cyclic incremental subgradient algorithm is studied in this the agents form a ring structure and pass the iterate in a cycle when there are stochastic errors in the subgradient evaluations sufficient conditions on the moments of the stochastic errors are obtained that guarantee almost sure convergence when a diminishing step size is used in addition almost sure bounds on the algorithm s performance with a constant step size are also obtained next the markov randomized incremental subgradient method is studied this is a noncyclic version of the incremental algorithm where the sequence of computing agents is modeled as a time nonhomogeneous markov chain such a model is appropriate for mobile networks as the network topology changes across time in these networks convergence results and error bounds for the markov randomized method in the presence of stochastic errors for diminishing and constant step sizes are obtained

stability analysis and control of rigid body systems with impacts and friction many critical tasks in robotics such as locomotion or manipulation involve collisions between a rigid body and the environment or between multiple bodies methods based on sums of squares sos for numerical computation of lyapunov certificates are a powerful tool for analyzing the stability of continuous nonlinear systems and can additionally be used to automatically synthesize stabilizing feedback controllers here we present a method for applying sums of squares verification to rigid bodies with coulomb friction undergoing discontinuous inelastic impact events the proposed algorithm explicitly generates lyapunov certificates for stability positive invariance and safety over admissible non penetrating states and contact forces we leverage the complementarity formulation of contact which naturally generates the semialgebraic constraints that define this admissible region the approach is demonstrated on multiple robotics examples including simple models of a walking robot a perching aircraft and control design of a balancing robot

an implicit finite volume method for the solution of 3d low mach number viscous flows using a local preconditioning technique this paper presents a cell centered high order finite volume scheme for the solution of the three dimensional 3d navier stokes equations with low mach number the system of non linear equations is solved by means of a fully implicit pseudo transient scheme each pseudo time step is solved by a newton gmres procedure a local preconditioning technique is used to scale the speed of sound and to improve the system condition number for low mach number and low cell reynolds number this preconditioning is applied to the ausm up flux vector splitting function the method is tested on 2d and 3d low mach number laminar flows

computational study of incompressible turbulent flows with method of characteristics the current study presents numerical investigation of incompressible turbulent flow momentum and continuity equations are coupled by the artificial compressibility method acm the one equation spalart allmaras turbulence model along with rans reynolds averaged navier stokes equations is used to calculate reynolds stresses in 2 d problems for convective fluxes a characteristic based cb finite volume solution has been developed also a revised jameson averaging avr method was implemented in comparison the proposed cb upwind scheme demonstrated very accurate results high stability and faster convergence for time discretization the fifth order runge kutta scheme is used as the convergence acceleration techniques the local time stepping and implicit residual smoothing were applied considering flow behavior suitable boundary conditions have been implemented cross flow around a horizontal circular cylinder at high reynolds numbers has been studied as a benchmark the results obtained using the new proposed scheme are in good agreement with the standard available solutions in the literature

stability analysis of velocity aided attitude observers for accelerated vehicles an advanced nonlinear observer for rigid bodies evolving in 3d space relying on measurement data provided by an imu and linear velocity measured in the body fixed frame has been recently proposed but without specifying its domain of convergence and stability with respect to conventional attitude observers which do not involve linear velocity measurements this observer is better adapted for vehicles subjected to sustained accelerations this paper presents further modifications yielding two velocity aided attitude observers with rigorous almost global convergence and stability analysis moreover the estimation of the gravity direction is globally decoupled from magnetometer measurements

an invariant observer for a chemostat model in this paper we tackle the problem of designing an invariant observer for a chemostat model with adjustable and robust convergence the main idea of the paper is to build a new class of observers for chemostat model using hidden symmetries the effectiveness of the proposed observer is shown through simulations

lie algebraic stability conditions for nonlinear switched systems and differential inclusions abstract we present a stability criterion for switched nonlinear systems which involves lie brackets of the individual vector fields but does not require that these vector fields commute a special case of the main result says that a switched system generated by a pair of globally asymptotically stable nonlinear vector fields whose third order lie brackets vanish is globally uniformly asymptotically stable under arbitrary switching this generalizes a known fact for switched linear systems and provides a partial solution to the open problem posed in d liberzon lie algebras and stability of switched nonlinear systems in v blondel a megretski eds unsolved problems in mathematical systems and control theory princeton university press nj 2004 pp 203 207 to prove the result we consider an optimal control problem which consists in finding the most unstable trajectory for an associated control system and show that there exists an optimal solution which is bang bang with a bound on the total number of switches this property is obtained as a special case of a reachability result by bang bang controls which is of independent interest by construction our criterion also automatically applies to the corresponding relaxed differential inclusion

the structure of nonlinear control systems possessing symmetries a concept of symmetry is defined for general nonlinear control systems it is shown under various technical conditions that nonlinear control systems with symmetries admit local and or global decompositions in terms of lower dimensional subsystems and feedback loops the structure of the individual subsystems is dependent on the structure of the symmetry group for example if the symmetry group is abelian one of the subsystems is a quadrature an additional feature of the decomposition is that the state space dimensions of the subsystems sum to the state space dimension of the original system

lyapunov theory for zeno stability zeno behavior is a dynamic phenomenon unique to hybrid systems in which an infinite number of discrete transitions occurs in a finite amount of time this behavior commonly arises in mechanical systems undergoing impacts and optimal control problems but its characterization for general hybrid systems is not completely understood the goal of this paper is to develop a stability theory for zeno hybrid systems that parallels classical lyapunov theory that is we present lyapunov like sufficient conditions for zeno behavior obtained by mapping solutions of complex hybrid systems to solutions of simpler zeno hybrid systems defined on the first quadrant of the plane these conditions are applied to lagrangian hybrid systems which model mechanical systems undergoing impacts yielding simple sufficient conditions for zeno behavior finally the results are applied to robotic bipedal walking

