Roberto Genesio

University of Florence | UNIFI · Centre for Excellence for the Study at Molecular and Clinical Level of Chronic, Degenerative and Neoplastic Diseases to Develop Novel Therapies (DENOTHE)

The paper discusses the application of two recently proposed feedback control techniques for stabilizing chaotic motions to periodic ones in a CO 2 laser with modulated losses. The first method employs delayed control signals for stabilizing unstable periodic orbits embedded in the chaotic attractor, while the second one is based on the cancellatio...

In this paper the problem of local exponential stability of periodic orbits in a general class of forced nonlinear systems is considered. Some lower bounds for the degree of local exponential stability of a given periodic solution are provided by mixing results concerning the analysis of linear time-varying systems and the real parametric stability...

The paper presents a new approach to the control of chaotic systems for the stabilization of a periodic orbit. The problem formulation requires preserving a number of original system characteristics and making use of a low energy control. The proposed method follows a frequency harmonic balance technique employed in the approximate analysis of comp...

The paper considers the existence of quasi-periodic solutions in three-dimensional systems. Since these solutions commonly arise as a consequence of a Neimark–Sacker bifurcation of a limit cycle, a fairly general relation connected to this phenomenon is pointed out as the main result of the paper. Then, the application of harmonic balance technique...

The paper illustrates a novel approach to modify the Hopf bifurcation nature via a nonlinear state feedback control, which leaves the equilibrium properties unchanged. This result is achieved by recurring to linear and nonlinear transformations, which lead the system to locally assume the ordinary differential equation representation. Third-order m...

The paper deals with the characterization of Hopf bifurcations in families of third order autonomous systems involving quadratic nonlinearities. By employing Harmonic Balance (HB) tools, the set of system parameters corresponding to supercritical and subcritical bifurcations is analytically determined, together with an approximation of the actual b...

The paper considers the neuron model of Hindmarsh-Rose and studies in detail the system dynamics which controls the transition between the spiking and bursting regimes. In particular, such a passage occurs in a chaotic region and different explanations have been given in the literature to represent the process, generally based on a slow-fast decomp...

This paper is concerned with the study of third order quadratic and autonomous systems and the interest is oriented to the stable periodic oscillations. From the "jerk" equation model, the classes of minimal complexity presenting a Hopf bifurcation are derived and their local characterization is carried out by means of a suitable harmonic balance t...

The aim of the Letter is a global study of the well-known Rössler system to point out the main complex dynamics that it can exhibit. The structural analysis is based on the periodic solutions of the system investigated by a harmonic balance technique. Simplified expressions of such limit cycles are first derived and characterized, then their local...

The paper considers stability of periodic solutions in a class of periodically forced nonlinear systems depending on a scalar parameter and subject to disturbances. A result concerning local existence of a family of periodic solutions for such systems is also given. The stability analysis — based on a combined use of linearization techniques and fr...

The paper investigates Hopf bifurcations in a class of simple nonlinear systems, i.e., third order affine control systems described in terms of "quadratic plus cubic" normal forms and subject to linear state feedback control laws. By employing Harmonic Balance (HB) tools, the set of system parameters corresponding to supercritical and subcritical b...

The dynamical phases of the Hindmarsh-Rose neuronal model are analyzed in detail by varying the external current I. For increasing current values, the model exhibits a peculiar cascade of nonchaotic and chaotic period-adding bifurcations leading the system from the silent regime to a chaotic state dominated by bursting events. At higher I-values, t...

This paper considers the problem of determining the minimum euclidean distance of a point from a polynomial surface in R n. It is well known that this problem is in general non-convex. The main purpose of the paper is to investigate to what extent Linear Matrix Inequality (LMI) techniques can be exploited for solving this problem. The first result...

The paper deals with the classical problem of the absolute stability in a SISO Lur'e system. The circle criterion is applied to different overlapping sectors and then, for all the functions in the 'union sector', a set of constraints is defined, so that they make globally asymptotically stable the closed loop system. The conclusion is that in every...

The paper deals with the characterization of Hopf bifurcations in families of simple nonlinear systems, i.e., third-order autonomous systems with few nonlinear terms. By employing Harmonic Balance (HB) tools, the complete set of system parameters corresponding to supercritical and subcritical bifurcations is determined. In addition, it is shown how...

This paper deals with a central issue in bifurcations and chaos control applications, i.e., the stabilization of periodic motions in sinusoidally forced nonlinear systems. Specifically, the problem of designing multi-input–multi-output (MIMO) finite-dimensional linear time-invariant controllers maximizing the amplitude of the sinusoidal input for w...

