polynomial filtering for linear discrete time non gaussian systems in this work we propose a new filtering approach for linear discrete time non gaussian systems that generalizes a previous result concerning quadratic filtering a de santis a germani and m raimondi ieee trans automat control 40 1995 pp 1274 1278 a recursive nu th order polynomial estimate of finite memory delta is achieved by defining a suitable extended state which allows one to solve the filtering problem via the classical kalman linear scheme the resulting estimate will be the mean square optimal one among those estimators that take into account nu polynomials of the last delta observations numerical simulations show the effectiveness of the proposed method

further results on stabilizing controllers for discrete non linear stochastic systems more relationships that exist among stabilizability conditions of controllers designed for a class of discrete non linear stochastic systems are described the conditions are in terms of both mean square and almost sure asymptotic stability of the controlled systems and provide converse results to those presented earlier

technical communique discrete time optimal control with control dependent noise and generalized riccati difference equations the optimal control law is derived for discrete time linear stochastic systems with quadratic performance criterion and control dependent noise the analysis includes the study of a generalized riccati difference equation and of the asymptotic behavior of its solutions

some complexity issues in digital signal processing over the past decade a large class of problems called np complete 5 have been shown to be equivalent in the sense that if a fast algorithm can be found for one fast algorithms can be found for all at the same time despite much effort no fast algorithms have been found for any and these problems are widely regarded as intractable this class includes such notoriously difficult problems as the traveling salesman problem graph coloring and satisfiability of boolean expressions using fir filter implementation as an illustration we describe some problems in digital signal processing that are np complete these include 1 minimize the number of additions needed to implement a fixed fir filter 2 minimize the number of registers needed to implement a fixed fir filter and 3 minimize the time to perform the additions of such an fir filter using p adders large seale instances of such problems may become important with the use of programmable chips to implement signal processing our main purpose in this paper is to illustrate the usefulness of asymptotic complexity theory in the field of digital signal processing the theory discriminates between tractable and intractable problems sometimes identifies fast algorithms for the former and justifies heuristics for the latter

disturbance observer based elegant anti disturbance saturation control for a class of stochastic systems in this paper the elegant anti disturbance saturation control problem is discussed for a class of stochastic systems with multiple heterogeneous disturbances which include three kinds of disturba

stationary optimal control of stochastically sampled continuous time systems abstract this paper solves the digital stationary optimal control problem in the case of linear stochastic continuous time systems long term average integral criteria complete state information and where the sampling periods are independent identically distributed stochastic variables using the notions of mean square stabilizability and mean square detectability it is shown that stochastic sampling may increase or restore stabilizability and may decrease or destroy stability if the presence of stochastic sampling is not taken into account in the determination of the optimal controller

filtering and fault detection for nonlinear systems with polynomial approximation this paper is concerned with polynomial filtering and fault detection problems for a class of nonlinear systems subject to additive noises and faults the nonlinear functions are approximated with polynomials of a chosen degree different from the traditional methods the approximation errors are not discarded but formulated as low order polynomial terms with norm bounded coefficients the aim of the filtering problem is to design a least squares filter for the formulated nonlinear system with uncertain polynomials and an upper bound of the filtering error covariance is found and subsequently minimized at each time step the desired filter gain is obtained by recursively solving a set of riccati like matrix equations and the filter design algorithm is therefore applicable for online computation based on the established filter design scheme the fault detection problem is further investigated where the main focus is on the determination of the threshold on the residual due to the nonlinear and time varying nature of the system under consideration a novel threshold is determined that accounts for the noise intensity and the approximation errors and sufficient conditions are established to guarantee the fault detectability for the proposed fault detection scheme comparative simulations are exploited to illustrate that the proposed filtering strategy achieves better estimation accuracy than the conventional polynomial extended kalman filtering approach the effectiveness of the associated fault detection scheme is also demonstrated

control of randomly varying systems with prescribed degree of stability the control of linear discrete time systems with stochastic parameter matrices is discussed two control techniques are particularly used infinite horizon and finite moving horizon optimal regulators it is shown that it is possible to design controllers with a guaranteed degree of exponential stochastic stability by properly modifying the performance indexes in this way the deterministic regulator problem with a prescribed degree of stability is extended to the case of stochastic parameter systems

parametrization of all linear compensators for discrete time stochastic parameter systems abstract for discrete time stochastic parameter systems this paper presents a characterization of all state covariances assignable by a linear controller and a parametrization of all controllers that achieves a desired covariance these results indirectly provide the parametrization of all linear fixed order compensators which are mean square stabilizing for this class of systems the paper also includes robustification of the derived compensators and an example to illustrate the results

optimal quadratic solution for the non gaussian finite horizon regulator problem in this paper the problem of the optimal quadratic regulator for non gaussian discrete time stochastic systems with a quadratic cost function is considered the main result here obtained is that such optimal control can be derived from the classical lqg solution by substituting the linear filtering part with a quadratic optimal filter numerical results show high performance of this method

robustness results in linear quadratic gaussian based multivariable control designs the robustness of control systems with respect to model uncertainty is considered using simple frequency domain criteria available and new results are derived under a common framework in which the minimum singular value of the return differences transfer matrix is the key quantity in particular robustness results associated with multivariable control systems designed on the basis of linear quadratic lq and the linear quadratic gaussian lqg design methodologies are presented