a general framework for population based distributed optimization over networks abstract this paper presents a population based solution for the distributed optimization problem where the overall objective function is defined as an average of local cost functions corresponding to the nodes of a network populations are introduced for the nodes to cooperatively find the global optimum of the overall objective function the main challenge is that each population cannot know the overall objective function and thus cannot directly evaluate the quality of their individuals in each iteration to overcome this difficulty we introduce consensus methods to design a message passing protocol under which the local estimates can converge to the same value we present a general framework that consists of consensus search consensus evaluation population evolution and local stopping steps compared with mathematical methods this framework solves in network distributed optimization problems without requiring a convexity assumption on the objective functions the standard pso and one of its variants called mco are introduced for testing and comparison two simulated examples under different network topologies illustrate the feasibility of our approach

an asymptotic preserving all speed scheme for the euler and navier stokes equations we present an asymptotic preserving all speed scheme for the simulation of compressible flows valid at all mach numbers ranging from very small to order unity the scheme is based on a semi implicit discretization which treats the acoustic part implicitly and the convective and diffusive parts explicitly this discretization which is the key to the asymptotic preserving property provides a consistent approximation of both the hyperbolic compressible regime and the elliptic incompressible regime the divergence free condition on the velocity in the incompressible regime is respected and an the pressure is computed via an elliptic equation resulting from a suitable combination of the momentum and energy equations the implicit treatment of the acoustic part allows the time step to be independent of the mach number the scheme is conservative and applies to steady or unsteady flows and to general equations of state one and two dimensional numerical results provide a validation of the asymptotic preserving all speed properties

steady turbulent flow computations using a low mach fully compressible scheme a recently proposed modification to fully compressible schemes significantly improves the resolution of low mach number features tackling the problem of excessive numerical dissipation as the mach number reduces this paper explores the application of this modification to reynolds averaged navier stokes simulations using second and fifth order in space schemes following verification of the modeling approach four test cases are employed to highlight the scheme performance including a backward facing step a two dimensional lid driven cavity the naca 4412 airfoil incorporating a trailing edge separation and finally a mach 2 25 oblique shock wave boundary layer interaction it demonstrates first that the converged solution is grid and scheme independent as expected and that the low mach number correction provides a significant improvement in low mach number regions because this correction is easy to implement computationally inexpensive and stable the conclusion is that it should be recommend

nonlinear complementary filters on the special linear group this article proposes a nonlinear complementary filter for the special linear lie group sl 3 that fuses low frequency state measurements with partial velocity measurements and adaptive estimation of unmeasured slowly changing velocity components the obtained results have direct application on the problem of filtering a sequence of image homographies acquired from low quality video data the considered application motivates us to derive results that provide adaptive estimation of the full group velocity or part of the group velocity that cannot be measured from sensors attached to the camera we demonstrate the performance of the proposed filters on real world homography data

a high order numerical algorithm for dns of low mach number reactive flows with detailed chemistry and quasi spectral accuracy a novel and efficient algorithm is presented in this paper to deal with dns of turbulent reacting flows under the low mach number assumption with detailed chemistry and a quasi spectral accuracy the temporal integration of the equations relies on an operating split strategy where chemical reactions are solved implicitly with a stiff solver and the convection diffusion operators are solved with a runge kutta chebyshev method the spatial discretisation is performed with high order compact schemes and a fft based constant coefficient spectral solver is employed to solve a variable coefficient poisson equation the numerical implementation takes advantage of the 2decomp fft libraries developed by 1 which are based on a pencil decomposition method of the domain and are proven to be computationally very efficient an enhanced pressure correction method is proposed to speed up the achievement of machine precision accuracy it is demonstrated that a second order accuracy is reached in time while the spatial accuracy ranges from fourth order to sixth order depending on the set of imposed boundary conditions the software developed to implement the present algorithm is called holomac and its numerical efficiency opens the way to deal with dns of reacting flows to understand complex turbulent and chemical phenomena in flames

on the regularization of zeno hybrid automata fundamental properties of hybrid automata such as existence and uniqueness of executions are studied particular attention is devoted to zeno hybrid automata which are hybrid automata that take infinitely many discrete transitions in finite time it is shown that regularization techniques can be used to extend the zeno executions of these automata to times beyond the zeno time different types of regularization may however lead to different extensions a water tank control problem and a bouncing ball system are used to illustrate the results

zeno stability of the set valued bouncing ball hybrid dynamical systems consist of both continuous time and discrete time dynamics a fundamental phenomenon that is unique to hybrid systems is zeno behavior where the solution involves an infinite number of discrete transitions occurring in finite time as best illustrated in the classical example of a bouncing ball in this note we study the hybrid system of the set valued bouncing ball for which the continuous time dynamics has a set valued right hand side this system is typically used for deriving bounds on the solution of nonlinear single valued hybrid systems in a small neighborhood of a zeno equilibrium point in order to establish its local stability we utilize methods of lyapunov analysis and optimal control to derive a necessary and sufficient condition for zeno stability of the set valued bouncing ball system and to obtain a tight bound on the zeno time as a function of initial conditions