The paper deals with harmonic balance analysis of tapping mode atomic force microscopes. The separation-amplitude curve is analytically evaluated for a large class of common tip-sample interaction potentials. The proposed approach provides an useful insight of many nonlinear known phenomena with respect to fully numerical approaches.

The chapter addresses bifurcations of limit cycles for a general class of nonlinear control systems depending on parameters. A set of simple approximate analytical conditions characterizing all generic limit cycle bifurcations is determined via a first order harmonic balance analysis in a suitable frequency band. Moreover, due to the existing conne...

In this note, the problem of state feedback H_∞ control for a class of nonlinear systems is considered. The class under study is a generalization of the well-known Lur'e systems. The H_∞ problem is addressed via a class of storage functions of the Lur'e-Postnikov type whose integral term is parameterized by a nonlinear scalar fu...

The problem of two-body impact dynamics is considered providing a general class of models based on hysteresis functions. The structure of the model and its flexibility allows for a direct application of harmonic balance techniques for the analysis of periodic impacts when the forces involved are repulsive, repulsive-attractive and dissipative. An a...

The paper is concerned with the study of oscillations in linear dynamic systems with relay feedback. The specific interest is about the bifurcations of these periodic solutions, with regard to phenomena which also occur in smooth systems and to others due to the relay discontinuity. The followed approach moves from the describing function method, l...

The use of finite-dimensional linear time-invariant controllers for the stabilization of periodic solutions in sinusoidally forced nonlinear systems is investigated. By mixing results concerning absolute stability of nonlinear systems and robustness of linear systems, a linear matrix inequality-based controller synthesis technique is developed. The...

Delayed feedback controllers are an appealing tool for stabilization of periodic orbits in chaotic systems. Despite their conceptual sim-plicity, specific and reliable design procedures are difficult to obtain, partly also because of their inherent infinite-dimensional structure. This chapter considers the use of finite dimensional linear time in-v...

In this paper, we revisit an existing chaos control scheme by using simple frequency-domain analysis criteria. In particular, we highlight some interesting links with other proposed chaos control techniques and envisage the possibility of applying well-known sufficient stability criteria, such as the circle criterion and generalizations thereof, to...

This paper considers the problem of determining the minimum Euclidean distance of a point from a polynomial surface in . It is well known that this problem is in general non-convex. The main purpose of the paper is to investigate to what extent linear matrix inequality (LMI) techniques can be exploited for solving this problem. The first result of...

In this paper, we revisit an existing chaos control scheme by using simple frequency-domain analysis criteria. In particular, we highlight some interesting links with other proposed chaos control techniques and envisage the possibility of applying well-known sufficient stability criteria, such as the circle criterion and generalizations thereof, to...

Secure transmission of information is an important aspect of modern telecommunication systems. Data encryption is applied in several contexts, whenever privacy is a fundamental aspect, e.g., in modern mobile networks. In this work, a stream cipher based on discrete time nonlinear dynamic systems is proposed. The Henon's map is used to generate a ch...

Secure transmission of information is an important aspect of modern telecommunication systems. Data encryption is applied in several contexts, whenever privacy is a fundamental aspect, e.g., in modern mobile networks. In this work, a stream cipher based on discrete time nonlinear dynamic systems is proposed. The Henon's map is used to generate a ch...

In this paper the problem of local exponential stability of periodic orbits in a general class of forced nonlinear systems is considered. Some lower bounds for the degree of local exponential stability of a given periodic solution are provided by mixing results concerning the analysis of linear time-varying systems and the real parametric stability...

Delayed feedback controllers are an appealing tool for the stabilization of periodic orbits in nonlinear systems. Unfortunately, their inherent infinite dimensional structure prevents the definition of reliable design procedures. This paper considers the use of finite dimensional linear time invariant controllers for the stabilization of periodic s...

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The paper considers the problem of designing controllers to stabilize periodic orbits in a class of sinusoidally forced nonlinear systems. This problem is formulated as an absolute stability problem of a linear periodic feedback system, in order to employ the circle criterion. In this setting, we provide an LMI-based synthesis of the optimal stabil...

A standard target in controlling chaos is the stabilization of one of the unstable periodic orbits (UPOs) embedded in the chaotic attractor. In this paper a new approach for the design of controllers ensuring small signal input-output L2-stability of periodic orbits in a class of nonlinear systems is proposed. A classical criterion due to Freedman...

