truncation nonlinear filters for state estimation with nonlinear inequality constraints the paper focuses on the state estimation problem of nonlinear non gaussian systems with state subject to a nonlinear inequality constraint taking into account the available additional information about the state given by the constraint increases the estimate quality compared to classical state estimation methods which cannot utilize the information considering the constraint in the form of an inequality involving a nonlinear function of the state makes the state estimation problem difficult and hence treated only marginally in this paper a generic local filter for the inequality constrained estimation problem is proposed it covers the extended kalman filter unscented kalman filter and divided difference filter as special cases and enforces the constraint by truncating the conditional density of the state the truncation is computationally cheap yet it provides high estimate quality of the constrained estimate the same idea is then utilized in a truncation gaussian mixture filter which is also proposed in the paper to increase the estimate quality further by providing a global constrained estimate superior estimate quality and computational efficiency of the proposed filters are illustrated in two numerical examples

moving horizon state estimation for nonlinear systems using neural networks moving horizon mh state estimation is addressed for nonlinear discrete time systems affected by bounded noises acting on system and measurement equations by minimizing a sliding window least squares cost function such a problem is solved by searching for suboptimal solutions for which a certain error is allowed in the minimization of the cost function nonlinear parameterized approximating functions such as feedforward neural networks are employed for the purpose of design thanks to the offline optimization of the parameters the resulting mh estimation scheme requires a reduced online computational effort simulation results are presented to show the effectiveness of the proposed approach in comparison with other estimation techniques

brief constrained linear state estimation a moving horizon approach this article considers moving horizon strategies for constrained linear state estimation additional information for estimating state variables from output measurements is often available in the form of inequality constraints on states noise and other variables formulating a linear state estimation problem with inequality constraints however prevents recursive solutions such as kalman filtering and consequently the estimation problem grows with time as more measurements become available to bound the problem size we explore moving horizon strategies for constrained linear state estimation in this work we discuss some practical and theoretical properties of moving horizon estimation we derive sufficient conditions for the stability of moving horizon state estimation with linear models subject to constraints on the estimate we also discuss smoothing strategies for moving horizon estimation our framework is solely deterministic

jump and sharp cusp detection by wavelets summary a method is proposed to detect jumps and sharp cusps in a function which is observed with noise by checking if the wavelet transformation of the data has significantly large absolute values across fine scale levels asymptotic theory is established and practical implementation is discussed the method is tested on simulated examples and applied to stock market return data the analysis of change points which describe sudden localised changes has recently found increasing interest change points can be used to model practical problems arising in fields such as quality control economics medicine signal and image processing and physical sciences for example in electroencephalogram signals sharp cusps exhibit the accelerations and decelerations in the beating of the hearts many practical problems like this involve functions which have jumps and sharp cusps the recently developed theory of wavelets has drawn much attention from both math ematicians statisticians and engineers in the seminal work of donoho 1993 donoho johnstone 1994 1995a b and donoho johnstone et al 1995 orthonormal bases of compactly supported wavelets have been used to estimate functions the theory of wavelets permits decomposition of functions into localised oscillating components this is an ideal tool to study localised changes such as jumps and sharp cusps in one dimension as well as several dimensions unlike traditional smoothing methods based on a fixed spatial scale the wavelet method is a multiresolution approach and has local adaptivity in this

internal homs via extensions of dg functors abstract we provide a simple proof of the existence of internal homs in the localization of the category of dg categories with respect to all quasi equivalences and of some of their main properties such as the so called derived morita theory this was originally proved in a seminal paper by toen

survey constrained model predictive control stability and optimality model predictive control is a form of control in which the current control action is obtained by solving at each sampling instant a finite horizon open loop optimal control problem using the current state of the plant as the initial state the optimization yields an optimal control sequence and the first control in this sequence is applied to the plant an important advantage of this type of control is its ability to cope with hard constraints on controls and states it has therefore been widely applied in petro chemical and related industries where satisfaction of constraints is particularly important because efficiency demands operating points on or close to the boundary of the set of admissible states and controls in this review we focus on model predictive control of constrained systems both linear and nonlinear and discuss only briefly model predictive control of unconstrained nonlinear and or time varying systems we concentrate our attention on research dealing with stability and optimality in these areas the subject has developed in our opinion to a stage where it has achieved sufficient maturity to warrant the active interest of researchers in nonlinear control we distill from an extensive literature essential principles that ensure stability and use these to present a concise characterization of most of the model predictive controllers that have been proposed in the literature in some cases the finite horizon optimal control problem solved on line is exactly equivalent to the same problem with an infinite horizon in other cases it is equivalent to a modified infinite horizon optimal control problem in both situations known advantages of infinite horizon optimal control accrue

