Gabriella Mavelli | Consiglio Nazionale delle Ricerche (CNR) (original) (raw)

Papers by Gabriella Mavelli

F1000Research, Jul 30, 2019

IEEE Transactions on Automatic Control, Apr 1, 2010

This note investigates the optimal linear quadratic control problem in the discrete-time framewor... more This note investigates the optimal linear quadratic control problem in the discrete-time framework, for stochastic systems affected by disturbances generated by a nonlinear stochastic exosystem. The application of the maximum principle to nonlinear optimal control problems does not admit, in general, implementable solutions. Therefore, it is worthwhile to look for finite-dimensional approximation schemes. The approach followed in this note is based on the-degree Carleman approximation of a stochastic nonlinear system applied to the exosystem and provides a real-time algorithm to design an implementable control law. Simulations support theoretical results and show the improvements when the approximation index is increased.

Journal of Mathematical Modelling and Algorithms, Jun 19, 2010

The modern systems biology approach to the study of molecular cellular biology, consists in the d... more The modern systems biology approach to the study of molecular cellular biology, consists in the development of computational tools to support the formulation of new hypotheses on the molecular mechanisms underlying the observed cell behavior. Recent biotechnologies are able to provide precise measures of gene expression time courses in response to a large variety of internal and environmental perturbations. In this paper, we propose a simple algorithm for the selection of the "best" regulatory network motif among a number of alternatives, using the expression time course of the genes which are the final targets of the activated signalling pathway. To this aim, we considered the Hill nonlinear ODEs model to simulate the behavior of two ubiquitous motifs: the single input motif and the multi output feed-forward loop motif. Our algorithm has been tested on simulated noisy data assuming the presence of a step-wise regulatory signal. The results clearly show that our method is potentially able to robustly discriminate between alternative motifs, thus providing a useful in silico identification tool for the experimenter. 3.

Systems & Control Letters, Dec 1, 1999

In this paper, the problem of the optimal quadratic regulator for non-Gaussian discrete-time stoc... more 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.

The paper investigates the optimal control problem for a stochastic linear di®erential system, dr... more The paper investigates the optimal control problem for a stochastic linear di®erential system, driven by a persistent disturbance generated by a nonlinear stochastic exogenous system. The assumption of incomplete information has been assumed, that is neither the state of the system, nor the state of the exosystem are directly measurable. The standard quadratic cost functional has been considered. The approach followed consists of applying the º-degree Carleman approximation scheme to the exosystem, which provides a stochastic bilinear system. Then, the optimal regulator is obtained (i.e. the solution to the minimum control problem among all the a±ne transformations of the measurements). Better performances of the regulator are expected using higher order system approximations.

F1000 prime reports, Oct 1, 2014

Like other cellular modules, the secretory pathway and the Golgi complex are likely to be supervi... more Like other cellular modules, the secretory pathway and the Golgi complex are likely to be supervised by control systems that support homeostasis and optimal functionality under all conditions, including external and internal perturbations. Moreover, the secretory apparatus must be functionally connected with other cellular modules, such as energy metabolism and protein degradation, via specific rules of interaction, or "coordination protocols". These regulatory devices are of fundamental importance for optimal function; however, they are generally "hidden" at steady state. The molecular components and the architecture of the control systems and coordination protocols of the secretory pathway are beginning to emerge through studies based on the use of controlled transport-specific perturbations aimed specifically at the detection and analysis of these internal regulatory devices. Modularity, control systems and coordination protocols in manmade and biological machines Recent findings on the regulation of the secretory pathway [1,2] can be best understood in the context of the theory of control [3]. It is generally accepted that complex cellular behaviors are achieved through an internal organization based on modularity [4-6]. According to this concept, cells are composed of modules, or subsystems, often embodied in physical cellular structures, or organelles, that execute functions, such as protein synthesis or folding, metabolism, membrane transport, autophagy, and apoptosis [4-7]. Modules are partially independent of each other, but their activities must be coordinated to achieve harmonic global responses [5-7]. Moreover, modules and the related organelles must be able to preserve their homeostasis and to operate in a complex, sensitive, and robust fashion [8]. These features are essential for cells and cellular subsystems to survive and compete. But in what way and through which sophisticated regulatory devices is all this achieved?