The problem of estimating the domain of validity of state feedback H_∞ controllers for a class of nonlinear systems is considered. Such a class is a generalization of the well-known Lur'e systems. A class of storage functions of the Lur'e-Postnikov type depending on a free scalar parameter is considered. For each value of this parameter,...

The problem of local exponential stability of periodic orbits in a general class of forced nonlinear systems is considered. A criterion for designing a finite dimensional linear time invariant controller that improves the degree of local exponential stability with respect to the uncontrolled case is provided. Such a criterion is based on a well-kno...

The paper deals with the problem of controlling complex dynamics in periodically forced systems. A general framework for the stabilization of periodic orbits based on the so-called “delayed feedback” technique is presented. We formulate the periodic orbit stabilization as an input-output L₂-stability problem and employ frequency methods...

Considers reaction-diffusion systems in excitable media for studying the dynamics of related travelling waves. In particular, the one-dimensional Fitzhugh-Nagumo model is considered to apply two classical approaches of feedback systems and derive results of structural kind. The comparison with simulations obtained by a new integration procedure ind...

This paper considers the problem of determining the min-imum euclidean distance of a point from a polynomial surface in R n . It is well known that this problem is in general non-convex. The main purpose of the paper is to investigate to what extent Linear Matrix Inequality (LMI) techniques can be exploited for solving this problem. The first resul...

The paper considers the problem of designing time delayed feedback controllers to stabilize unstable periodic orbits of a class of sinusoidally forced nonlinear systems. This problem is formulated as an absolute stability problem of a linear periodic feedback system, in order to employ the well-known circle criterion. In particular, once a single t...

The paper addresses bifurcations of limit cycles for a class of feedback control systems depending on parameters. A set of simple approximate analytical conditions characterizing all the generic limit cycle bifurcations is determined via a first-order harmonic balance analysis in a suitable frequency band. Based on the results of this analysis, an...

The paper considers local bifurcations of limit cycles in nonlinear dynamical systems. Embedding harmonic balance results in Floquet theory, an approach for locating the characteristic multipliers is developed. The resulting technique, based on a first order approximation, analyses the loss of stability of the limit cycles and gives effective condi...

The algorithms for computing estimates of the domain of attraction of an equilibrium point essentially consists of two distinct steps: 1) a Lyapunov function is selected according to some rules; 2) an estimate of the domain of attraction is computed for the chosen Lyapunov function. While step (1) strongly depends on the algorithm used, step (2) is...

In many nonequilibrium dynamical situations delays are crucial in inducing chaotic scenarios. In particular, a delayed feedback in an oscillator can break the regular oscillation into trains mutually uncorrelated in phase, whereby the phase jumps are localized as defects in an extended system. We show that an adaptive control procedure is effective...

This brief deals with the problem of designing linear time-invariant feedback controllers to stabilize unstable periodic orbits for a class of sinusoidally forced nonlinear systems. Exploiting the classical circle criterion, a sufficient condition for the stabilization of unstable periodic solutions is derived for a class of controllers that genera...

The paper considers a single-mode CO2 laser that exhibits a cascade of period doubling bifurcations leading to chaos when it is driven by a sinusoidal signal of increasing amplitude. The requirement of a proper working of the laser, for relatively large amplitude of the forcing signal, naturally leads to the control problem of stabilizing periodic...

Characteristic exponents assignment and harmonic balance techniques are exploited to derive simple nonlinear models approximating a class of nonlinear dynamical systems with sinusoidal input

The paper deals with the problem of designing feedback controllers to stabilize unstable periodic orbits of chaotic systems. Moving from Pyragas time-delayed controllers (1992), classical frequency-domain stability criteria are exploited in order to select an optimal solution. An example illustrates the efficacy of the proposed method

This paper proposes a control design method for stabilizing a chaotic signal of a non-linear system to a periodic signal. The underlying idea of the method is the cancellation via feedback control of the subharmonic components of the considered signal. The resulting feedback control scheme possesses a high degree of robustness against system uncert...

The paper studies the bifurcations of limit cycles in a rather general class of nonlinear dynamic systems. Relying on the classical harmonic balance approach as applied in control engineering neat frequency conditions for such bifurcations are derived. These results, approximate in nature, make clear the structural mechanism of the considered pheno...