a solution for the partitioning problem in partition based moving horizon estimation in addition to being observable systems composed of interconnected subsystems must typically exhibit a particular subsystem structure if their state is to be estimated successfully by a partition based moving horizon estimator pmhe suitable subsystem structures also called system partitionings can be unknown may not be desirable for a particular application or may not exist at all in this contribution we present the first pmhe without any restrictions on the system partitioning we analyze the convergence of its iterations at each time step and the stability of its estimation error dynamics the benefits of our solution are illustrated on a numerical example

lagrangian duality between constrained estimation and control we show that the lagrangian dual of a constrained linear estimation problem is a particular nonlinear optimal control problem the result has an elegant symmetry which is revealed when the constrained estimation problem is expressed as an equivalent nonlinear optimisation problem the results extend and enhance known connections between the linear quadratic regulator and linear quadratic state estimation problems

further results on nonlinear receding horizon observers further results are proposed that concern the design and the convergence of receding horizon nonlinear observers the key feature is the definition of observability radius in relation with a prespecified compact set of initial configurations this enables a semiglobal convergence result to be derived that turns out to be a global convergence result when appropriate regularity assumptions are made a simple example is proposed to illustrate the basic features of the note

moving horizon numerical observers of nonlinear control systems in this note we develop moving horizon numerical observers and analyze the error in the error estimation we take into consideration both the integration error and the optimization error the design facilitates the use of a variety of numerical algorithms to form different observers as a special case an euler newton observer is introduced the numerical observer is independent of any optimization software or toolbox furthermore the observer is formulated in a way that is especially efficient for systems with sampled measurement

riccati equations in optimal filtering of nonstabilizable systems having singular state transition matrices until recently it was believed that a necessary and sufficient condition for convergence of the riccati difference equation of optimal filtering was that the system be both delectable and stabilizable recently it has been shown that the stabilizability condition can be removed but convergence has only established under restrictive assumptions including the requirement that the state transition matrix be nonsingular the present paper generalizes these results in several directions first properties of the algebraic riccati equation are established for the case of singular state transition matrix second several assumptions previously imposed in establishing convergence of the riccati difference equation for systems with unreachable modes on the unit circle are relaxed including replacing observability by detectability weakening the conditions on the initial covariance and allowing the state transition matrix to be singular third results on the convergence and properties of the riccati equations are expressed as both necessary and sufficient conditions whereas previous results were only sufficient these extensions mean that the results have wider applicability including fixed lag smoothing problems and filtering for systems with time delays the implications of the results in the dual problem of optimal control are also studied

on estimation error bounds for receding horizon filters using quadratic boundedness quadratic boundedness is used to deal with stability and design of receding horizon estimators upper bounds on the norm of the estimation error have been found by means of invariant sets that can be constructed by using quadratic boundedness moreover these bounds are expressed in terms of linear matrix inequalities and are well suited to being minimized for the purpose of design

abstract dynamic programming models under commutativity conditions the unifying purpose of the abstract dynamic programming models is to find sufficient conditions on the recursive definition of the objective function that guarantee the validity of the dynamic programming iteration this paper presents backward forward and backward forward models that weaken previous sufficient conditions and that include but are not restricted to optimization problems the backward forward model is devoted to the simultaneous solution of a collection of interrelated sequential problems based on the independent computation of a cost to arrive function and a cost to go function several extremization and nonextremization problems illustrate the applicability of the proposed models

simultaneous nonlinear model predictive control and state estimation an output feedback approach to model predictive control that combines state estimation and control into a single minmax optimization is introduced for discrete time nonlinear systems specifically a criterion that involves finite forward and backward horizons is minimized with respect to control input variables and is maximized with respect to the unknown initial state as well as disturbance and measurement noise variables under appropriate assumptions that encode controllability and observability we show that the state of the closed loop remains bounded and that a bound on tracking error can be found for trajectory tracking problems we also introduce a primaldual interior point method that can be used to efficiently solve the minmax optimization problem and show in simulation examples that the method succeeds even for severely nonlinear and non convex problems

neural approximators for nonlinear finite memory state estimation no general analytical tools are available to estimate the state of a nonlinear stochastic system observed through a nonlinear noisy channel this problem is addressed in this paper under the assumption that the statistics of the random variables are unknown hence a statistical approach is followed instead of a probabilistic one the following approximations are enforced i the state estimator is a finite memory one ii the estimation functions are given fixed structures in which a certain number of parameters have to be optimized multilayer feedforward neural networks are chosen from among various possible nonlinear approximators iii the algorithms for optimizing the parameters i e the network weights rely on a stochastic approximation simulation results are reported to compare the behaviour of the proposed estimator with the extended kalman filter and the estimators based on the on line minimization of the estimation error

