Viorica Ungureanu | University of Bucharest (original) (raw)

Papers by Viorica Ungureanu

$Research paper thumbnail of Optimal control of discrete-time linear fractional-order systems with multiplicative noise$

International Journal of Control, Dec 29, 2016

A finite horizon linear quadratic(LQ) optimal control problem is studied for a class of discrete-... more A finite horizon linear quadratic(LQ) optimal control problem is studied for a class of discrete-time linear fractional systems (LFSs) affected by multiplicative, independent random perturbations. Based on the dynamic programming technique, two methods are proposed for solving this problem. The first one seems to be new and uses a linear, expanded-state model of the LFS. The LQ optimal control problem reduces to a similar one for stochastic linear systems and the solution is obtained by solving Riccati equations. The second method appeals to the Principle of Optimality and provides an algorithm for the computation of the optimal control and cost by using directly the fractional system. As expected, in both cases the optimal control is a linear function in the state and can be computed by a computer program. Two numerical examples proves the effectiveness of each method.

Annals of the Academy of Romanian Scientists Series on Mathematics and Its Application

This paper considers stability problems for discrete-time linear fractional -order systems (LFOSs... more This paper considers stability problems for discrete-time linear fractional -order systems (LFOSs) with Markovian jumps and/ or multiplicative noise. For the case of LFOSs with finite delays and Markovian jumps, we provide sufficient conditions for the mean-square asymptotic (MSA) stability or instability of the system by using Lyapunov type equations. In the absence of the Markovian perturbations, we use Ztransform and operator spectral properties to derive instability criteria for fractional-order systems with multiplicative random perturbations and either finite or infinite delays. Four numerical results accompanied by computer simulations illustrate the effectiveness of the theoretical results.

In this paper we consider the linear discrete time systems with periodic coefficients and indepen... more In this paper we consider the linear discrete time systems with periodic coefficients and independent random perturbations (see [4] for the finite dimensional case). We give necessary and sufficient conditions for the exponential stability property of the discussed systems. In order to obtain these characterizations we use either the representations of the solutions of these systems obtained by the authoress in [5] or the Lyapunov equations. These results are the periodic versions of those given in [5].

"The book contains two major parts : Foundations and Stochastic differential equations. Part... more "The book contains two major parts : Foundations and Stochastic differential equations. Part 1 introduces and outlines the basic properties of nuclear and Hilbert Schmidt operators and gives a brief presentation of certain notions and results commonly used in probability theory. Part 2 of the book deals with stability and optimal control problems for linear stochastic differential equations. Chapter 2, the first chapter of Part 2, concerns results, many of which used later, on perturbed evolution operators. In Chapter 3, our attention has been focused on representation results, stability and uniform observability problems for stochastic differential equations. The representation results play an important role in the stability analysis and optimal control problems as well as in obtaining a deterministic characterization of stochastic uniform observability. Note that, under stronger hypotheses, the same characterization of the stochastic uniform observability property follows dir...

In this paper we consider the affine discrete-time, periodic systems with independent random pert... more In this paper we consider the affine discrete-time, periodic systems with independent random perturbations and we solve, under stabilizability and uniform observability or detectability conditions, the discrete time version of the quadratic control problem introduced in [1].

The aim of this paper is to discuss the problem of the uniform exponential stability and uniform ... more The aim of this paper is to discuss the problem of the uniform exponential stability and uniform observability of autonomous linear stochastic equations with unbounded coecients in Hilbert spaces.

In this paper we discuss stability problems for a class of positive evolution operators on certai... more In this paper we discuss stability problems for a class of positive evolution operators on certain ordered Banach spaces. Our approach is based upon a new representation result obtained in [V.M. Ungureanu and V. Dragan, Stability of discrete-time positive evolution operators on ordered Banach spaces and applications, J. Differ. Eqns. Appl., 19(2013), 6, 952-980.] that links a positive operator with the adjoint operator of its restriction to a Hilbert subspace formed by sequences of Hilbert-Schmidt operators. This class includes, the positive evolution operators generated by Lyapunov type operators involved in stability and optimal control problems for linear differential stochastic systems. The inclusion is strict because, following the results of M. Choi, we have proved in [V.M. Ungureanu and V. Dragan, Stability of discrete-time positive evolution operators on ordered Banach spaces and applications, J. Differ. Eqns. Appl., 19(2013), 6, 952-980.] that there are positive operators o...

Geometry Integrability and Quantization, 2020

Electronic Journal of Qualitative Theory of Differential Equations, 2004

The main object of this paper is to give a representation of the covariance operator associated t... more The main object of this paper is to give a representation of the covariance operator associated to the mild solutions of time-varying, linear, stochastic equations in Hilbert spaces. We use this representation to obtain a characterization of the uniform exponential stability of linear stochastic equations with periodic coefficients.

