duality for extended infinite monotropic optimization problems we establish necessary and sufficient conditions for strong duality of extended monotropic optimization problems with possibly infinite sum of separable functions the results are applied to a minimization problem of the infinite sum of proper convex functions we consider a truncation method for duality and obtain the zero duality gap by using only dual variable of finite support an application to minimum cost flow problems in infinite networks is also discussed

closed loop identification for the best asymptotic performance of adaptive robust control discrete linear systems subjected to both additive and parametric deterministic disturbances are considered the certainty equivalence principle is used for the design of adaptive control two different estimation algorithms are proposed to meet different control objectives in the regulation problem with the worst case limsup performance index

set inversion via interval analysis for nonlinear bounded error estimation abstract in the context of bounded error estimation one is interested in characterizing the set of all the values of the parameters to be estimated that are consistent with the data in the sense that the errors between the data and model outputs fall within prior bounds while the problem can be considered as solved when the model output is linear in the parameters the situation is far less advanced in the general nonlinear case in this paper the problem of nonlinear bounded error estimation is viewed as one of set inversion an original algorithm is proposed based upon interval analysis that makes it possible to characterize the feasible set for the parameters by enclosing it between internal and external unions of boxes the convergence of the algorithm is proved and the algorithm is applied to two test cases the results obtained are compared with those provided by signomial analysis

fault detection for lpv systems using set valued observers a coprime factorization approach abstract this paper addresses the problem of fault detection for linear parameter varying systems in the presence of measurement noise and exogenous disturbances using set valued observers svos the applicability of current methods is limited in the sense that to increase accuracy the detection requires a large number of past measurements and the boundedness of the set valued estimates is only guaranteed for stable systems in order to widen the class of systems to be modeled and also to reduce the associated computational cost the aforementioned issues must be addressed a solution involving left coprime factorization and deadbeat observers is proposed that reduces the required number of past measurements without compromising accuracy and allowing the design of svos for fault detection of unstable systems by using the resulting coprime factorization stable subsystems the algorithm is shown to produce bounded set valued estimates and an example is provided performance is assessed through simulations illustrating in particular that small magnitude faults compared to exogenous disturbances can be detected under mild assumptions

robust output feedback model predictive control of constrained linear systems this paper provides a solution to the problem of robust output feedback model predictive control of constrained linear discrete time systems in the presence of bounded state and output disturbances the proposed output feedback controller consists of a simple stable luenberger state estimator and a recently developed robustly stabilizing tube based model predictive controller the state estimation error is bounded by an invariant set the tube based controller ensures that all possible realizations of the state trajectory lie in a simple uncertainty tube the center of which is the solution of a nominal disturbance free system and the cross section of which is also invariant satisfaction of the state and input constraints for the original system is guaranteed by employing tighter constraint sets for the nominal system the complexity of the resultant controller is similar to that required for nominal model predictive control

zonotopic guaranteed state estimation for uncertain systems this paper presents a new approach for guaranteed state estimation based on zonotopes for linear discrete time multivariable systems with interval multiplicative uncertainties in the presence of bounded state perturbations and noises at each sample time the presented approach computes a zonotope which contains the real system state a p radius based criterion is minimized in order to decrease the size of the zonotope at each sample time and to obtain an increasingly accurate state estimation the proposed approach allows one to efficiently handle the trade off between the complexity of the computation and the accuracy of the estimation an illustrative example is analyzed in order to highlight the advantages of the proposed state estimation technique

distributed set membership observers for interconnected multi rate systems abstract this paper presents a new distributed observer for interconnected multi rate systems the developed observer belongs to the family of set membership estimators and the use of zonotopes is proposed to mathematically describe the sets a choice motivated by the available mathematical background in operations such as intersections combinations and linear manipulations the main features of the proposed distributed observer are a the actual state of any subsystem always belongs to the computed sets b the volume of these sets is minimized in real time c under equivalent assumptions the performance of the observer approaches to that of an analogous distributed kalman filter