moving horizon estimation for discrete time linear systems with binary sensors algorithms and stability results abstract the paper addresses state estimation for linear discrete time systems with binary threshold measurements a moving horizon estimation mhe approach is followed and different estimators characterized by two different choices of the cost function to be minimized and or by the possible inclusion of constraints are proposed specifically the cost function is either quadratic when only the information pertaining to the threshold crossing instants is exploited or piece wise quadratic when all the available binary measurements are taken into account stability results are provided for the proposed mhe algorithms in the presence of unknown but bounded disturbances and measurement noise performance of the proposed techniques is also assessed by means of simulation examples

on the uniform observability of discrete time nonlinear systems in constructing an observer for a discrete time nonlinear system the system is commonly required to satisfy a certain kind of uniform observability condition that is the state should always be reconstructible from observation windows of a specific length irrespective of the values of the state and inputs in this technical note it is proved that this uniform requirement is unnecessary in the sense that if the initial state and inputs are on a compact set then the uniform observability is derived from its non uniform counterpart

the homotopy theory of dg categories and derived morita theory the main purpose of this work is to study the homotopy theory of dg categories up to quasi equivalences our main result is a description of the mapping spaces between two dg categories c and d in terms of the nerve of a certain category of c d bimodules we also prove that the homotopy category ho dg cat possesses internal hom s relative to the derived tensor product of dg categories we use these two results in order to prove a derived version of morita theory describing the morphisms between dg categories of modules over two dg categories c and d as the dg category of c d bi modules finally we give three applications of our results the first one expresses hochschild cohomology as endomorphisms of the identity functor as well as higher homotopy groups of the classifying space of dg categories i e the nerve of the category of dg categories and quasi equivalences between them the second application is the existence of a good theory of localization for dg categories defined in terms of a natural universal property our last application states that the dg category of continuous morphisms between the dg categories of quasi coherent resp perfect complexes on two schemes resp smooth and proper schemes is quasi equivalent to the dg category of quasi coherent resp perfect complexes on their product

state observation by on line minimization a new approach is presented to observing the state of a nonlinear control system the class considered consists of nonlinear observable systems described by an ordinary differential equation in combination with a measurement equation the system functions are required to be twice differentiable based on newton s method an iterative process of state approximation is derived the algorithm computes a piecewise continuous function which is an approximation of the true state the convergence of the proposed algorithm is proved finally several examples show the performance characteristics of the method

non uniqueness of fourier mukai kernels we prove that the kernels of fourier mukai functors are not unique in general on the other hand we show that the cohomology sheaves of those kernels are unique we also discuss several properties of the functor sending an object in the derived category of the product of two smooth projective schemes to the corresponding fourier mukai functor

distributed moving horizon estimation for linear constrained systems this paper presents a novel distributed estimation algorithm based on the concept of moving horizon estimation under weak observability conditions we prove convergence of the state estimates computed by any sensors to the correct state even when constraints on noise and state variables are taken into account in the estimation process simulation examples are provided in order to show the main features of the proposed method

output to state stability and detectability of nonlinear systems the notion of input to state stability iss has proved to be useful in nonlinear systems analysis this paper discusses a dual notion output to state stability oss a characterization is provided in terms of a dissipation inequality involving storage lyapunov functions combining iss and oss there results the notion of input output to state stability ioss which is also studied and related to the notion of detectability the existence of observers and output injection

moving horizon observers and observer based control in this paper two topics are explored a new approach to the problem of obtaining an estimate of the state of a nonlinear system is proposed the moving horizon observer produces an estimate of the state of the nonlinear system at time t either by minimizing or approximately minimizing a cost function over the preceding interval horizon t t t as t advances so does the horizon convergence of the estimator is established under the assumption that the corresponding global optimization problem can be approximately solved and a uniform reconstructability condition is satisfied the latter condition is automatically satisfied for linear observable systems the utility of the estimator for receding horizon control is explored in particular stability of a composite moving horizon system comprising a moving horizon regulator and a moving horizon observer is established