IMA Journal of Mathematical Control and Information, 2015

ABSTRACT In this paper, we consider an infinite-dimensional rmH2{\rm H}_{2}rmH2-optimal control problem... more ABSTRACT In this paper, we consider an infinite-dimensional rmH2{\rm H}_{2}rmH2-optimal control problem for a class of periodic, discrete-time Markov-jump linear systems with multiplicative and additive white noise and countably infinite state space for the Markov chain. The presence of the three types of stochastic perturbations as well as the infinite-dimensional approach of the problem are the main novelties of this work. Extending finite-dimensional results, we introduce and characterize an rmH2{\rm H}_{2}rmH2-norm and we prove the existence of the solution for the associated rmH2{\rm H}_{2}rmH2-control problem.

Taiwanese Journal of Mathematics, 2010

A class of stochastic networks with ring structure is considered in which the flow of information... more A class of stochastic networks with ring structure is considered in which the flow of information depends on a Markov chain. We find sufficient conditions such that the mean square differences between the even or odd or all units in the network will eventually tend to zero. Such probabilistic synchronization then leads to pattern formation in our networks. Although we have discussed only one or two colored patterns, it is hoped that our investigations will lead to more interesting patterns in stochastic networks in the future.

Lecture Notes in Electrical Engineering, 2016

This paper studies stability problems for a class of discrete-time linear fractional systems (LFS... more This paper studies stability problems for a class of discrete-time linear fractional systems (LFSs) affected by multiplicative, independent random perturbations. Sufficient conditions for the mean square (MS) stability and mean square asymptotic (MSA) stability properties of the stochastic LFSs are given. A numerical simulation illustrates the effectiveness of the theory.

Proceedings of The 9'th Colloquium on the Qualitative Theory of Differential Equations (June 28--July 1, 2011, Szeged, Hungary) edited by: László Hatvani, Tibor Krisztin and Róbert Vajda, 2012

In this paper we consider a general class of time-varying nonlinear differential equations on inf... more In this paper we consider a general class of time-varying nonlinear differential equations on infinite dimensional ordered Banach spaces, which includes as special cases many known differential Riccati equations of optimal control. Using a linear matrix inequalities (LMIs) approach we provide necessary and sufficient conditions for the existence of some global solutions such as maximal, stabilizing and minimal solutions for this class of generalized Riccati equations. The obtained results extend to infinite dimensions and unify corresponding results in the literature. They provide useful tools for solving infinite-time linear quadratic (LQ) control problems for linear differential systems affected by countably-infinite-state Markovian jumps and/or multiplicative noise.

The aim of this paper is to solve the tracking problem for linear periodic discrete-time systems ... more The aim of this paper is to solve the tracking problem for linear periodic discrete-time systems with independent random perturbations, in Hilbert spaces. Under stabilizability conditions, we will find an optimal control, which minimize the cost function associated to this problem, in the case when the control weight cost is only nonnegative and not necessarily uniformly positive.

Bollettino della Unione Matematica Italiana B

The optimal control problem for linear discrete-time, time-varying systems with state dependent n... more The optimal control problem for linear discrete-time, time-varying systems with state dependent noise and quadratic control is considered. The asymptotic behavior of the solution of the related discrete-time Riccati equation is investigated. The existence of an optimal control, under stabilizability and uniform observability (respectively detectability) conditions, for the given quadratic cost function is proved.

G.Da Prato and I. Ichikawa solved in [3] the quadratic control problem (1), (2), under stabilizab... more G.Da Prato and I. Ichikawa solved in [3] the quadratic control problem (1), (2), under stabilizability and detectability conditions. We replace the detectability condition with the uniform observability property and we obtain an optimal control and the minimal value of the cost functional (2). So, we generalize the results obtained by T.Morozan in [7] for finite dimensional case and we also conclude that our result is distinct from the one of G.Da Prato and I. Ichikawa. We use the above results to give a method for the numerical computation of the optimal cost. Under the same hypotheses we solve the tracking problem (1), (3).

In this survey we recall the results obtained in [Ungureanu,Electronic Journal of Qualitative The... more In this survey we recall the results obtained in [Ungureanu,Electronic Journal of Qualitative Theory of Differential Equations, 2004] where we gave a representation theorem for the solutions of stochastic differential equations in Hilbert spaces. Using this representation theorem we obtained deterministic characterizations of exponential stability and uniform observability in [Ungureanu,Electronic Journal of Qualitative Theory of Differential Equations, 2004], [Ungureanu, Operator Theory: Advances and Applications, Birkhauser Verlag Basel, 2005] and we will prove a result of Datko type concerning the exponential dichotomy of stochastic equations.