cubification of σπ sde and exact moment equations abstract for an ito like stochastic differential equation sde system with drift and diffusion that are formal polynomials of the independent variables we show that all moments satisfy an infinite countable set of linear ordinary differential equations this result is achieved by means of the exact cubification of the sde which consists in a set of deterministic transformations of the state variables giving place to a new sde with further finitely many state variables exact cubification can be considered as an extension to the stochastic case of the exact quadratization of deterministic nonlinear systems available in the literature an example is finally shown taken from systems biology in which for a basic chemical reaction network the exact moment equation is written down and an approximate solution is calculated through a moment closure method

detectability observability and lyapunov type theorems of linear discrete time varying stochastic systems with multiplicative noise abstractthe objective of this paper is to study detectability observability and related lyapunov type theorems of linear discrete time time varying stochastic systems with multiplicative noise some new concepts such as uniform detectability k exact detectability resp kwft exact detectability kft exact detectability kn exact detectability and k exact observability resp kwft exact detectability kft exact detectability kn exact detectability are introduced respectively and nice properties associated with uniform detectability exact detectability and exact observability are also obtained moreover some lyapunov type theorems associated with generalised lyapunov equations and exponential stability in mean square sense are presented under uniform detectability kn exact observability and kn exact detectability respectively

robustness of feedback stabilized systems in the presence of non linear and random perturbations the general robustness problem is discussed for a controlled discrete time system subject to a lur e type feedback non linearity together with random multiplicative noises effective on state input and the non linearity a sufficient condition is given utilizing the discrete stochastic version of the second method of lyapunov to guarantee that any stabilizing controller designed for the deterministic linear part of the system renders the closed loop system with perturbations asymptotically stable with probability one then specializations to systems given in controllability and controller canonical forms are made independent noise signals are assumed to be effective on individual parameters of these canonical forms whose inputs are designed to assign the closed loop poles to zero in these cases stronger results are obtained in terms of system parameters and known characteristics of perturbations

robust h sub spl infin control of discrete time markovian jump linear systems with mode dependent time delays considers the class of discrete time markovian jump linear system with norm bounded uncertainties and time delay which is dependent on the system mode linear matrix inequality lmi based sufficient conditions for the stability stabilization and h sub spl infin control are developed a numerical example is worked out to show the usefulness of the theoretical results

the influence of finite word length on digital optimal control this paper is concerned with the performance of linear discrete time systems controlled by a finite word length computer with floating point arithmetic and of which the state is directly measurable with an a d converter of the same word length the effect of using finite word length is twofold first roundings are made after addition or multiplication of two rounded numbers second the control parameters are represented in the controller s memory by rounded numbers the first effect can be accounted for by considering the control parameters stochastic the second effect is deterministic after a description of the stochastlcs of the roundoff errors has been derived the influence of both effects on the optimality and stability of digital control systems in the steady state in relation to a quadratic cost function is considered

relationships between several novel control schemes proposed for a class of non linear stochastic systems several different novel controllers are proposed to stabilize a class of discrete time non linear stochaslic systems where the non linearity involves the state and input of the system as well as a white noise sequence vector it is shown that the conditions of stabilizability by these controllers are closely related

geometrical properties of optimal volterra filters for signal detection linear quadratic filters are a special example of volterra filters that are limited to the second order it is shown that all the results recently published which are valid in the linear quadratic case can be extended with the appropriate notations to volterra filters of arbitrary order particularly the optimum volterra filter giving the maximum of the deflection for detecting a signal in noise is wholly calculated in addition several geometrical properties of optimal volterra filters are investigated by introducing appropriate scalar products in particular the concept of space orthogonal to the signal and the noise alone reference nar property are introduced allowing a decomposition of the optimal filter that exhibits a relation between detection and estimation extensions to the infinite case and relations with the likelihood ratio are also investigated

descriptor recursive estimation for multiple sensors with different delay rates in this article the problem of recursive estimation is studied for a class of descriptor systems measured by multiple sensors with different delay rates the delay phenomenon occurs in a random way and the delay rate for each sensor is characterised by an individual binary switching sequence obeying a conditional probability distribution the original descriptor system is transformed into two non descriptor stochastic subsystems with autocorrelated and cross correlated noises by using the singular value decomposition and the state augmentation applying an innovation analysis approach and the orthogonal projection theorem recursive estimators including filter predictor and smoother are first derived for each subsystem and the process noise then based on the newly obtained recursive state estimators and process noise estimators the recursive filter predictor and smoother are obtained for the original descriptor system measured by multiple sensors with different delay rates a numerical simulation ex

on the identifiability of non gaussian arma models using cumulants a fixed set of output cumulants of order greater than two guarantees unique identification of known order causal arma autoregressive moving average models which are driven by unobservable non gaussian i i d noise the models are allowed to be non minimum phase and their outputs may be corrupted by additive colored gaussian noise of unknown covariance the arma parameters can be estimated either by means of linear equations and closed form expressions or by minimizing quadratic cumulant matching criteria the latter approach requires computation of cumulants in terms of the arma parameters which is carried out in the state space using kronecker products