minimizing euclidian state estimation error for linear uncertain dynamic systems based on multisensor and multi algorithm fusion in this paper a multisensor linear dynamic system with model uncertainty and bounded noises is considered based on previously developed set valued estimation methods in terms of convex optimization we propose several efficient algorithms of centralized sensor fusion distributed sensor fusion and multi algorithm fusion to minimize the euclidian estimation error of the state vector obviously an ellipsoid box with a larger size cannot be in general guaranteed to contain another ellipsoid box with a smaller size since centers and shapes of the two ellipsoids boxes may be different from each other this fact and the complementary advantages of multiple sensors and multiple algorithms motivate us to construct multiple estimation ellipsoids boxes squashed along each entry of the state vector as much as possible respectively by using the technique of multiple differently weighted objectives then intersection fusion of these estimation ellipsoids boxes yields a final euclidian error minimized state estimate numerical examples show that the new method with multi algorithm at both the sensors and the fusion center can significantly reduce the euclidian estimation error of the state

constrained zonotopes this article introduces a new class of sets called constrained zonotopes that can be used to enclose sets of interest for estimation and control the numerical representation of these sets is sufficient to describe arbitrary convex polytopes when the complexity of the representation is not limited at the same time this representation permits the computation of exact projections intersections and minkowski sums using very simple identities efficient and accurate methods for computing an enclosure of one constrained zonotope by another of lower complexity are provided the advantages and disadvantages of these sets are discussed in comparison to ellipsoids parallelotopes zonotopes and convex polytopes in halfspace and vertex representations moreover extensive numerical comparisons demonstrate significant advantages over other classes of sets in the context of set based state estimation and fault detection

set theoretic estimation based on a priori knowledge of the noise distribution a new algorithm for estimation of a linear in parameters model is developed and tested by simulation the method is based on the assumption of independent identically distributed noise samples with a triangular density function such a noise model well approximates the symmetrically distributed sources of noise frequently encountered in practice and the inclusion of a distribution assumption allows the computation of a pseudo mean estimate to complement the set solution the proposed algorithm recursively incorporates incoming observations with decreasing computational complexity as the number of updates increases simulations demonstrate that the algorithm has very favorable convergence rates and estimation accuracy and is very robust to deviations from the assumed noise properties comparisons with other set theoretic algorithms and with conventional rls are given

symplectic and poisson geometry on b manifolds abstract let m 2 n be a poisson manifold with poisson bivector field we say that m is b poisson if the map n m 2 n t m intersects the zero section transversally on a codimension one submanifold z m this paper will be a systematic investigation of such poisson manifolds in particular we will study in detail the structure of m in the neighborhood of z and using symplectic techniques define topological invariants which determine the structure up to isomorphism we also investigate a variant of de rham theory for these manifolds and its connection with poisson cohomology

interval observers for time varying discrete time systems this techical note deals with interval state observer design for time varying discrete time systems the problem of a similarity transformation computation which connects a time varying matrix and its nonnegative representation is studied three solutions are proposed for a generic time varying system a system with positive state and for a particular class of periodical systems numerical simulations are provided to demonstrate advantages of the developed techniques

interval estimation methods for discrete time linear time invariant systems this paper investigates interval estimation methods for discrete time linear time invariant systems we propose a novel interval estimation method by integrating robust observer design with reachability analysis by introducing h infty design into interval estimation the proposed method is effective in improving the accuracy of interval estimation moreover the comparisons and relationships between the existing methods and the proposed method are discussed in detail finally simulation results are presented to demonstrate the effectiveness of the proposed method

structure selection for bounded parameter models consistency conditions and selection criterion strong consistency conditions for structure selection in bounded parameter models are studied a certain robust selection criterion based on the volume of the exact parameter bounding polytope is proposed for linear regression models the effectiveness of the polytope volume criterion is demonstrated on a model nonlinear in its variables but linear in its parameters its strong consistency is proved for a large class of noise distributions the usual assumptions on the noise namely independence constant variance or martingale difference properties need not be made but asymptotic independence is assumed