intrinsic observer based stabilization for simple mechanical systems on lie groups this paper presents a dynamic observer for a class of simple mechanical systems on lie groups this observer provides velocity estimates based on configuration measurements the observer is textit intrinsic so its performance does not depend on the choice of coordinates and it is textit coordinate free in the sense that the equations may be written explicitly without specifying coordinates for the configuration space our main result is obtained by specializing a previous result of aghannan and rouchon concerning velocity estimation of simple mechanical systems on riemannian manifolds to such systems on lie groups this specialization is nonobvious and extremely powerful further we extend the original result to include velocity dependent external forces this estimator combined with a coordinate free formulation of passivity based state feedback control allows the construction of a coordinate free intrinsic dynamic output feedback compensator this is to our knowledge the first time such a result has been reported explicit expressions are computed for the lie groups so 3 and se 3 allowing easy specialization to practical problems of rigid body motion the theory is illustrated via application to the axisymmetric top and to a six degrees of freedom microelectromechanical system

stability and completion of zeno equilibria in lagrangian hybrid systems this paper studies lagrangian hybrid systems which are a special class of hybrid systems modeling mechanical systems with unilateral constraints that are undergoing impacts this class of systems naturally display zeno behavior an infinite number of discrete transitions that occur in finite time leading to the convergence of solutions to limit sets called zeno equilibria this paper derives simple conditions for stability of zeno equilibria utilizing these results and the constructive techniques used to prove them the paper introduces the notion of a completed hybrid system which is an extended hybrid system model allowing for the extension of solutions beyond zeno points a procedure for practical simulation of completed hybrid systems is outlined and conditions guaranteeing upper bounds on the incurred numerical error are derived finally we discuss an application of these results to the stability of unilaterally constrained motion of mechanical systems under perturbations that violate the constraint

symmetry preserving observers this paper presents the theory of invariant observers i e symmetry preserving observers we consider an observer to consist of a copy of the system and a correction term and we propose a constructive method based on the cartan moving frame method to find all the symmetry preserving correction terms the construction relies on an invariant frame a classical notion and on an invariant output error a less standard notion precisely defined here using the theory we build three non linear observers for three examples of engineering interest a non holonomic car a chemical reactor and an inertial navigation system for each example the design is based on physical symmetries and the convergence analysis relies on the use of invariant state errors a symmetry preserving way to define the estimation error

state estimation for invariant systems on lie groups with delayed output measurements this paper proposes a state estimation methodology for invariant systems on lie groups where outputs of the system are measured with delay the proposed method is based on cascading an observer and a predictor the observer uses delayed measurements and provides estimates of delayed states the predictor uses those estimates together with the current inputs of the system to compensate for the delay and to provide a prediction of the current state of the system we consider three classes of left invariant right invariant and mixed invariant systems and propose predictors tailored to each class the key contribution of the paper is to exploit the underlying symmetries of systems to design novel predictors that are computationally simple and generic in the sense that they can be combined with any stable observer or filter we provide a rigorous stability analysis demonstrating that the prediction of the current state converges to the current system trajectory if the observer state converges to the delayed system trajectory the good performance of the proposed approach is demonstrated using a sophisticated software in the loop simulator indicating the robustness of the observer predictor methodology even when large measurement delays are present

invariance principles for hybrid systems with connections to detectability and asymptotic stability this paper shows several versions of the lasalle s invariance principle for general hybrid systems the broad framework allows for nonuniqueness of solutions zeno behaviors and does not insist on continuous dependence of solutions on initial conditions instead only a mild structural property involving graphical convergence of solutions is posed the general invariance results are then specified to hybrid systems given by set valued data further results involving invariance as well as observability detectability and asymptotic stability are given

distributed parameter estimation in sensor networks nonlinear observation models and imperfect communication the paper studies distributed static parameter vector estimation in sensor networks with nonlinear observation models and noisy intersensor communication it introduces separably estimable observation models that generalize the observability condition in linear centralized estimation to nonlinear distributed estimation it studies two distributed estimation algorithms in separably estimable models the nu with its linear counterpart lu and the nlu their update rule combines a consensus step where each sensor updates the state by weight averaging it with its neighbors states and an innovation step where each sensor processes its local current observation this makes the three algorithms of the consensus innovations type very different from traditional consensus this paper proves consistency all sensors reach consensus almost surely and converge to the true parameter value efficiency and asymptotic unbiasedness for lu and nu it proves asymptotic normality and provides convergence rate guarantees the three algorithms are characterized by appropriately chosen decaying weight sequences algorithms lu and nu are analyzed in the framework of stochastic approximation theory algorithm nlu exhibits mixed time scale behavior and biased perturbations and its analysis requires a different approach that is developed in this paper

invariant feedback control for the kinematic car on the sphere abstract the design of an invariant tracking control law for the kinematic car driving on a sphere is discussed using a lie group framework a left invariant description on so 3 is derived basic geometric considerations allow a direct comparison of the model with the planar case using a geometrically motivated invariant tracking error on s 2 an invariant feedback design is proposed finally one possible design of an invariant asymptotic observer is sketched

on distributed convex optimization under inequality and equality constraints we consider a general multi agent convex optimization problem where the agents are to collectively minimize a global objective function subject to a global inequality constraint a global equality constraint and a global constraint set the objective function is defined by a sum of local objective functions while the global constraint set is produced by the intersection of local constraint sets in particular we study two cases one where the equality constraint is absent and the other where the local constraint sets are identical we devise two distributed primal dual subgradient algorithms based on the characterization of the primal dual optimal solutions as the saddle points of the lagrangian and penalty functions these algorithms can be implemented over networks with dynamically changing topologies but satisfying a standard connectivity property and allow the agents to asymptotically agree on optimal solutions and optimal values of the optimization problem under the slater s condition