galloping instability of viscous shock waves abstract motivated by physical and numerical observations of time oscillatory galloping spinning and cellular instabilities of detonation waves we study poincare hopf bifurcation of traveling wave solutions of viscous conservation laws the main difficulty is the absence of a spectral gap between oscillatory modes and essential spectrum preventing standard reduction to a finite dimensional center manifold we overcome this by direct lyapunov schmidt reduction using detailed pointwise bounds on the linearized solution operator to carry out a nonstandard implicit function construction in the absence of a spectral gap the key computation is a space time stability estimate on the transverse linearized solution operator reminiscent of duhamel estimates carried out on the full solution operator in the study of nonlinear stability of spectrally stable traveling waves

fir filter design over a discrete powers of two coefficient space fir digital filters with discrete coefficient values selected from the powers of two coefficient space are designed using the methods of integer programming the frequency responses obtained are shown to be superior to those obtained by simply rounding the coefficients both the weighted minimax and the weighted least square error criteria are considered using a weighted least square error criterion it is shown that it is possible to predict the improvement that can be expected when integer quadratic programming is used instead of simple coefficient rounding

near optimal control for time varying linear discrete systems with additive nonlinearities and random gains in this technical note the near optimal control problem is investigated for a class of time varying linear discrete systems subject to additive nonlinearities and random gains first certain upper bound on the cost function is proposed to quantify the control performance subsequently in virtue of the time varying discrete riccati like recursions drlrs the near optimal control strategy is designed such that this upper bound is minimized over the finite horizon to reflect the steady state behavior of the dynamic system the upper bound of the derived time varying drlrs is also analyzed over the infinite horizon by resorting to the semidefinite programming method finally a numerical example is provided to verify the validity and advantages of the proposed methodology

statistical and stabilizability properties of equivalent discrete time systems with stochastic parameters this paper considers the influence of the statistics of a scalar continuous time system with white stochastic parameters on the statistics the correlation and the stabilizability of the corresponding scalar equivalent discrete time system by means of numerical examples some insight into the behaviour of the equivalent discrete time system is given furthermore these examples illustrate the crucial influence of the correlation between the state and control dependent noise of the continuous time system on the stabilizability of the equivalent discrete time system

observer design for stochastic parameter systems constant gain linear observer design is utilized to reconstruct the state vector of stochastic systems with both multiplicative and additive noises it is shown that if the system model is mean square stable then it is very easy to design an effective estimation scheme

optimal stochastic control for performance and stability robustness a design method for discrete time control systems that maintain stability with minimum performance degradation in the presence of a variety of deterministic and stochastic perturbation disturbances is presented deterministic perturbation and modeling errors are represented by maximum deviations from a nominal linear discrete time system and stochastic perturbations are modeled by generalization of the sector bound nonlinearity concept to the stochastic case based on the given bounds on deterministic and stochastic perturbations an upper bound on the quadratic performance index which is useful in assessing the performance deterioration according to the feedback gain used is found then the optimal feedback gain which minimizes this bound on the performance index is derived in the time invariant case the existence of a stabilizing property of the bound optimal controller which is obtained by minimizing an average cost per stage is shown

filtering of stochastic nonlinear differential systems via a carleman approximation approach this paper deals with the state estimation problem for stochastic nonlinear differential systems driven by standard wiener processes and presents a filter that is a generalization of the classical extended kalman bucy filter ekbf while the ekbf is designed on the basis of a first order approximation of the system around the current estimate the proposed filter exploits a carleman like approximation of a chosen degree v ges 1 the approximation procedure applied to both the state and the measurement equations allows to define an approximate representation of the system by means of a bilinear system for which a filtering algorithm is available from the literature numerical simulations on an example show the improvement in terms of sample error covariance of the filter based on the first order second order and third order system approximations v 1 2 3

on lmi formulations of some problems arising in nonlinear stochastic system analysis this work involves formulation of some problems arising in the analysis of a class of discrete time nonlinear stochastic systems in terms of linear matrix inequalities this allows one to utilize a wide variety of numerical techniques available for tackling both the feasibility problem and the actual numerical solution in an efficient manner

compensatability and optimal compensation of systems with white parameters the optimal compensation problem is considered in the case of linear discrete time systems with stationary white parameters and quadratic criteria a generalization of the notion of mean square stabilizability namely mean square compensatability is introduced it is shown that suitable mean square compensatability and detectability conditions are sufficient and necessary in general for the existence of a unique optimal mean square stabilizing compensator tests are given to determine whether or not a system is mean square compensatable it is indicated how to calculate numerically the tests and the optimal mean square stabilizing compensator the results are illustrated with examples

a kalman filter approach for denoising and deblurring 3 d microscopy images this paper proposes a new method for removing noise and blurring from 3d microscopy images the main contribution is the definition of a space variant generating model of a 3 d signal which is capable to stochastically describe a wide class of 3 d images unlike other approaches the space variant structure allows the model to consider the information on edge locations if available a suitable description of the image acquisition process including blurring and noise is then associated to the model a state space realization is finally derived which is amenable to the application of standard kalman filter as an image restoration algorithm the so obtained method is able to remove at each spatial step both blur and noise via a linear minimum variance recursive one shot procedure which does not require the simultaneous processing of the whole image numerical results on synthetic and real microscopy images confirm the merit of the approach