on the value of information in system identification bounded noise case assuming instantaneous bounds on the noise system parameter identification is formulated as membership set estimation problem sequential algorithms are constructed to estimate the membership sets of the parameters which are consistent with the measurements and the noise constraints the important new feature of the proposed algorithms is their ability to ignore redundant data the efficient data extraction property of the new algorithms is achieved with small computational effort and with improved performance when compared to the least square algorithm the convergence properties and the notion of identifiability in the set theoretic context are also studied

technical communique robust state estimation and model validation for discrete time uncertain systems with a deterministic description of noise and uncertainty the paper presents a new approach to robust state estimation for a class of uncertain discrete time systems with a deterministic description of noise and uncertainty the main result is a recursive scheme for constructing an ellipsoidal state estimation set of all states consistent with the measured output and the given noise and uncertainty description the paper also includes a result on model validation whereby it can be determined if the assumed model is consistent with measured data

nonsmooth neural network for convex time dependent constraint satisfaction problems this paper introduces a nonsmooth ns neural network that is able to operate in a time dependent td context and is potentially useful for solving some classes of ns td problems the proposed network is named nonsmooth time dependent network ntn and is an extension to a td setting of a previous ns neural network for programming problems suppose c t t ge 0 is a nonempty td convex feasibility set defined by td inequality constraints the constraints are in general ns nondifferentiable functions of the state variables and time ntn is described by the subdifferential with respect to the state variables of an ns td barrier function and a vector field corresponding to the unconstrained dynamics this paper shows that for suitable values of the penalty parameter the ntn dynamics displays two main phases in the first phase any solution of ntn not starting in c 0 at t 0 is able to reach the moving set c cdot in finite time t h whereas in the second phase the solution tracks the moving set i e it stays within c t for all subsequent times t ge t h ntn is thus able to find an exact feasible solution in finite time and also to provide an exact feasible solution for subsequent times this new and peculiar dynamics displayed by ntn is potentially useful for addressing some significant td signal processing tasks as an illustration this paper discusses a number of examples where ntn is applied to the solution of ns td convex feasibility problems

block recursive parallelotopic bounding in set membership identification in this paper a procedure for the recursive approximation of the feasible parameter set of a linear model with a set membership uncertainty description is provided approximating regions of parallelotopic shape are considered the new contribution of this paper consists in devising a general procedure allowing for block processing of q 1 measurements at each recursion step based on this several approximation strategies for polytopes are presented simulation experiments are performed showing the effectiveness of the algorithm as compared to the original algorithm processing one measurement at each step

input design for guaranteed fault diagnosis using zonotopes abstract an input design method is presented for guaranteeing the diagnosability of faults from the outputs of a system faults are modeled by discrete switches between linear models with bounded disturbances and measurement errors zonotopes are used to efficiently characterize the set of inputs that are guaranteed to lead to outputs that are consistent with at most one fault scenario provided that this set is nonempty an element is then chosen that is minimally harmful with respect to other control objectives this approach leads to a nonconvex optimization problem but is shown to be equivalent to a mixed integer quadratic program that can be solved efficiently methods are given for reducing the complexity of this program including an observer based method that drastically reduces the number of binary variables when many sampling times are required for diagnosis

interval state estimation for uncertain polytopic systems the aim of this article is the state estimation of uncertain polytopic dynamic systems the parametric uncertainties affecting the system are time varying unknown and bounded with known bounds the objective is to determine the state estimates consisting in the smallest interval containing the real state value caused by the parametric uncertainties this set will be characterized by the lower and upper bounds of the state trajectory given the uncertainty bounds the set can be computed by a direct simulation of the system but a more accurate estimation is obtained with a luenberger type observer fed with the system measurements the proposed observer is designed to minimize the interval width of the estimates the observer gains are obtained by solving an optimization problem under lmi constraints the efficiency of the proposed approach is illustrated by numerical examples