preconditioning method for low speed flows a well known preconditioning method for low mach number e ows is implemented in an existing numerical simulator of viscous and inviscid e ows both details concerning the numerical method and the results of the validationphasearegiven themethodisbasedonatime derivativepreconditioningofthenavier stokesequations using the so called viscous set of variables the pseudoacoustic speed introduced equalizes the eigenvalues so that the history of convergence of the preconditioned system of equations exhibits an increased rate of convergence at low mach numbers the artie cial dissipative terms have been modie ed to let them scale correctly at low speeds in theinviscidcase thevelocitydistributioncalculatedoverthecylinderwiththedescribedmethodmatchesanalytical data numericalresultsconcerningthesimulationofinviscidandturbulente owspastairfoilsarepresented inviscid e ow over the onera m6 wing is also computed it is shown that the preconditioning technique allows both an acceleration in the rate of convergence and a reduction of the wall clock time of an order of magnitude also an improved accuracy of the solution at low mach numbers has been observed

incremental subgradient methods for nondifferentiable optimization we consider a class of subgradient methods for minimizing a convex function that consists of the sum of a large number of component functions this type of minimization arises in a dual context from lagrangian relaxation of the coupling constraints of large scale separable problems the idea is to perform the subgradient iteration incrementally by sequentially taking steps along the subgradients of the component functions with intermediate adjustment of the variables after processing each component function this incremental approach has been very successful in solving large differentiable least squares problems such as those arising in the training of neural networks and it has resulted in a much better practical rate of convergence than the steepest descent method in this paper we establish the convergence properties of a number of variants of incremental subgradient methods including some that are stochastic based on the analysis and computational experiments the methods appear very promising and effective for important classes of large problems a particularly interesting discovery is that by randomizing the order of selection of component functions for iteration the convergence rate is substantially improved

an intrinsic observer for a class of lagrangian systems we propose a new design method of asymptotic observers for a class of nonlinear mechanical systems lagrangian systems with configuration position measurements our main contribution is to introduce a state position and velocity observer that is invariant under any changes of the configuration coordinates the observer dynamics equations as the euler lagrange equations are intrinsic the design method uses the riemannian structure defined by the kinetic energy on the configuration manifold the local convergence is proved by showing that the jacobian of the observer dynamics is negative definite contraction for a particular metric defined on the state space a metric derived from the kinetic energy and the observer gains from a practical point of view such intrinsic observers can be approximated when the estimated configuration is close to the true one by an explicit set of differential equations involving the riemannian curvature tensor these equations can be automatically generated via symbolic differentiations of the metric and potential up to order two numerical simulations for the ball and beam system an example where the scalar curvature is always negative show the effectiveness of such approximation when the measured positions are noisy or include high frequency neglected dynamics

performance of three dimensional compressible navier stokes codes at low mach numbers the low mach number performance of two widely used three dimensional compressible navier stokes solvers is examined both of the codes employ a finite volume formulation but differ in their respective discretization and solution schemes in the first code a central difference discretization is employed and solutions are obtained using an explicit runge kutta time stepping scheme in the second code an upwind biased discretization is used and an implicit approximate factorization scheme is employed the accuracy and efficiency of the codes are assessed by comparison with results from an incompressible navier stokes solver and experimental data the test cases examined include an untwisted rectangular wing and a wing fuselage configuration the computed pressure distributions were nearly identical and agreed quite well with experimental data in addition the predicted pressure distributions were nearly identical to those predicted by the incompressible flow solver the influence of freestream mach number on the efficiency of both compressible flow solvers also is examined

a unifying review of linear gaussian models factor analysis principal component analysis mixtures of gaussian clusters vector quantization kalman filter models and hidden markov models can all be unified as variations of unsupervised learning under a single basic generative model this is achieved by collecting together disparate observations and derivations made by many previous authors and introducing a new way of linking discrete and continuous state models using a simple nonlinearity through the use of other nonlinearities we show how independent component analysis is also a variation of the same basic generative model we show that factor analysis and mixtures of gaussians can be implemented in autoencoder neural networks and learned using squared error plus the same regularization term we introduce a new model for static data known as sensible principal component analysis as well as a novel concept of spatially adaptive observation noise we also review some of the literature involving global and local mixtures of the basic models and provide pseudocode for inference and learning for all the basic models

dynamical properties of hybrid automata hybrid automata provide a language for modeling and analyzing digital and analogue computations in real time systems hybrid automata are studied here from a dynamical systems perspective necessary and sufficient conditions for existence and uniqueness of solutions are derived and a class of hybrid automata whose solutions depend continuously on the initial state is characterized the results on existence uniqueness and continuity serve as a starting point for stability analysis lyapunov s theorem on stability via linearization and lasalle s invariance principle are generalized to hybrid automata

brief paper a globally exponentially convergent immersion and invariance speed observer for mechanical systems with non holonomic constraints the problem of velocity estimation for general n degrees of freedom mechanical systems is of great practical and theoretical interest for unconstrained systems many partial solutions have been reported in the literature however even in this case the basic question of whether it is possible to design a globally convergent speed observer remains open in this paper an affirmative answer to the question is given for general mechanical systems with knon holonomic constraints by proving the existence of a 3n 2k 1 dimensional globally exponentially convergent speed observer an observer for unconstrained mechanical systems is obtained as a particular case of this general result instrumental for the construction of the speed observer is the use of the immersion and invariance technique in which the observer design problem is recast as a problem of rendering attractive and invariant a manifold defined in the extended state space of the plant and the observer

representations of symmetric linear dynamical systems the purpose of this paper is to study static symmetries in linear time invariant differential dynamical systems the main result is a representation theorem which brings the symmetry strongly into evidence this result is then applied to a number of examples involving permutations and rotations we close by proving a general result on the representation of compact groups on the ring of unimodular polynomial matrices