robustness of discrete time systems for unstructured stochastic perturbations several stochastic stability robustness measures are presented for nominally exponentially stable linear discrete time systems with unstructured perturbations having second moment bounds dependence of these measures on the stability degree of the nominal system and other parameters used in the procedure is illustrated by using the time evolution of the second moment of the system state and stochastic lyapunov stability results positive super martingale convergence theorems the ability of nominally exponentially stable systems to maintain stability in the presence of unstructured stochastic linear and nonlinear perturbations is demonstrated quantitative results are given to determine the maximum modeling uncertainty which can be tolerated in design upper bounds on the second moments of stochastic perturbations to maintain the mean square and almost sure stability of these systems in the presence of unstructured perturbations are obtained

control under stochastic multiplicative uncertainties part ii optimal design for performance this paper studies the optimal control design problem for linear discrete time systems with stochastic multiplicative uncertainties these uncertainties are assumed to be present in the control inputs and modeled as independent and identically distributed i i d random processes the optimal performance under study is defined in the mean square sense referred to as the mean square optimal h 2 performance it is shown that the mean square optimal h 2 control problem via state feedback can be solved using a mean square stabilizing solution to a modified algebraic riccati equation mare a necessary and sufficient condition for the existence of this solution is presented which constitutes a generalization of the solution to the classic optimal h 2 state feedback design problem whereas the latter can be obtained by solving an algebraic riccati equation are it is also proven that the optimal control design problem can be cast as an eigenvalue problem evp for the output feedback case with possible input delays we show that the mean square optimal h 2 control problem also amounts to solving an mare when the plant has no nonminimum phase zeros from the inputs to the measurement outputs that is the global optimal solution is obtained by solving an mare incorporating the delays the implication is that in this case a separation principle still holds

a note on the receding horizon control method in this correspondence the relation of receding horizon control method with the state deadbeat control is brought out it is shown for single input systems that the receding horizon control is a state deadbeat control if the horizon length is taken to be equal to the state dimension

the influence of uncertainty on stability and compensatability in this paper the influence of uncertainty of linear discrete time systems modelled with white parameters on the properties of mean square stability and compensatability is considered a measure for the uncertainty in the system matrices is introduced this measure is also a measure for the uncertainty in the system in the sense that stability and compensatability decreases if this system uncertainty increases it is indicated how to calculate numerically the mean square stability and compensatability the results are illustrated with examples

ilc based fixed structure controller design for output pdf shaping in stochastic systems using lmi techniques in this paper a generalized state space controller design for the shaping of the output probability density function pdf is presented for non gaussian dynamical stochastic systems a radial basis function rbf neural network is used to approximate the output pdf of the system such a neural network consists of a number of weights and corresponding basis functions using such an approximation the dynamics of the original stochastic system can be expressed as the dynamics between the control input and the weights of the rbf neural network the task of output pdf control can therefore be reduced to a rbf weight control together with an adaptive tuning of the basis function parameters i e the centers and widths of the basis functions to achieve this aim the control horizon is divided into certain intervals hereinafter called batches using these definitions the whole control strategy consists of three stages namely a sub space parameter identification of the dynamic nonlinear model that relates the control signal to the weights of the rbf neural network b weight tracking controller design using an lmi based convex optimization technique and c rbf basis functions shape tuning in terms of their centers and widths using an iterative learning control ilc framework among the above stages the first two are performed within each batch while stage c is carried out between any two adjacent batches such an algorithm has the advantage of the batch by batch improvement of the closed loop output pdf tracking performance moreover the controller mentioned in stage b is a general controller in a state space form stability analysis has been performed and simulation results are included to show the effectiveness of the proposed method where encouraging results have been made

stability robustness bounds for linear state space models with structured uncertainty in this note we consider the robust stability analysis problem in linear state space models we consider systems with structured uncertainty some lower bounds on allowable perturbations which maintain the stability of a nominally stable system are derived these bounds are shown to be less conservative than the existing ones

absolute stability approach to stochastic stability of infinite dimensional nonlinear systems recent applications of absolute stability methods to robustness analysis have led to a rebirth of interest in this topic this paper is concerned with the robust stability of feedback distributed parameter systems against nonlinear and random disturbances our analysis is based on the lyapunov direct method to derive a stochastic lyapunov function we introduce the special stochastic infinite dimensional counterparts of the kalman yakubovich lemma they are proved by use of dynamic programming methods in combination with the properties of hilbert space valued wiener processes examples exhibit extensions of the popov and circle criteria to the feedback stochastic heat and delay equations respectively

infinite horizon quadratic optimal control of a class of nonlinear stochastic systems the author considers a class of discrete time nonlinear stochastic control systems whose nonlinearities are described by statistical means by introducing the proper mean square stabilizability and detectability properties of such systems and giving a characterization of these properties in terms of system parameters he examines the steady state properties of quadratically optimal controllers a robustness property of these controllers is pointed out

linear and non linear filters for linear but not gaussian processes suppose xt is a zero mean second order stationary process satisfying the difference equation xt xt 1 where ut is a sequence of i i d random variables further we assume that we observe the process yt xt vt where vt is also a sequence of i i d random variables the object is to obtain a recursive filter for xt given yt if the process ut and vt are gaussian then the recursive filter is linear and this is the well known kalman bucy filter otherwise the optimal filters are non linear in this paper we define two non linear filters and compare their performance with respect to the linear filter