on set valued kalman filtering and its application to event based state estimation motivated by challenges in state estimation with event based measurement updates the properties of the exact and approximate set valued kalman filters with multiple sensor measurements for linear time invariant systems are investigated in this work first we show that the exact and the proposed approximate set valued filters are independent of the fusion sequence at each time instant second the boundedness of the size of the set of estimation means is proved for the exact set valued filter for the approximate set valued filter if the closed loop matrix is contractive then the set of estimation means has a bounded size asymptotically otherwise a nonsingular linear transform is constructed such that the size of the set of estimation means for the transformed states is asymptotically bounded third the effect of set valued measurements on the size of the set of estimation means is analyzed and conditions for performance improvement in terms of smaller size of the set of estimation means are proposed finally the results are applied to event based estimation which allow the event triggering conditions to be designed by considering requirements on performance and communication rates the efficiency of the proposed results are illustrated by simulation examples and comparison with the approximate event based mmse estimator and the kalman filter with intermittent observations

brief a set theoretic approach for time to contact estimation in dynamic vision this paper deals with the estimation of the time to contact in dynamic vision it is well known that differential invariants of the image velocity field can be used to characterize the shape changes of objects in the scene due to relative motion between the observer and the scene under the hypothesis of constant velocity along the optical axis the time to contact turns out to be a function of the area enclosed by the object contour and its time derivative in the paper a novel approach based on set membership estimation theory is proposed to estimate the variables involved in the computation of the time to contact both errors in the motion model and image measurement noise are described as unknown but bounded disturbances without requiring any statistical assumption the proposed technique allows for the computation of guaranteed bounds on the time to contact estimates in finite time a crucial issue in all problems where a robust evaluation of the time to contact is in order

the generalized moment based filter can we solve the filtering problem from the only knowledge of few moments of the noise terms in this technical note by exploiting set of distributions based filtering we solve this problem without introducing additional assumptions on the distributions of the noises e g gaussianity or on the final form of the estimator e g linear estimator given the moments e g mean and variance of random variable x it is possible to define the set of all distributions that are compatible with the moments information this set can be equivalently characterized by its extreme distributions a family of mixtures of dirac s deltas the lower and upper expectation of any function g of x are obtained in correspondence of these extremes and can be computed by solving a linear programming problem the filtering problem can then be solved by running iteratively this linear programming problem in this technical note we discuss theoretical properties of this filter we show the connection with set membership estimation and its practical applications

set membership filtering with incomplete observations abstract this study addresses the set membership estimation problem for a class of discrete time varying systems with incomplete observations a set membership filter is developed and a recursive algorithm is proposed to calculate the state estimate ellipsoid which contains the true value to solve the problem that the conventional set membership filter cannot guarantee the stability when applied to discrete time varying systems with incomplete observations a quantitative analysis method about incomplete observations is developed and a tight bound of the estimation error is found based on interval analysis and some bounded noise assumptions in terms of bounded assumptions the relationship between the bound of estimated error and the data dropout rate is obtained if the data dropout rate is less than a maximal value the set membership filter is asymptotically stable the proposed filter is applied to a two state example to demonstrate the effectiveness of theoretical results

brief paper a set membership state estimation algorithm based on dc programming this paper presents a new approach to guaranteed state estimation for nonlinear discrete time systems with a bounded description of noise and parameters the sets of states that are consistent with the evolution of the system the measured outputs and bounded noise and parameters are represented by zonotopes dc programming and intersection operations are used to obtain a tight bound an example is given to illustrate the proposed algorithm

tight error bounds for projection algorithms in conditional set membership estimation abstract in set membership estimation conditional problems arise when the estimate must belong to a given set of assigned structure conditional projection algorithms provide estimates that are suboptimal in terms of the worst case estimation error in order to precisely evaluate the suboptimality level of these estimators tight upper bounds on the estimation errors must be computed as a function of the conditional radius of information which represents the minimum achievable error in this paper tight bounds are derived for l and l 1 estimation errors in a general setting which allows to consider any compact set of feasible problem elements and linearly parameterized estimates

the local structure of poisson manifolds varietes de poisson et applications decomposition structures de poisson lineaires approximation lineaire systemes hamiltoniens le probleme de linearisation groupes de fonction realisations et applications impulsion paires duales et groupes de jauge existence des realisations unicite des realisations les problemes des 3 corps restreints et autres exemples