gradient convergence in gradient methods with errors we consider the gradient method x t 1 x t g t s t w t where s t is a descent direction of a function f rn to re and w t is a deterministic or stochastic error we assume that gr f is lipschitz continuous that the stepsize g t diminishes to 0 and that s t and w t satisfy standard conditions we show that either f x t to infty or f x t converges to a finite value and gr f x t to0 with probability 1 in the stochastic case and in doing so we remove various boundedness conditions that are assumed in existing results such as boundedness from below of f boundedness of gr f x t or boundedness of xt

symmetries in optimal control it is argued that the existence of symmetries may simplify as in classical mechanics the solution of optimal control problems a procedure for obtaining symmetries for the optimal hamiltonian resulting from the maximum principle is given this avoids the actual calculation of the optimal hamiltonian this procedure is based upon the notion of symmetry for the hamiltonian system with inputs and outputs associated with an optimal control problem

nonlinearizable single input control systems do not admit stationary symmetries the main result of the paper states that almost any analytic single input control system which is truly nonlinear that is not feedback linearizable with controllable linearization at an equilibrium point does not admit any symmetry preserving that point by almost any system we mean that we exclude a small class of odd systems that admit just one nontrivial symmetry conjugated to minus identity the obtained results are based on a recent classification of nonlinear single input systems under formal feedback we also describe symmetries of feedback linearizable systems

observer based hamiltonian identification for quantum systems a symmetry preserving observer based parameter identification algorithm for quantum systems is proposed starting with a 2 level quantum system qubit where the unknown parameters consist of the atom laser frequency detuning and coupling constant we prove an exponential convergence result the analysis is inspired by lyapunov and adaptive control techniques and is based on averaging theory the observer is then extended to the multi level case where all the atom laser coupling constants are unknown the extension of the convergence analysis is discussed through some heuristic arguments the relevance and the robustness with respect to various noises are tested through numerical simulations

observers for compressible navier stokes equation we consider a multidimensional model of a compressible fluid in a bounded domain we want to estimate the density and velocity of the fluid based on the observations for only velocity we build an

on the cancellation problem in calculating compressible low mach number flows in calculating low mach number flows one faces the stiffness problem in two different facets the applicable time steps become very small the constants of the cancellation errors become very large 1 usually the first point receives attention here we want toconcentrate on the cancellation problem only to our knowledge there is no detailed investigation of this problem in the related literature in primitive variable formulations the problem can be solved by using the pressure coefficient instead of the pressure and a similar variable for the temperature or the internal energy in conservative variable formulations this is thought not to be possible and therefore is sacrificed we are able to show that a local reference state can also be introduced into a conservative scheme if carefully applied to all quantities and applied to all constituent parts of the program a detailed error analysis is given for all these parts finally we show that we can perform a very low mach number calculation atm 10 11with a seven digits arithmetic only and still maintain the set of conservative variables the governing equations are unaltered and the method depends neither on the time integration scheme nor the specific discretization the method should be used in connection with the standard strategies like preconditioning multigrid or an semi implicit method if acceleration is desired

computation of low speed flow with heat addition a perturbation expansion is used to obtain a system of conservation laws for compressible flows that is valid at arbitrarily low mach numbers these equations are rendered hyperbolic by adding an artificial time derivative to the energy equation thus introducing pseudoacoustic waves with a speed the same order as the particle velocity traditional time iterative schemes are shown to be effective in solving this system numerically stability calculations of the complete vector system indicate unconditional stability at all mach numbers in the absence of gravity but the source term introduced by buoyancy becomes destabilizing at froude numbers below about 1 this instability is amplified by approximate factorization thus precluding solutions with gravity below this mach number level computations of strong heat addition in low mach number flow both with and without gravity confirm the stability predictions convergent solutions are maintained and are used to show the effect of gravity on such flowfields

local observers on linear lie groups with linear estimation error dynamics this technical note proposes local exponential observers for systems on linear lie groups we study two classes of systems in the first class the full state of the system evolves on a linear lie group and is available for measurement in the second class only part of the system s state evolves on a linear lie group and this portion of the state is available for measurement in each case we propose two different observer designs we show that depending on the observer chosen local exponential stability of one of the two observation error dynamics left or right invariant error dynamics is obtained for the first class of systems these results are developed by showing that the estimation error dynamics are differentially equivalent to a stable linear differential equation on a vector space for the second class of system the estimation error dynamics are almost linear we illustrate these observer designs on an attitude estimation problem

integral control on lie groups in this paper we extend the popular integral control technique to systems evolving on lie groups more explicitly we provide an alternative definition of integral action for proportional derivative controlled systems whose configuration evolves on a nonlinear space where configuration errors cannot be simply added up to compute a definite integral we then prove that the proposed integral control allows to cancel the drift induced by a constant bias in both first order velocity and second order torque control inputs for fully actuated systems evolving on abstract lie groups we illustrate the approach by 3 dimensional motion control applications

intrinsic filtering on lie groups with applications to attitude estimation this paper proposes a probabilistic approach to the problem of intrinsic filtering of a system on a matrix lie group with invariance properties the problem of an invariant continuous time model with discrete time measurements is cast into a rigorous stochastic and geometric framework building upon the theory of continuous time invariant observers we introduce a class of simple filters and study their properties without addressing the optimal filtering problem we show that akin to the kalman filter for linear systems the error equation is a markov chain that does not depend on the state estimate thus when the filter s gains are held fixed the noisy error s distribution is proved to converge to a stationary distribution under some convergence properties of the filter with noise turned off we also introduce two novel tools of engineering interest the discrete time invariant extended kalman filter for which the trusted covariance matrix is shown to converge and the invariant ensemble kalman filter the methods are applied to attitude estimation allowing to derive novel theoretical results in this field and illustrated through simulations on synthetic data