model free control of nonlinear stochastic systems with discrete time measurements consider the problem of developing a controller for general nonlinear and stochastic systems where the equations governing the system are unknown using discrete time measurement this paper presents an approach for estimating a controller without building or assuming a model for the system such an approach has potential advantages in accommodating complex systems with possibly time varying dynamics the controller is constructed through use of a function approximator such as a neural network or polynomial this paper considers the use of the simultaneous perturbation stochastic approximation algorithm which requires only system measurements a convergence result for stochastic approximation algorithms with time varying objective functions and feedback is established it is shown that this algorithm can greatly enhance the efficiency over more standard stochastic approximation algorithms based on finite difference gradient approximations

stabilization of discrete time systems with stochastic parameters abstract this letter presents a solution to the problem of stabilization by a constant feedback of a linear system whose system and control matrices are multiplied by scalar correlated noise sequences

robust stability and stabilization of discrete time non linear systems the lmi approach the purpose of this paper is to convert the problem of robust stability of a discrete time system under non linear perturbation to a constrained convex optimization problem involving linear matrix inequalities lmi the nominal system is linear and time invariant while the perturbation is an uncertain non linear time varying function which satisfies a quadratic constraint we show how the proposed lmi framework can be used to select a quadratic lyapunov function which allows for the least restrictive non linear constraints when the nominal system is unstable the framework can be used to design a linear state feedback which stabilizes the system with the same maximal results regarding the class of non linear perturbations of particular interest in this context is our ability to use the lmi formulation for stabilization of interconnected systems composed of linear subsystems with uncertain non linear and time varying coupling by assuming stabilizability of the subsystems we can produce local control la

on the stabilizing control of a class of nonlinear stochastic systems a class of discrete time nonlinear stochastic control systems is considered by using previously established proper mean square stabilizability and observability conditions the author shows the relationship between the stabilization conditions for the moving and infinite horizon quadratic optimal controllers in this way the existence of the mean square stabilizing infinite horizon controller implies the existence of a multitude of moving finite horizon controllers with different horizon lengths with the same stability property the results allow the use of finite stage solutions of a riccati like matrix equation in a stabilizing control design which can drastically reduce the computation time

robustness of the exponential stability on a non linear controlled system under some state and control perturbations given a deterministic controlled system in continuous time or in discrete time we assume that we have computed a feedback control which stabilizes the system we show that the system remains exponentially stable under some stochastic perturbations of the applied control and of the system equation

robust h infinity control in the presence of stochastic uncertainty this paper considers a robust h infinity state feedback control problem for linear uncertain systems with stochastic uncertainty the uncertainty class considered in the paper involves uncertain multiplicative white noise perturbations which satisfy a certain variance constraint a state feedback controller is presented which guarantees a prescribed level of disturbance attenuation for all admissible stochastic uncertainties

a stability criterion for a class of discrete nonlinear systems with random parameters abstract in this paper discrete nonlinear models with random parameters are studied a new frame to classify and analyze discrete stochastic nonlinear systems has been developed from deterministic nonlinear systems to stochastic nonlinear systems this frame is broad and includes a large class of stochastic nonlinear systems a stability criterion developed for this frame is a non lyapunov method of stability analysis and is easily applied in addition this derived sufficient condition of stability is obtained without the assumption of stationarity for the random noise as frequently assumed in the literature

static output feedback and guaranteed cost control of a class of discrete time nonlinear systems with partial state measurements abstract in this paper both the static output feedback issue and the observer based control of a class of discrete time nonlinear systems are considered thanks to a newly developed linearization lemma it is shown that the solution of the discrete time output feedback problem is conditioned by a set of simple convex optimization conditions that are numerically tractable and free from any equality constraint an illustrative example is provided to show the usefulness of the proposed control designs

robust design of stochastic controllers for nonlinear systems the previous results are generalized on the stabilizing property of a control scheme designed for a class of discrete time nonlinear stochastic systems first the existing controller is made more robust with a prescribed degree of stability by proper modifications next the inherent robustness is illustrated by a design utilizing erroneous noise characteristics reconsideration of the stability analysis used allows one to treat a larger class of nonlinear stochastic systems with more general structures

robust filtering for bilinear uncertain stochastic discrete time systems this paper deals with the robust filtering problem for uncertain bilinear stochastic discrete time systems with estimation error variance constraints the uncertainties are allowed to be norm bounded and enter into both the state and measurement matrices we focus on the design of linear filters such that for all admissible parameter uncertainties the error state of the bilinear stochastic system is mean square bounded and the steady state variance of the estimation error of each state is not more than the individual prespecified value it is shown that the design of the robust filters can be carried out by solving some algebraic quadratic matrix inequalities in particular we establish both the existence conditions and the explicit expression of desired robust filters a numerical example is included to show the applicability of the present method

stabilization of deterministic and stochastic parameter discrete systems a class of suboptimal control laws having the stabilizing property is used for treating linear discrete time systems with deterministic and stochastic parameters known stabilization results in the deterministic case are extended to systems with singular state transition matrices and optimization horizon lengths shorter than the controllability indices of these systems it is shown that in the case where the state transition and input matrices contain stochastic components the stabilization of these systems in the sense of both almost sure asymptotic and mean square exponential stability is possible using the same line of reasoning