analysis of consensus protocols with bounded measurement errors this paper analyzes two classes of consensus algorithms in the presence of bounded measurement errors the considered protocols adopt an updating rule based either on constant or vanishing weights under the assumption of bounded error the consensus problem is cast in a set membership framework and the agreement of the team is studied by analyzing the evolution of the feasible state set bounds on the asymptotic difference between the states of the agents are explicitly derived in terms of the bounds on the measurement noise and the values of the weight matrix

a linear matrix inequality approach to robust h sub spl infin filtering we consider the robust h sub spl infin filtering problem for a general class of uncertain linear systems described by the so called integral quadratic constraints iqcs this problem is important in many signal processing applications where noise nonlinearity quantization errors time delays and unmodeled dynamics can be naturally described by iqcs the main contribution of this paper is to show that the robust h spl infin filtering problem can be solved using linear matrix inequality lmi techniques which are numerically efficient owing to recent advances in convex optimization the paper deals with both continuous and discrete time uncertain linear systems

set valued observers and optimal disturbance rejection a set valued observer also called guaranteed state estimator produces a set of possible states based on output measurements and models of exogenous signals we consider the guaranteed state estimation problem for linear time varying systems with a priori magnitude bounds on exogenous signals we provide an algorithm to propagate the set of possible states based on output measurements and show that the centers of these sets provide optimal estimates in an l sup spl infin induced norm sense we then consider the utility of set valued observers for disturbance rejection with output feedback and derive the following general separation structure an optimal controller can consist of a set valued observer followed by a static nonlinear function on the observed set of possible states a general construction of this function is provided in the scalar control case furthermore in the special case of full control i e the number of control inputs equals the number of states optimal output feedback controllers can take the form of an optimal estimate of the full state feedback controller

brief paper recursive state bounding by parallelotopes in this paper the problem of recursively estimating the state uncertainty set of a discrete time linear dynamical system is addressed a novel approach based on minimum volume bounding parallelotopes is introduced and an algorithm of polynomial complexity is derived simulation results and performance comparisons with ellipsoidal recursive state bounding algorithms are also given

brief paper an algorithm for bounded error identification of nonlinear systems based on dc functions this paper presents a guaranteed method for the parameter estimation of nonlinear models in a bounded error context this method is based on functions which consists of the difference of two convex functions called dc functions the method considers dc representations of the functional form of the dynamic system to obtain an outer bound of the set of parameters that are consistent with the measurements the system and the considered bounded error at each iteration the proposed algorithm solves several convex optimization problems to discard from the initial search region subregions that are proved not consistent this operation is repeated while the obtained solution is improved four examples are provided to clarify the proposed identification algorithm

technical communique interval constraint propagation with application to bounded error estimation for a large class of bounded error estimation problems the posterior feasible set s for the parameters can be defined by nonlinear inequalities the set inversion approach combines classical interval analysis with branch and bound algorithms to characterize s unfortunately as bisections have to be done in all directions of the parameter space this approach is limited to problems involving a small number of parameters techniques based on interval constraint propagation make it possible to drastically reduce the number of bisections in this paper these techniques are combined with set inversion to bracket s between inner and outer subpavings union of nonoverlapping boxes when only interested in the feasible intervals for the parameters the set inversion approach becomes inefficient and a new algorithm able to compute these intervals is given this algorithm uses a new interval based local research to compute the smallest box that contains s it is then compared with existing methods on an example taken from the literature

singularities of bi hamiltonian systems we study the relationship between singularities of bi hamiltonian systems and algebraic properties of compatible poisson brackets as the main tool we introduce the notion of linearization of a poisson pencil from the algebraic viewpoint a linearized poisson pencil can be understood as a lie algebra with a fixed 2 cocycle in terms of such linearizations we give a criterion for non degeneracy of singular points of bi hamiltonian systems and describe their types

robust filtering for discrete time systems with bounded noise and parametric uncertainty this note presents a new approach to finite horizon guaranteed state prediction for discrete time systems affected by bounded noise and unknown but bounded parameter uncertainty our framework handles possibly nonlinear dependence of the state space matrices on the uncertain parameters the main result is that a minimal confidence ellipsoid for the state consistent with the measured output and the uncertainty description may be recursively computed in polynomial time using interior point methods for convex optimization with n states l uncertain parameters appearing linearly in the state space matrices with rank one matrix coefficients the worst case complexity grows as o l n l sup 3 5 with unstructured uncertainty in all system matrices the worst case complexity reduces to o n sup 3 5