Mathematical Problems in Engineering, Oct 10, 2019

is work investigates an optimal control problem for a class of stochastic differential bilinear s... more is work investigates an optimal control problem for a class of stochastic differential bilinear systems, affected by a persistent disturbance provided by a nonlinear stochastic exogenous system (nonlinear drift and multiplicative state noise). e optimal control problem aims at minimizing the average value of a standard quadratic-cost functional on a finite horizon. It has been supposed that neither the state of the system nor the state of the exosystem is directly measurable (incomplete information case). e approach is based on the Carleman embedding, which allows to approximate the nonlinear stochastic exosystem in the form of a bilinear system (linear drift and multiplicative noise) with respect to an extended state that includes the state Kronecker powers up to a chosen degree. is way the stochastic optimal control problem may be restated in a bilinear setting and the optimal solution is provided among all the affine transformations of the measurements. e present work is a nontrivial extension of previous work of the authors, where the Carleman approach was exploited in a framework where only additive noises had been conceived for the state and for the exosystem. Numerical simulations support theoretical results by showing the improvements in the regulator performances by increasing the order of the approximation.

IEEE Transactions on Automatic Control, Aug 1, 2002

A new approach for the solution of the regulator problem for linear discrete-time dynamical syste... more A new approach for the solution of the regulator problem for linear discrete-time dynamical systems with non-Gaussian disturbances is proposed. This approach generalizes a previous result concerning the definition of the quadratic optimal regulator. It consists in the definition of the polynomial optimal algorithm of order for the solution of the linear quadratic non-Gaussian stochastic regulator problem for systems with partial state information. The validity of the separation principle has also been proved in this case. Numerical simulations show the high performance of the proposed method with respect to the classical linear regulation techniques.

Dottorato di ricerca in ingegneria dei sistemi. A.a. 1997-98. 11. ciclo. Tutori Salvatore Monaco ... more Dottorato di ricerca in ingegneria dei sistemi. A.a. 1997-98. 11. ciclo. Tutori Salvatore Monaco e Alfredo Germani. Coordinatore Carlo BruniConsiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7, Rome; Biblioteca Nazionale Centrale - P.za Cavalleggeri, 1, Florence / CNR - Consiglio Nazionale delle RichercheSIGLEITItal

IEEE Transactions on Automatic Control, 1999

A minimax filtering problem for a class of uncertain linear stochastic systems is studied. Uncert... more A minimax filtering problem for a class of uncertain linear stochastic systems is studied. Uncertainties involving fourth-order moments of the noise distribution and of the initial state are considered. Under the hypothesis that the second-order statistics are known (hence the linear filter is available) the quadratic minimax filter is found. Moreover, it is shown that the minimax filter gives a

Biotechnology Advances, 2012

systems and coordination protocols of the secretory pathway

Journal of Computational and Applied Mathematics

Chemical Master Equations (CMEs) provide a comprehensive way to model the probabilistic behavior ... more Chemical Master Equations (CMEs) provide a comprehensive way to model the probabilistic behavior in biochemical networks. Despite their widespread diffusion in systems biology, the explicit computation of their solution is often avoided in favor of purely statistic Monte Carlo methods, due to the dramatically high dimension of the CME system.In this work, we investigate some structural properties of CMEs and their solutions, focusing on the efficient computation of the stationary distribution. We introduce a generalized notion of one-step process, which results in a sparse dynamic matrix describing the collection of the scalar CMEs, showing a recursive block-tridiagonal structure as well. Further properties are inferred by means of a graph-theoretical interpretation of the reaction network. We exploit this structure by proposing different methods, including a dedicated LU decomposition, to compute the explicit solution.Examples are included to illustrate the introduced concepts and to show the effectiveness of the proposed approach.