infinite horizon optimal control of linear discrete time systems with stochastic parameters the infinite horizon optimal control problem is considered in the general case of linear discrete time systems and quadratic criteria both with stochastic parameters which are independent with respect to time a stronger stabilizability property and a weaker observability property than usual for deterministic systems are introduced it is shown that the infinite horizon problem has a solution if the system has the first property if in addition the problem has the second property the solution is unique and the control system is stable in the mean square sense a simple necessary and sufficient condition explicit in the system matrices is given for the system to have the stronger stabilizability property this condition also holds for deterministic systems to be stabilizable in the usual sense the stronger stabilizability and weaker observability properties coincide with the usual ones if the parameters are deterministic

new robustness bounds for discrete systems with random perturbations some new stochastic stability robustness bounds for state space models are reported nominally exponentially stable discrete time systems are assumed to be subject to random parameter perturbations and novel bounds are obtained on the maximum variances of these random perturbations to maintain stability robustness the methods employed in the analysis are the existing ones used in the deterministic framework after transforming the stochastic robustness problem to a deterministic one the results are compared with each other and with the exact stability region in an example

absolute stabilization and minimax optimal control of uncertain systems with stochastic uncertainty this paper is concerned with existence and optimality properties of so called guaranteed cost controllers for an uncertain system subject to structured uncertainty the uncertainty in the system is assumed to have a stochastic character and to satisfy certain stochastic integral constraints it is shown that a minimax optimal guaranteed cost state feedback controller for a stochastic system can be synthesized as a state feedback controller absolutely stabilizing this system for each initial state of the system this controller can be found by parametric optimization of solutions of a parameter dependent generalized matrix riccati equation arising in stochastic h infty theory

symmetry breaking for toral actions in simple mechanical systems for simple mechanical systems bifurcating branches of relative equilibria with breaking symmetry from a given set of relative equilibria with toral symmetry are found lyapunov stability conditions along these branches are given

robust stability and stabilization of a class of nonlinear discrete time stochastic systems an lmi approach abstract a problem of robust state feedback stability and stabilization of nonlinear discrete time stochastic processes is considered the linear rate vector of a discrete time system is perturbed by a nonlinear function that satisfies a quadratic constraint our objective is to show how linear constant feedback laws can be formulated to stabilize this type of nonlinear discrete time systems and at the same time maximize the bounds on this nonlinear perturbing function which the system can tolerate without becoming unstable the state dependent diffusion is modeled by a normal sequence of identically independently distributed random variables the new formulation provides a suitable setting for robust stabilization of nonlinear discrete time systems where the underlying deterministic systems satisfy the generalized matching conditions our method which is based on linear matrix inequalities lmis is distinctive from the existing robust control and absolute stability techniques examples are given to demonstrate the obtained results

feedback stabilizability of non linear stochastic systems with state dependent noise this paper deals with non linear stochastic systems with state dependent noise based on the solution of the stochastic algebraic riccati equation sufficient conditions are derived which assure the existence of state feedback control laws such that the closed loop system is locally and globally stable in probability

deterministic and stochastic robustness measures for discrete systems deterministic and stochastic lyapunov theorems are used to demonstrate the robustness of a stable linear time variant discrete time nominal system to both unknown deterministic and stochastic perturbations time domain conditions are presented on the appropriate deterministic or random characteristics of perturbations to maintain the proper stability behavior of the overall system it is concluded that the novel robustness conditions proposed can find application in the feedback design of control systems where the closed loop system is known to be stable with a certain degree e g as in the case of linear quadratic optimal control with alpha degree of prescribed stability

optimal projection equations for discrete time fixed order dynamic compensation of linear systems with multiplicative white noise the optimal projection equations for discrete time reduced order dynamic compensation are generalized to include the effects of state control and measurement dependent noise in addition the discrete time static output feedback problem with multiplicative disturbances is considered for both problems the design equations are presented in a concise unified manner to facilitate their accessibility for developing numerical algorithms for practical applications

polynomial filtering of discrete time stochastic linear systems with multiplicative state noise the problem of finding an optimal polynomial state estimate for the class of stochastic linear models with a multiplicative state noise term is studied for such models a technique of state augmentation is used leading to the definition of a general polynomial filter the theory is developed for time varying systems with nonstationary and non gaussian noises moreover the steady state polynomial filter for stationary systems is also studied numerical simulations show the high performances of the proposed method with respect to the classical linear filtering techniques

adaptive stabilization of stochastic nonholonomic systems with nonlinear parameterization this paper investigates the problem of adaptive stabilization by state feedback for a class of stochastic nonholonomic systems in chained form with nonlinear parameterization a parameter separation technique is introduced to transform the nonlinear parameterized nonholonomic system into a linear like parameterized one then using input state scaling and backstepping techniques an adaptive state feedback controller is obtained based on switching strategy to eliminate the phenomenon of uncontrollability global asymptotic regulation in probability of the closed loop system states are guaranteed finally a simulation example is provided to illustrate the effectiveness of the proposed method