linear observed systems on groups abstract we propose a unifying and versatile framework for a class of discrete time systems whose state is an element of a general group g that we call linear observed systems on groups those systems strictly mimic linear systems in the sense that is replaced with group multiplication and linear maps with automorphisms we argue they are the true generalization of linear systems of the form x n 1 f n x n b n u n in the context of state estimation since 1 when g r n the latter systems are recovered 2 they are proved to possess the preintegration property a characteristic property of linear systems that relates continuous time to discrete time and has recently proved extremely useful in robotics applications and 3 we can build observers that ensure the evolution between the true state and estimated state does not depend on the followed trajectory a characteristic feature of luenberger and invariant observers the theory is applied to a 3d inertial navigation example interestingly this example cannot be put in the form of an invariant system and the proposed generalization is required

invariance principles for switching systems via hybrid systems techniques invariance principles and sufficient conditions for asymptotic stability for switching systems are given multiple lyapunov like functions are used and dwell time persistent dwell time and weak dwell time switching signals are considered the invariance principles are derived from general invariance principles for hybrid systems asymptotic stability is concluded under observability assumptions or common bounds on the lyapunov like functions

distributed convex optimization via continuous time coordination algorithms with discrete time communication this paper proposes a novel class of distributed continuous time coordination algorithms to solve network optimization problems whose cost function is a sum of local cost functions associated to the individual agents we establish the exponential convergence of the proposed algorithm under i strongly connected and weight balanced digraph topologies when the local costs are strongly convex with globally lipschitz gradients and ii connected graph topologies when the local costs are strongly convex with locally lipschitz gradients when the local cost functions are convex and the global cost function is strictly convex we establish asymptotic convergence under connected graph topologies we also characterize the algorithm s correctness under time varying interaction topologies and study its privacy preservation properties motivated by practical considerations we analyze the algorithm implementation with discrete time communication we provide an upper bound on the stepsize that guarantees exponential convergence over connected graphs for implementations with periodic communication building on this result we design a provably correct centralized event triggered communication scheme that is free of zeno behavior finally we develop a distributed asynchronous event triggered communication scheme that is also free of zeno with asymptotic convergence guarantees several simulations illustrate our results

symmetry based observers for some water tank problems in this paper we consider a tank containing fluid and we want to estimate the horizontal currents when the fluid surface height is measured the fluid motion is described by shallow water equations in two horizontal dimensions we build a simple nonlinear observer which takes advantage of the symmetries of fluid dynamics laws as a result its structure is based on convolutions with smooth isotropic kernels and the observer is remarkably robust to noise we prove the convergence of the observer around a steady state in numerical applications local exponential convergence is expected the observer is also applied to the problem of predicting the ocean circulation realistic simulations illustrate the relevance of the approach compared with some standard oceanography techniques

a nonlinear position and attitude observer on se 3 using landmark measurements this paper addresses the problem of position and attitude estimation based on landmark readings and velocity measurements a derivation of a nonlinear observer on se 3 is presented using a lyapunov function conveniently expressed as a function of the difference between the estimated and the measured landmark coordinates the resulting feedback laws are explicit functions of the landmark measurements and velocity readings exploiting the sensor information directly in the observer the proposed observer yields almost global asymptotic stabilization of the position and attitude errors and exponential convergence in any closed ball inside the region of attraction also it is shown that the asymptotic convergence of the estimation error trajectories is shaped by the landmark geometry and observer design parameters the problem of non ideal velocity readings is also considered and the observer is augmented to compensate for bias in the angular and linear velocity measurements the resulting position attitude and bias estimation errors are shown to converge exponentially fast to the desired equilibrium points for bounded initial estimation errors simulation results are presented to illustrate the stability and convergence properties of the observer

a simple intrinsic reduced observer for geodesic flow aghannan and rouchon proposed a new design method of asymptotic observers for a class of nonlinear mechanical systems lagrangian systems with configuration position measurements the position and velocity observer is based on the riemannian structure of the configuration manifold endowed with the kinetic energy metric and is intrinsic they proved local convergence when the system is conservative we propose an intrinsic reduced order velocity observer based on the jacobi metric which can be initialized such that it converges exponentially for any initial true velocity for non conservative systems the observer can be used as a complement to the one of aghannan and rouchon more generally the reduced observer provides velocity estimation for geodesic flow with position measurements thus it can be formally used as a fluid flow soft sensor in the case of a perfect incompressible fluid when the curvature is negative in all planes the geodesic flow is sensitive to initial conditions surprisingly in this case we have global exponential convergence and the more unstable the flow is faster is the convergence

explicit convergence rate of a distributed alternating direction method of multipliers consider a set of n agents seeking to solve distributively the minimization problem inf x sum n 1 n f n x where the convex functions f n are local to the agents the popular alternating direction method of multipliers has the potential to handle distributed optimization problems of this kind we provide a general reformulation of the problem and obtain a class of distributed algorithms which encompass various network architectures the rate of convergence of our method is considered it is assumed that the infimum of the problem is reached at a point x star the functions f n are twice differentiable at this point and sum nabla 2 f n x star 0 in the positive definite ordering of symmetric matrices with these assumptions it is shown that the convergence to the consensus x star is linear and the exact rate is provided application examples where this rate can be optimized with respect to the admm free parameter rho are also given

symmetries stability and control in nonlinear systems and networks this paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks specifically it combines standard results on symmetries and equivariance with recent convergence analysis tools based on nonlinear contraction theory and virtual dynamical systems this synergy between structural properties symmetries and convergence properties contraction is illustrated in the contexts of network motifs arising for example in genetic networks from invariance to environmental symmetries and from imposing different patterns of synchrony in a network