functional interval observer for discrete time systems with disturbances abstract this paper further investigates the design problem of the functional interval observer for discrete time systems with disturbances two methods are given to design functional interval observers given monotone system theory a luenberger like functional interval observer is constructed and sufficient conditions are achieved by sylvester equations in the first method the second approach is known as the two step method an h functional observer of the system is presented by the h technique and then the approach of the zonotope is used to estimate its upper and lower boundaries to improve the estimation accuracy the above methods are applied to two examples for comparison and to show the correctness

adaptive robust control for siso systems abstract this paper addresses the problem of nonconservative adaptive robust regulating a siso system allowing for model perturbations in the coprime factor representation of the system as well as external additive bounded disturbance signals the perturbations and disturbances are assumed to belong to a particular parameterized class and are norm bounded the norm bounds are not available for control design but the class knowledge is available the performance measure is the worst possible steady state absolute value of the controlled output over the class of allowable disturbances and model perturbations an identification based adaptive control method is proposed where the identification criterion coincides with the control objective the proposed adaptive scheme achieves near optimal performance simulations comparing the new scheme with an adaptive controller based on classical recursive least squares identification are presented

guaranteed active failure detection and isolation for linear dynamical systems a method for active failure detection and isolation in linear systems subject to inequality bounded perturbations is presented this method under a detectability condition can guarantee detection and isolation of failures to make the failures detectable the injection of a test signal is proposed a method for testing whether the test signal is proposed a method for testing whether the test signal does make the failures detectable is presented under certain conditions a method fro designing test signals which achieve detectability is also given

state estimation for markovian jump linear systems with bounded disturbances in this paper we investigate the state estimation problem for a class of markovian jump linear systems mjlss in the presence of bounded polyhedral disturbances a set membership estimation algorithm is first proposed to find the smallest consistent set of all possible states which is shown to be expressed by a union of multiple polytopes the posterior probabilities of the system jumping modes are then estimated by introducing the lebesgue measure based on which the optimal point estimate is further provided moreover a similarity relationship for polytopes is defined and an approximate method is presented to calculate the minkowski sum of polytopes which can help reduce the computational complexity of the overall estimation algorithm

asymptotically convergent modified recursive least squares with data dependent updating and forgetting factor for systems with bounded noise continual updating of estimates required by most recursive estimation schemes often involves redundant usage of information and may result in system instabilities in the presence of bounded output disturbances an algorithm which eliminates these difficulties is investigated based on a set theoretic assumption the algorithm yields modified least squares estimates with a forgetting factor it updates the estimates selectively depending on whether the observed data contain sufficient information the information evaluation required at each step involves very simple computations in addition the parameter estimates are shown to converge asymptotically at an exponential rate to a region around the true parameter

brief guaranteed state estimation by zonotopes this paper presents a new approach to guaranteed state estimation for non linear discrete time systems with a bounded description of noise and parameters the main result is an algorithm to compute a set that contains the states consistent with the measured output and the given noise and parameters this set is represented by a zonotope the size of the zonotope is minimized each sample time by an analytic expression or by solving a convex optimization problem interval arithmetic is used to calculate a guaranteed trajectory of the process state two examples have been provided to clarify the algorithm

construction of interval observers for continuous time systems with discrete measurements we consider continuous time systems with input output and additive disturbances in the particular case where the measurements are only available at discrete instants and have disturbances to solve a state estimation problem we construct continuous discrete interval observers that are asymptotically stable in the absence of disturbances these interval observers are composed of two copies of the studied system and of a framer accompanied with appropriate outputs which give componentwise upper and lower bounds for the solutions of the studied system

duality for optimization problems with infinite sums we introduce a new perturbation function for the problem of minimizing an infinite sum of functions on a locally convex space and obtain a dual problem of maximizing an infinite sum of conjugate fu