feedback properties of multivariable systems the role and use of the return difference matrix for linear time invariant multivariable feedback systems the feedback properties of plant disturbance attenuation sensor noise response stability margins and sensitivity to plant and sensor variation are quantitatively related to the bode magnitude versus frequency plots of the singular values of the return difference matrix i l and of the associated inverse return difference matrix i l 1 implied fundamental limits of feedback performance are quantitatively described and design tradeoffs are discussed the penalty function in the stochastic linear quadratic gaussian lqg optimal control problem is found to be a weighted sum of the singular values with the weights determined by the quadratic cost and noise intensity matrices this enables systematic tuning of lqg cost and noise matrices so that the resulting optimal return difference and inversereturn difference meet inequality constraints derived from design specifications on feedback properties the theory has been used to synthesize a multivariable automatic controller for the longitudinal dynamics of an advanced fighter aircraft

stabilizing compensator design for discrete time non linear stochastic systems with incomplete state information in this work an approach to stabilizing compensator design is presented that is suitable for a large class of discrete time non linear stochastic systems with incomplete state information the non linearity is contained either in the state or the measurement equation and it involves a white noise vector sequence the proposed compensator is a combination of a constant gain observer and a constant feedback control gain the stabilizability conditions depend upon the system and chosen design parameter characteristics and are given for both mean square and almost sure stochastic boundedness and stability of the controlled system a specific subclass of these systems subject to certain control laws is shown to possess stabilizability conditions that can be tested a priori

optimal quadratic filtering of linear discrete time non gaussian systems in this work the state estimation problem for linear discrete time systems with non gaussian state and output noises is dealt with by following a geometric approach an optimal recursive second order polynomial estimate is proposed which actually improves the widely used optimal linear one

stability and stabilizability of chemical reactors modelled with stochastic parameters abstract chemical reactors are considered where unknown parameter variations are model led by stochastic parameters the continuous time process is transformed to an equivalent discrete time system with stochastic parameters which is a natural approach in the context of digital control making the analysis much easier a stabilizability test for this discrete time model is used to analyse three cases from the chemical engineering literature it is shown that stability in a mean sense is too weak from an engineering point of view one should study stability at least in a mean square sense which is the approach given here

further results on the stabilizing property of certainty equivalent controllers the conditions which guarantee the stabilization of stochastic parameter systems by infinite horizon certainty equivalent controllers are generalized to the case of random matrices with possibly correlated elements the same conditions are shown to be sufficient for stabilizability by the corresponding optimal controllers

certainty equivalent control of stochastic systems stability property this work presents sufficient conditions for infinite and sliding finite horizon certainty equivalence controllers to stabilize discrete linear systems disturbed by scalar multiplicative white noise sequences these conditions also guarantee stabilizability by the optimal controllers

a control scheme for a class of discrete nonlinear stochastic systems a control scheme is presented for effective stabilization of discrete time nonlinear stochastic systems where the nonlinearity involves a zero mean independent random sequence the control is of a constant feedback type and makes use of finite time solutions of a riccati like matrix difference equation stability results are both in terms of mean square and almost sure stochastic stability moreover a matrix inequality is given to check the existence of weighting matrices which would result in a stable regulator problem

principal gains and principal phases in the analysis of linear multivariable feedback systems the concepts of principal gain and principal phase are introduced for linear multivariable systems and their use in the analysis of feedback behavior is demonstrated a sufficient nyquist type stability criterion is presented in terms of these quantities and is used to characterize the robustness of the closed loop stability property when the system model is subjected to a linear perturbation either multiplicative or additive at any point in the feedback configuration the results presented are less conservative than those obtained via the small gain theorem

minimal representation of matrix valued white stochastic processes and u d factorisation of algorithms for optimal control two different descriptions are used in the literature to formulate the optimal dynamic output feedback control problem for linear dynamical systems with white stochastic parameters and quadratic criteria called the optimal compensation problem one describes the matrix valued white stochastic processes involved using a sum of deterministic matrices each one multiplied by a scalar stochastic process that is independent of the others another that is more general and concise uses kronecker products instead this article relates the statistics of both descriptions and shows their advantages and disadvantages as to the first description an important result that comes out is the minimum number of matrices multiplied by scalar independent stochastic processes needed to represent a certain matrix valued white stochastic process together with an associated minimal representation as to the second description an important result concerns the generation of all kronecker products that represent relevant st

stabilization analysis of discrete nonlinear systems in this paper we set a new framework for the analysis of nonlinear discrete systems to carry out the stabilization theorem and to design stable controllers of the systems within that framework this framework includes many practically important systems described for example by lipschitz functions functions with arbitrary order bounded derivatives bilinear functions and all polynomial functions an important existence theorem for stabilizing has been proven for this framework the theorem basically states that under definite rather broad conditions the zero solution of the plants can be made stable by a nonlinear output feedback in addition this nonlinear feedback is from a larger class of functions than these classes given by current literature following these stabilization theorems a new design procedure for the output feedback control law is presented all results presented are easy to use and convenient to apply the application is illustrated by several examples including the design of stabilizing control for a bilinear control system