on the minimisation of l sp p error in mode estimation we show that for l p convergence of the mode of a nonparametric density estimator to the mode of an unknown probability density finiteness of the pth moment of the underlying distribution is both necessary and sufficient the basic requirement of existence of finite variance has been overlooked by statisticians who have earlier considered mean square convergence of nonparametric mode estimators they have focussed on mean squared error of the asymptotic distribution rather than on asymptotic mean squared error the effect of bandwidth choice on the rate of l p convergence is analysed and smoothed bootstrap methods are used to develop an empirical approximation to the l p measure of error the resulting bootstrap estimator of l p error may be minimised with respect to the bandwidth of the nonparametric density estimator and in this way an empirical rule may be developed for selecting the bandwidth for mode estimation particular attention is devoted to the problem of selecting the appropriate amount of smoothing in the bootstrap algorithm

directional sensitivity of continuous least squares state estimators abstract least squares state estimators present an alternative to luenberger observers and yield an exact deadbeat estimate of the state vector of a dynamic system as the optimal solution to a least squares problem in some vector or functional space for instance the conventional l 2 optimal finite memory observer is shown to be a special case of the continuous least squares state estimator sensitivity of these estimators to structured uncertainty in the system matrix of the plant is studied using the frechet derivative it is shown that the state estimation error caused by the plant model s mismatch is proportional to the frechet derivative of the symbol of the parameterization operator used for the estimator implementation evaluated for the nominal value of the system matrix for the special case of state estimation in a single tone continuous oscillator the crucial impact of the parameterization operator choice on the state estimator sensitivity to the plant model s uncertainty is investigated in detail

optimization based non linear observers revisited optimization based non linear observers are those where the integrated output prediction error is used to define the dynamic of the observer s state their main advantage is genericity and the natural assumptions that are needed for the related convergence results to hold here we present some new theoretical results concerning these observers despite the title we use our observer is not based on the search for a global minimum of a cost function it is based on a descent like approach without the use of the hessian matrix a nice feature is that the resulting observer takes a classical form of in the sense that it is defined by a set of ordinary differential equations besides the theoretical results some implementation issues are discussed in particular we propose to use the post stabilization approach well known when dealing with differential systems with invariant submanifolds this enables to increase the sampling period while keeping very good precision two illustrative examples are presente

robust receding horizon state estimation for uncertain discrete time linear systems an approach to robust receding horizon state estimation for discrete time linear systems is presented estimates of the state variables can be obtained by minimizing a worst case quadratic cost function according to a sliding window strategy this leads to state the estimation problem in the form of a regularized least squares one with uncertain data the optimal solution involving on line scalar minimization together with a suitable closed form approximation are given the stability properties of the estimation error for both the optimal filter and the approximate one have been studied and conditions to select the design parameters are proposed simulation results are reported to show the effectiveness of the proposed approach

conditions for optimality of naive quantized finite horizon control this paper presents properties of a control law which quantizes the unconstrained solution to a unitary horizon quadratic programme this naive quantized control law underlies many popular algorithms such as converters and decision feedback equalities and is easily shown to be globally optimal for horizon one however the question arises as to whether it is also globally optimal for horizons greater than one i e whether it solves a finite horizon quadratic programme where decision variables are restricted to belonging to a quantized set by using dynamic programming we develop sufficient conditions for this to hold the present analysis is restricted to first order plants however this case already raises a number of highly non trivial issues the results can be applied to arbitrary horizons and quantized sets which may contain a finite or an infinite though countable number of elements

uniqueness of enhancement for triangulated categories the paper contains general results on the uniqueness of a dg enhancement for trian gulated categories as a consequence we obtain such uniqueness for the unbounded categories of quasi coherent sheaves for the triangulated categories of perfect complexes and for the bounded de rived categories of coherent sheaves on quasi projective schemes if a scheme is projective then we also prove a strong uniqueness for the triangulated category of perfect complexes and for the bounded de rived categories of coherent sheaves these results directly imply that fully faithful functors from the bounded derived categories of coherent sheaves and the triangulated categories of perfect complexes on projective schemes can be represented by objects on the product

observability and observers for nonlinear systems this paper deals with observability and observers for general nonlinear systems in the non control affine case we characterize systems that are observable independently of the inputs an exponential observer for these systems is also exhibited

further results on the uniform observability of discrete time nonlinear systems in this technical note the relation between notions of uniform observability of discrete time nonlinear systems based on injectivity of an observation map window the full rankness of its jacobian and a k function is investigated it is proven that a system is uniformly observable in the sense of injectivity of the observation map together with the full rankness of its jacobian if and only if it is so in some k function senses