cotangent models for integrable systems we associate cotangent models to a neighbourhood of a liouville torus in symplectic and poisson manifolds focusing on b poisson b symplectic manifolds the semilocal equivalence with such models uses the corresponding action angle theorems in these settings the theorem of liouville mineur arnold for symplectic manifolds and an action angle theorem for regular liouville tori in poisson manifolds laurent gengoux et al intmath res notices imrn 8 1839 1869 2011 our models comprise regular liouville tori of poisson manifolds but also consider the liouville tori on the singular locus of a b poisson manifold for this latter class of poisson structures we define a twisted cotangent model the equivalence with this twisted cotangent model is given by an action angle theorem recently proved by the authors and scott math pures appl 9 105 1 66 85 2016 this viewpoint of cotangent models provides a new machinery to construct examples of integrable systems which are especially valuable in the b symplectic case where not many sources of examples are known at the end of the paper we introduce non degenerate singularities as lifted cotangent models on b symplectic manifolds and discuss some generalizations of these models to general poisson manifolds

zonotopes and kalman observers state bounding observation based on zonotopes is the subject of this paper dealing with zonotopes is motivated by set operations resulting in simple matrix calculations with regard to the often huge number of facets and vertices of the equivalent polytopes discrete time ltv lpv systems with state and measurement uncertainties are considered based on a new zonotope size criterion called f w radius and by merging optimal and robust observer gain designs a zonotopic kalman filter zkf is proposed with a proof of robust convergence the notion of covariation is introduced and results in an explicit bridge between the zonotopic set membership and the stochastic paradigms for kalman filtering no intersection is used and the influence of the reduction operator limiting to a tunable maximum the size of the matrices involved in the zonotopic set computations is fully taken into account in the lmi based robust stability analysis a numerical example illustrates the effectiveness of the proposed zkf

interval state estimation for a class of nonlinear systems the goal of this technical note is to design interval observers for a class of nonlinear continuous time systems the first part of this work shows that it is usually possible to design an interval observer for linear systems by means of linear time invariant changes of coordinates even if the system is not cooperative this result is extended to a class of nonlinear systems using partial exact linearisations the proposed observers guarantee to enclose the set of system states that is consistent with the model the disturbances and the measurement noise moreover it is only assumed that the measurement noise and the disturbances are bounded without any additional information such as stationarity uncorrelation or type of distribution the proposed observer is illustrated through numerical simulations

estimation of model quality this paper provides an introduction to recent work on the problem of quantifying errors in the estimation of models for dynamic systems this is a very large field we therefore concentrate on approaches that have been motivated by the need for reliable models for control system design this will involve a discussion of efforts that go under the titles of estimation in th worst case estimation estimation in l1 and stochastic embedding of undermodelling a central theme of this survey is to examine these new methods with reference to the classic bias variance tradeoff in model structure selection

bounds on the reachable sets of nonlinear control systems the computation of rigorous enclosures of the reachable sets of nonlinear control systems is considered with a focus on applications for which speed is crucial low computational costs make interval methods based on differential inequalities an attractive option unfortunately such methods are prone to large overestimation and often produce useless results in practice from physical considerations however it is common that some crude set is known to contain the reachable set we establish a general bounding result based on differential inequalities which enables the effective use of such sets during the bounding procedure in the case where this set is a convex polyhedron an efficient implementation using interval computations is developed using readily available physical information from practical examples this method is shown to provide significant advantages over alternative methods in terms of both efficiency and accuracy

filtering and smoothing in an h sup infinity setting the problems of filtering and smoothing are considered for linear systems in an h sup infinity setting i e the plant and measurement noises have bounded energies are in l sub 2 but are otherwise arbitrary two distinct situations for the initial condition of the system are considered the initial condition is assumed known in one case while in the other the initial condition is not known but the initial condition the plant and measurement noise are in some weighted ball of r sup n xl sub 2 finite horizon and infinite horizon cases are considered necessary and sufficient conditions are presented for the existence of estimators both filters and smoothers that achieve a prescribed performance bound and algorithms that result in performance within the bounds are developed in case of smoothers the optimal smoother is also presented the approach uses basic quadratic optimization theory in a time domain setting as a consequence of which both linear time varying and time invariant systems can be considered with equal ease in the smoothing problem for linear time varying systems one considers only the finite horizon case