non linear symmetry preserving observers on lie groups in this technical note we give a geometrical framework for the design of observers on finite dimensional lie groups for systems which possess some specific symmetries the design and the error between true and estimated state equation are explicit and intrinsic we consider also a particular case left invariant systems on lie groups with right equivariant output the theory yields a class of observers such that the error equation is autonomous the observers converge locally around any trajectory and the global behavior is independent from the trajectory which is reminiscent of the linear stationary case

performance of compressible flow codes at low mach numbers the accuracy and the performance of three two dimensional compressible flow codes at freestream mach numbers as low as 0 001 are examined two of the codes employ a finite volume discretization scheme along with a multistage time stepping algorithm to solve the euler equations the two codes differ in their respective use of cell centered and node centered differencing schemes the third code uses an implicit finite difference procedure to solve the unsteady navier stokes equations computational test cases are the inviscid steady flow over a circular cylinder and the impulsively started viscous flow over a cylinder

hybrid nonlinear observers for inertial navigation using landmark measurements this article considers the problem of attitude position and linear velocity estimation for rigid body systems relying on inertial measurement unit and landmark measurements we propose two hybrid nonlinear observers on the matrix lie group text se 2 3 leading to global exponential stability the first observer relies on fixed gains while the second one uses variable gains depending on the solution of a continuous riccati equation these observers are then extended to handle biased angular velocity and linear acceleration measurements both simulation and experimental results are presented to illustrate the performance of the proposed observers

output regulation for systems on matrix lie groups abstract this paper deals with the problem of output regulation for left invariant systems defined on general matrix lie groups reference trajectories to be tracked are generated by a right invariant exosystem defined on the same lie group and driven by a linear oscillator defined on the lie algebra only partial relative geometrical information of the exosystem with respect to actual system is available in the form of invariant measurements in a homogeneous space a quotient of the lie group in the spirit of the internal model principle the proposed control structure contains an embedded copy of the exosystem kinematics the dynamics associated with the mechanical systems can be handled by dynamic extension of the proposed control approach we demonstrate the approach by providing the details of this extension for the specific case of rotational dynamics on s o 3 the problem formulation considered is motivated by a wide range of real applications in robotics aerospace and computer vision where the state space of systems such as mobile robots aerial robots unmanned drones and camera homographies are naturally lie groups associated with inherent symmetry properties of the underlying physical system

coordinated motion design on lie groups the present paper proposes a unified geometric framework for coordinated motion on lie groups it first gives a general problem formulation and analyzes ensuing conditions for coordinated motion then it introduces a precise method to design control laws in fully actuated and underactuated settings with simple integrator dynamics it thereby shows that coordination can be studied in a systematic way once the lie group geometry of the configuration space is well characterized applying the proposed general methodology to particular examples allows to retrieve control laws that have been proposed in the literature on intuitive grounds a link with brockett s double bracket flows is also made the concepts are illustrated on so 3 se 2 and se 3

distributed and recursive parameter estimation in parametrized linear state space models we consider a network of sensors deployed to sense a spatio temporal field and infer parameters of interest about the field we are interested in the case where each sensor s observation sequence is modeled as a state space process that is perturbed by random noise and the models across sensors are parametrized by the same parameter vector the sensors collaborate to estimate this parameter from their measurements and to this end we propose a distributed and recursive estimation algorithm which we refer to as the incremental recursive prediction error algorithm this algorithm has the distributed property of incremental gradient algorithms and the on line property of recursive prediction error algorithms

gradient like observers for invariant dynamics on a lie group this paper proposes a design methodology for non linear state observers for invariant kinematic systems posed on finite dimensional connected lie groups and studies the associated fundamental system structure the concept of synchrony of two dynamical systems is specialized to systems on lie groups for invariant systems this leads to a general factorization theorem of a nonlinear observer into a synchronous internal model term and an innovation term the synchronous term is fully specified by the system model we propose a design methodology for the innovation term based on gradient like terms derived from invariant or non invariant cost functions the resulting nonlinear observers have strong almost global convergence properties and examples are used to demonstrate the relevance of the proposed approach

linear complementarity systems zeno states a linear complementarity system lcs is a hybrid dynamical system defined by a linear time invariant ordinary differential equation coupled with a finite dimensional linear complementarity problem lcp the present paper is the first of several papers whose goal is to study some fundamental issues associated with an lcs specifically this paper addresses the issue of zeno states and the related issue of finite number of mode switches in such a system the cornerstone of our study is an expansion of a solution trajectory to the lcs near a given state in terms of an observability degree of the state on the basis of this expansion and an inductive argument we establish that an lcs satisfying the p property has no strongly zeno states we next extend the analysis for such an lcs to a broader class of problems and provide sufficient conditions for a given state to be weakly non zeno while related mode switch results have been proved by brunovsky and sussmann for more general hybrid systems our analysis exploits the special structure of the lcs and yields new results for the latter that are of independent interest and complement those by these two and other authors

parallel recursive prediction error algorithm for training layered neural networks a new recursive prediction error algorithm is derived for the training of feedforward layered neural networks the algorithm enables the weights in each neuron of the network to be updated in an efficient parallel manner and has better convergence properties than the classical back propagation algorithm the relationship between this new parallel algorithm and other existing learning algorithms is discussed examples taken from the fields of communication channel equalization and nonlinear systems modelling are used to demonstrate the superior performance of the new algorithm compared with the back propagation routine

distributed adaptive convex optimization on directed graphs via continuous time algorithms this note considers the distributed optimization problem on directed graphs with nonconvex local objective functions and the unknown network connectivity a new adaptive algorithm is proposed to minimize a differentiable global objective function by introducing dynamic coupling gains and updating the coupling gains using relative information of system states the nonconvexity of local objective functions unknown network connectivity and the uncertain dynamics caused by locally lipschitz gradients are tackled concurrently consequently the global asymptotic convergence is established when the global objective function is strongly convex and the gradients of local objective functions are only locally lipschitz when the communication graph is strongly connected and weight balanced the algorithm is independent of any global information then the algorithm is naturally extended to unbalanced directed graphs by using the left eigenvector of the laplacian matrix associated with the zero eigenvalue several numerical simulations are presented to verify the results