moving horizon state estimation for nonlinear discrete time systems new stability results and approximation schemes a moving horizon state estimation problem is addressed for a class of nonlinear discrete time systems with bounded noises acting on the system and measurement equations as the statistics of such disturbances and of the initial state are assumed to be unknown we use a generalized least squares approach that consists in minimizing a quadratic estimation cost function defined on a recent batch of inputs and outputs according to a sliding window strategy for the resulting estimator the existence of bounding sequences on the estimation error is proved in the absence of noises exponential convergence to zero is obtained moreover suboptimal solutions are sought for which a certain error is admitted with respect to the optimal cost value the approximate solution can be determined either on line by directly minimizing the cost function or off line by using a nonlinear parameterized function simulation results are presented to show the effectiveness of the proposed approach in comparison with the extended kalman filter

a neural state estimator with bounded errors for nonlinear systems a neural state estimator is described acting on discrete time nonlinear systems with noisy measurement channels a sliding window quadratic estimation cost function is considered and the measurement noise is assumed to be additive no probabilistic assumptions are made on the measurement noise nor on the initial state novel theoretical convergence results are developed for the error bounds of both the optimal and the neural approximate estimators to ensure the convergence properties of the neural estimator a minimax tuning technique is used the approximate estimator can be designed offline in such a way as to enable it to process on line any possible measure pattern almost instantly

dg quotients of dg categories abstract keller introduced a notion of quotient of a differential graded category modulo a full differential graded subcategory which agrees with verdier s notion of quotient of a triangulated category modulo a triangulated subcategory this work is an attempt to further develop his theory

an iterative partition based moving horizon estimator with coupled inequality constraints we propose an iterative partition based moving horizon state estimator for large scale linear systems that consist of interacting subsystems every subsystem estimates its own state and disturbance variables taking into account the estimates received from neighboring subsystems compared to other partition based moving horizon estimators the proposed method has two unique features it can handle coupled inequality constraints on the estimated variables and its state estimates come arbitrarily close to the optimal state estimates of a centralized moving horizon estimator the applicability and performance of the proposed method are demonstrated on a numerical example and convergence and asymptotic stability are rigorously proven

change points in nonparametric regression analysis an otherwise smooth regression model are proposed the assumptions needed are much weaker than those made in parametric models the proposed estimators apply as well to the detection of discontinuities in derivatives and therefore to the detection of change points of slope and of higher order curvature the proposed estimators are based on a comparison of left and right one sided kernel smoothers weak convergence of a stochastic process in local differences to a gaussian process is established for properly scaled versions of estimators of the location of a change point the continuous mapping theorem can then be invoked to obtain asymptotic distributions and corresponding rates of convergence for change point estimators these rates are typically faster than n 1 2 rates of global lp convergence of curve estimates with appropriate kernel modifications adapting to estimated change points are derived as a consequence it is shown that these rates of convergence are the same as if the location of the change point was known the methods are illustrated by means of the well known data on the annual flow volume of the nile river between 1871 and 1970 1 introduction nonparametric regression methods are usually applied in order to obtain a smooth fit of a regression curve without having to specify a parametric class of regression functions sometimes a generally smooth curve might contain an isolated discontinuity or change point in the curve or in a possibly higher order derivative and in many cases interest focuses on the occurrence of such change points in parametric approaches to the regression change point problem simple linear regressions before and after a possible change point are assumed and then the possibility of a discontinuity in the form of a jump or of a jump in the first derivative or equivalently a slope change is incorporated into the model see for instance hinkley 1969 and brown durbin and evans 1975 the analysis of change points which describe sudden localized changes typically occurring in economics medicine and the physical sciences has recently found increasing interest general smoothness assumptions allowing for a large class of regression functions to be considered seem to be more appropriate in a variety of applied problems than parametric modelling an

the asymptotic distributions of kernel estimators of the mode in a decreasing sequence of intervals centered on the true mode the normalized kernel estimate of the density converges weakly to a nonstationary gaussian random process the expected value of this process is a parabola through the origin the covariance function of this process depends on the smoothness of the kernel when the kernel is mean square differentiable the location of the maximum of this process has a normal distribution when the kernel is discontinuous the location of the maximum has a distribution related to a solution of the heat equation

monotonicity and stabilizability properties of solutions of the riccati difference equation propositions lemmas theorems fallacious conjectures and counterexamples abstract the problem considered is that of selecting an initial covariance matrix for the kalman filter to ensure that the closed loop filter at every subsequent time instant is exponentially asymptotically stable as a time invariant filter sufficient conditions are derived based on monotonicity properties of the solution of the riccati difference equation the results have application in observer design and the cases of filtering for nonstabilizable systems and systems with singular system matrices are included