a state set estimation algorithm for linear systems in the presence of bounded disturbances this paper concerns the problem of state set estimation for discrete time linear systems the linear system is given in state space form and the system s uncertainty is described by bounded scalar variations we present a recursive algorithmic procedure of computing guaranteed estimated state sets in particular a polyhedron variation algorithm is presented the new algorithm is based on linear programming and sensitivity analysis techniques for improved computational efficiency and practicability

minimum volume ellipsoids containing compact sets application to parameter bounding abstract the problem of finding the minimum volume ellipsoid containing a compact set is shown to be equivalent to the determination of an optimal distribution of weights over several equivalent conditions for optimality of this distribution are obtained and used to construct algorithms guaranteed to converge to the optimum these algorithms can be used to approximate the posterior feasible set for the parameters of a model in the bounded error context linear and nonlinear illustrative examples are treated

an easy design for interval observers this paper deals with the problem of interval estimation the proposed approach is based on the use of successive derivatives in continuous time or forward measurements in discrete time in an alg

exact recursive polyhedral description of the feasible parameter set for bounded error models a method is described which exactly characterizes the set of all the values of the parameter vector of a linear model that are consistent with bounded errors on the measurements it provides a parameterized expression of this set which can be used for robust control design or for optimizing any criterion over the set this approach is based on a new variant of the double description method for determining the edges of a polyhedral cone it can be used in real time and provides a suitable context for implementation on a computer whenever a new measurement modifies the set the characterization is updated the technique is illustrated with a simple example

duality for constrained robust sum optimization problems given an infinite family of extended real valued functions f i i in i and a family mathcal h of nonempty finite subsets of i the mathcal h partial robust sum of f i i in i is the supremum for j in mathcal h of the finite sums sum j in j f j these infinite sums arise in a natural way in location problems as well as in functional approximation problems and include as particular cases the well known sup function and the so called robust sum function corresponding to the set mathcal h of all nonempty finite subsets of i whose unconstrained minimization was analyzed in previous papers of three of the authors https doi org 10 1007 s11228 019 00515 2 and https doi org 10 1007 s00245 019 09596 9 in this paper we provide ordinary and stable zero duality gap and strong duality theorems for the minimization of a given mathcal h partial robust sum under constraints as well as closedness and convex criteria for the formulas on the subdifferential of the sup function

estimation theory and uncertainty intervals evaluation in presence of unknown but bounded errors linear families of models and estimators the problem of parameter estimation and of the evaluation of related uncertainty intervals is considered in the case that a probabilistic description of noise and errors is not available of suitable but only a bound on them is known in the present paper only linear parametrizations and estimators are considered very simple and computationally feasible algorithms are derived for evaluating two different types of uncertainty intervals estimates uncertainty intervals parameter uncertainty intervals the relationships between the eui s and the pui s are established and the solution to the problem of the minimum uncertainty intervals estimator is given the latter can be obtained by means of a simple linear programming algorithm

bounded error tracking of time varying parameters bounded error estimation aims at characterizing the set of all parameter vectors consistent with given data and prior bounds on acceptable values for the errors in this paper two recursive polyhedric description algorithms are presented for tracking time varying parameters of models with outputs linear in their parameters the performances of the two algorithms are illustrated on an example with both smooth and abrupt variations of parameters

feasible parameter set for linear models with bounded errors in all variables abstract when all observed variables of a model are affected by noise parameter estimation is known as the errors in variables problem while parameter bounding methods and algorithms have been extensively developed in the case of exactly known regressor variables little attention has been paid to the bounded errors in variables problem in this paper a formal proof of a previous result on the description of the feasible parameter region for linear models in the presence of bounded errors in all variables is given topological features of the feasible parameter region such as convexity and connectedness are also discussed

technical communique nonlinear bounded error state estimation of continuous time systems this paper presents a first study on the application of interval analysis and consistency techniques to state estimation of continuous time systems described by nonlinear ordinary differential equations the approach is presented in a bounded error context and the resulting methodology is illustrated by an example