detection of weak signals in non gaussian noise a locally optimum detector structure is derived for the detection of weak signals in non gaussian environments optimum performance is obtained by employing a zero memory nonlinearity prior to the matched filter that would be optimum for detecting the signal were the noise gaussian the asymptotic detection performance of the locally optimum detector under non gaussian conditions is derived and compared with that for the corresponding detector optimized for operations in gaussian noise numerical results for the asymptotic detection performance are shown for signal detection in noise environments of practical interest

optimal stabilizing control of a stochastic system driven by randomly correlated noise the problem of optimal stabilization of a discrete time linear system subjected to additive correlated noise disturbances with an uncertain model is considered this problem is first converted to one of stabilizing a system with multiplicative and additive noises with time wise uncorrelated characteristics a novel controller different from the infinite horizon optimal controller is then chosen from among the class or constant feedback controllers in order to stabilize the system in the mean square sense it is shown that for a special case of this problem stronger results of both mean square and almost sure asymptotic stability are possible we also present a simpler stabilizability condition to make it easier to use the particular method proposed an example is incorporated to illustrate the new technique

estimation and control of discrete time stochastic systems having cone bounded non linearities this paper addresses the problems of suboptimal estimation and control of discrete time stochastic systems with cone bounded non linearities and state dependent noise upper bounds for the estimation error covariance as well as the quadratic control cost are derived the behaviour of these upper bounds over the infinite time interval is then considered and sufficient conditions for their stability are given finally sufficient conditions for the stability of the closed loop stochastic control system are obtained these results provide verifiable conditions for the performance evaluation of simple estimators and controllers for this class of cone bounded non linear stochastic systems

a suboptimal terminal controller for linear discrete time systems abstract in this work we consider what happens when the receding horizon control laws are designed with finite final state penalization matrices a sufficient condition in terms of system and performance index parameters is given for the discrete receding horizon control rhc laws to be stabilizing when used for suboptimal regulation this condition enables the weighting matrices in the quadratic criterion to be pro assigned so that stability of design is secured the exact value of rhc cost in terms of optimal cost and an easily computable upper bound on its deviation from the optimal cost is found fast algorithms are included to calculate the particular rhc feedback gains introduced dual results in estimation theory are pointed out in this way rhc is proposed as an attractive suboptimal alternative to the optimal terminal control of linear discrete time systems

stability robustness of linear discrete time systems in the presence of uncertainty the stability robustness problem is considered for nominally stable linear discrete time systems using time domain analysis methods and lyapunov theory bounds on the norms of the time varying non linear perturbations are given to maintain the asymptotic stability of these systems in the presence of such perturbations

balanced truncation for a class of stochastic jump linear systems and model reduction for hidden markov models this paper develops a generalization of the balanced truncation algorithm applicable to a class of discrete time stochastic jump linear systems the approximation error which is captured by means of the stochastic l 2 gain is bounded from above by twice the sum of singular numbers associated to the truncated states similar to the case of linear time invariant systems a two step model reduction algorithm for hidden markov models is also developed the first step relies on the aforementioned balanced truncation algorithm due to a topological equivalence established between hidden markov models and a subclass of stochastic jump linear systems in a second step the positivity constraints which reflect the hidden markov model structure are enforced by solving a low dimensional optimization problem

the polynomial approach to the lq non gaussian regulator problem through output injection in this paper an improved approach for the solution of the regulator problem for linear discrete time dynamical systems with non gaussian disturbances and quadratic cost functional is proposed it is known that a suboptimal recursive control can be derived from the classical linear quadratic gaussian lqg solution by substituting the linear filtering part with a quadratic or in general polynomial filter however we show that when the system is not asymptotically stable the polynomial control does not improve over the classical lqg solution due to the lack of the internal stability of the polynomial filter in order to enlarge the class of systems that can be controlled we propose a new method based on a suitable rewriting of the system by means of an output injection term we show that this allows us to overcome the problem and to design a polynomial optimal controller also for non asymptotically stable systems numerical results show the effectiveness of the method

exact and approximate algorithms for the filter design optimization problem the filter design optimization fdo problem is defined as finding a set of filter coefficients that yields a filter design with minimum complexity satisfying the filter constraints it has received a tremendous interest due to the widespread application of filters assuming that the coefficient multiplications in the filter design are realized under a shift adds architecture the complexity is generally defined in terms of the total number of adders and subtractors in this paper we present an exact fdo algorithm that can guarantee the minimum design complexity under the minimum quantization value but can only be applied to filters with a small number of coefficients we also introduce an approximate algorithm that can handle filters with a large number of coefficients using less computational resources than the exact fdo algorithm and find better solutions than existing fdo heuristics we describe how these algorithms can be modified to handle a delay constraint in the shift adds designs of the multiplier blocks and to target different filter constraints and filter forms experimental results show the effectiveness of the proposed algorithms with respect to prominent fdo algorithms and explore the impact of design parameters such as the filter length quantization value and filter form on the complexity and performance of filter designs

brief paper optimal estimation of linear discrete time systems with stochastic parameters this paper considers optimal linear state estimation in the general case of linear discrete time systems with stochastic parameters which are statistically independent with respect to time the estimator is derived by transforming the system to one with deterministic parameters and state dependent additive system and observation noise it is shown that mean square stability of the system is a sufficient and almost necessary condition for the existence uniqueness and stability of the time invariant estimator