53rd IEEE Conference on Decision and Control, 2014

The Chemical Master Equation (CME) provides an accurate stochastic description of complex biochem... more The Chemical Master Equation (CME) provides an accurate stochastic description of complex biochemical processes in terms of probability distribution of the underlying chemical population. By reason of that, CMEs are usually considered stochastic methods for the analysis of biochemical reactions, in contrast to deterministic methods, handling biochemical processes by means of Ordinary Differential Equations (ODE) expressing the evolution of the concentration for each involved species. In this deterministic framework, a common practice is to exploit Quasi-Steady State Approximations (QSSAs) to reduce the dimensionality of the system and fasten numerical simulations. In the present paper, we investigate the applicability of QSSAs from a stochastic viewpoint, by making use of the CMEs in the specific case of the double phosphorylation-dephosphorylation reaction. To this end, the stochastic approach is applied to the non-approximated original chemical network, as well as to the standard and total QSSAs, confirming by simulations the effectiveness and superiority of the latter with respect to the former.

Mathematics and Mechanics of Complex Systems

Because of the unavoidable intrinsic noise affecting biochemical processes, a stochastic approach... more Because of the unavoidable intrinsic noise affecting biochemical processes, a stochastic approach is usually preferred whenever a deterministic model gives too rough information or, worse, may lead to erroneous qualitative behaviors and/or quantitatively wrong results. In this work we focus on the chemical master equation (CME)-based method which provides an accurate stochastic description of complex biochemical reaction networks in terms of the probability distribution of the underlying chemical populations. Indeed, deterministic models can be dealt with as first-order approximations of the average-value dynamics coming from the stochastic CME approach. Here we investigate the double phosphorylation/dephosphorylation cycle, a well-studied enzymatic reaction network where the inherent double time scale requires one to exploit quasisteady state approximation (QSSA) approaches to infer qualitative and quantitative information. Within the deterministic realm, several researchers have deeply investigated the use of the proper QSSA, agreeing to highlight that only one type of QSSA (the total QSSA) is able to faithfully replicate the qualitative behavior of bistability occurrences, as well as the correct assessment of the equilibrium points, accordingly to the not approximated (full) model. Based on recent results providing CME solutions that do not resort to Monte Carlo simulations, the proposed stochastic approach shows some counterintuitive facts arising when trying to straightforwardly transfer bistability deterministic results into the stochastic realm, and suggests how to handle such cases according to both theoretical and numerical results.

Mathematical Problems in Engineering

This work investigates an optimal control problem for a class of stochastic differential bilinear... more This work investigates an optimal control problem for a class of stochastic differential bilinear systems, affected by a persistent disturbance provided by a nonlinear stochastic exogenous system (nonlinear drift and multiplicative state noise). The optimal control problem aims at minimizing the average value of a standard quadratic-cost functional on a finite horizon. It has been supposed that neither the state of the system nor the state of the exosystem is directly measurable (incomplete information case). The approach is based on the Carleman embedding, which allows to approximate the nonlinear stochastic exosystem in the form of a bilinear system (linear drift and multiplicative noise) with respect to an extended state that includes the state Kronecker powers up to a chosen degree. This way the stochastic optimal control problem may be restated in a bilinear setting and the optimal solution is provided among all the affine transformations of the measurements. The present work i...

Research Report Series of Iasi Cnr Rome Italy, 1997

ABSTRACT In this paper, the problem of the optimal quadratic regulator for non-Gaussian discrete-... more ABSTRACT 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.

Proceedings of the 2004 American Control Conference, 2004

The asymptotic properties of the filtering section in a feedback-control scheme for the stochasti... more The asymptotic properties of the filtering section in a feedback-control scheme for the stochastic regulation problem of noisy-observed linear systems with state-dependent noise, are studied in the present work. The feedback-control scheme consists in the suboptimal quadratic controller for which we proved a separation property and gave the complete set of equation in a previous paper. In this paper we focus our attention on the filtering part of the control scheme and prove that, under some (reasonable) conditions involving the system to be controlled, the set of matrix differential equations describing the evolution of the covariances of the system state, state-estimate, and error-estimate, have a limiting solution that can be used to implement the overall control scheme.