observers for invariant systems on lie groups with biased input measurements and homogeneous outputs this paper provides a new observer design methodology for invariant systems whose state evolves on a lie group with outputs in a collection of related homogeneous spaces and where the measurement of system input is corrupted by an unknown constant bias the key contribution of the paper is to study the combined state and input bias estimation problem in the general setting of lie groups a question for which only case studies of specific lie groups are currently available we show that any candidate observer with the same state space dimension as the observed system results in non autonomous error dynamics except in the trivial case where the lie group is abelian this precludes the application of the standard non linear observer design methodologies available in the literature and leads us to propose a new design methodology based on employing invariant cost functions and general gain mappings we provide a rigorous and general stability analysis for the case where the underlying lie group allows a faithful matrix representation we demonstrate our theory in the example of rigid body pose estimation and show that the proposed approach unifies two competing pose observers published in prior literature

near optimal deterministic filtering on the rotation group this technical note considers the problem of obtaining minimum energy state estimates for a system defined on the rotation group the signals of the system are modeled as purely deterministic signals we derive a nonlinear observer filter posed directly on that respects the geometry of the group and achieves a performance that is close to optimal in the sense of minimizing an integral cost that is measuring the state energy the performance of the proposed filter is demonstrated in simulations involving large initialization process and measurement errors where the results are compared against a quaternion implementation of an extended kalman filter our results indicate that the proposed filter achieves better robustness against a range of noise levels and initialization errors

analysis of zeno behaviors in a class of hybrid systems this note investigates conditions for existence of zeno behaviors where a system undergoes an unbounded number of discrete transitions in a finite length of time in a class of hybrid systems zeno behavior occurs for example when a controller unsuccessfully attempts to satisfy an invariance specification by switching the system among different configurations faster and faster two types of zeno systems are investigated 1 strongly zeno systems where all runs of the system are zeno and 2 weakly zeno systems where only some runs of the system are zeno for constant rate and bounded rate hybrid systems and some nonlinear generalizations necessary and sufficient conditions for both zenoness and strong zenoness are derived the analysis is based on studying the trajectory set of a certain equivalent continuous time system that is associated with the dynamic equations of the hybrid system the relation between the possibility of existence of zeno behaviors in a system and the problem of existence of non zeno safety controllers that keep the system in a specified region of its operating space is also examined it is shown that in certain zeno systems a minimally interventive safety controller may not exist even if a safety controller exists disproving a conjecture made earlier in the literature

analysis of non linear attitude observers for time varying reference measurements this paper provides a comprehensive stability analysis of a suite of nonlinear attitude observers that have been developed over the last few years the observers considered are based on vectorial measurements of an a priori known reference direction by treating the reference direction and the measurement in the same analysis framework and allowing time variation of either we are able to define general persistency of excitation criteria that incorporate and generalize convergence criteria used in prior work a key outcome is conditions that ensure almost global asymptotic and local exponential stability of attitude observers based on a single vector measurement as long as the excitation conditions are met on the reference and system trajectory the approach generalizes stability results provided in prior work based on rank conditions that required at least two or more vector measurements

higher order nonlinear complementary filtering on lie groups nonlinear observer design for systems whose state space evolves on lie groups is considered the proposed method is similar to previously developed nonlinear observers in that it involves propagating the state estimate using a process model and corrects the propagated state estimate using an innovation term on the tangent space of the lie group in the proposed method the innovation term is constructed by passing the gradient of an invariant cost function resolved in a basis of the tangent space through a linear time invariant system the introduction of the linear system completes the extension of linear complementary filters to nonlinear lie group observers by allowing higher order filtering in practice the proposed method allows for greater design freedom and with the appropriate selection of the linear filter the ability to filter bias and noise over specific bandwidths a disturbance observer that accounts for constant and harmonic disturbances in group velocity measurements is also considered local asymptotic stability about the desired equilibrium point is demonstrated a numerical example that demonstrates the desirable properties of the observer is presented in the context of pose estimation

the invariant extended kalman filter as a stable observer we analyze the convergence aspects of the invariant extended kalman filter iekf when the latter is used as a deterministic nonlinear observer on lie groups for continuous time systems with discrete observations one of the main features of invariant observers for left invariant systems on lie groups is that the estimation error is autonomous in this paper we first generalize this result by characterizing the much broader class of systems for which this property holds for those systems the lie logarithm of the error turns out to obey a linear differential equation then we leverage this log linear property of the error evolution to prove for those systems the local stability of the iekf around any trajectory under the standard conditions of the linear case one mobile robotics example and one inertial navigation example illustrate the interest of the approach simulations evidence the fact that the ekf is capable of diverging in some challenging situations where the iekf with identical tuning keeps converging

momentum variable procedure for solving compressible and incompressible flows navier stokes equations are solved for both compressible and incompressible flows using momentum component variables instead of the usual velocity variables as the dependent variables the numerical procedure is developed in a control volume based finite element context the procedure is determined in a pressure based algorithm rather than the density based algorithms which compressible methods normally use the proper selection of the connections between the variables on control volume surfaces and the main nodal values allow the use of a collocated grid arrangement the compressible and incompressible results of this algorithm are investigated by testing a number of test cases including the driven cavity an entrance region flow and a converging diverging nozzle flow the results indicate that the momentum component procedure is quite successful for solving compressible and incompressible flows within a single algorithm