In this work the problem of designing a secure communication system is addressed. Discrete time chaotic signals are used to mask information samples. Dead-beat synchronizing systems permit exact synchronization in finite time. This property can be used in secure communication schemes. An alternative approach uses a combination of chaotic signals to...

The problem of estimating the stability domain of the origin of an n-order polynomial system is considered. Exploiting the structure of this class of systems it is shown that, for a given quadratic Lyapunov function, an estimate of the stability domain can be obtained by solving a suitable convex optimization problem. This estimate is shown to be o...

The harmonic balance method is applied to the analysis of period-doubling bifurcations in a general class of nonlinear feedback systems. Compact conditions for the prediction and stability analysis of period-doubling bifurcations are obtained. Specializations of these conditions for systems in which the nonlinear subsystem is static are given. The...

Three rate equations describing the single-mode CO₂ laser dynamics are derived by applying the theory of linear filters to an improved four-level model. The model is studied in the case of periodic modulations of the losses and compared with the outcome of an experiment, revealing a good agreement

The paper studies the bifurcations of limit cycles of feedback systems depending on a parameter, and uses the harmonic balance method in a suitable frequency band to derive simplified conditions for their existence. These conditions give a picture of every kind of such (generic) bifurcations and can be applied to synthesize in a simple way nonlinea...

A structural approach is presented for the synthesis of self-synchronizing chaotic systems from an important class of systems studied in nonlinear control theory. A general system decomposition leads to the derivation of conditions for self-synchronization. Continuous-time self-synchronizing systems and dead-beat discrete-time self-synchronizing sy...

A study of complex dynamics in a simple important class of nonlinear systems has been developed. The well-known phenomena of period doubling and homoclinic orbit have been analysed and simple conditions, approximate in nature, for their occurrence are derived. They allow one to establish some connections of such complex behaviours with structural c...

The problem of synchronizing discrete-time chaotic systems is investigated. A new appealing property, the dead-beat synchronization, or exact synchronization in finite time, is presented, and conditions for its accomplishment in a simple important class of nonlinear maps are given. An original secure communication scheme which effectively exploits...

The problem of estimating the stability domain of the origin of an n-order polynomial system is considered. Exploiting the structure of this class of systems it is shown that, for a given quadratic Lyapunov function, an estimate of the stability domain can be obtained by solving a suitable convex optimization problem. This estimate is shown to be o...

The paper studies the bifurcations of limit cycles for a class of feedback systems depending on a parameter. The use of harmonic balance methods in a suitable frequency band of the system leads to conditions in terms of simple equations which give a complete picture of every kind of generic bifurcation. Examples of application concerning the predic...

The problem of the existence of equivalent self-synchronizing systems for a given chaotic system containing a unique stationary and memoryless nonlinear element is addressed. By employing classical frequency domain stability results, one-parameter families of equivalent self-synchronizing systems are given in an explicit way. This degree of freedom...

The use of the harmonic balance method for the control of period doubling bifurcations is considered. The objectives of the control design can include delay of a given period doubling bifurcation as well as stabilization. The results are inherently approximate in nature

The paper presents a frequency domain approach for studying the chaotic dynamics of an important class of nonlinear circuits. By formulating an elementary model of chaos and using the harmonic balance principle, techniques for the analysis and the stabilization to a periodic solution of complex systems are developed. They result in engineering tool...

The problem of estimating the stability domain of the origin of an n-order polynomial system containing linear, quadratic and cubic terms is considered. Exploiting the structure of this class of systems, it is shown that for a given quadratic Lyapunov function an estimate of the stability domain can be obtained by solving a suitable optimization pr...

A software implementation of PLASMO (Plasmopara Simulation Model) model for downy mildew (Plasmopara viticola Berl. et De Toni) of grapevine (Vitis vinifera L.) development forecasting is presented in this paper. The computer program has been developed to facilitate validation and further improvements and to allow direct model use in vineyard manag...

The recent interest in the area of the control of chaos is remarked and the various approaches to this problem presented in the literature are briefly summarized. The Harmonic Balance (HB) technique for the approximate analysis of systems with complex behaviour is outlined and the general idea of using this technique for control problems is propose...

The recent interest in the area of the control of chaos is remarked and the various approaches to this problem presented in the literature are briefly summarized. The Harmonic Balance (HB) technique for the approximate analysis of systems with complex behaviour is outlined and the general idea of using this technique for control problems is propose...

The paper considers the problem of determining the conditions under which a nonlinear dynamical system can give rise to a chaotic behaviour. On the basis of the harmonic balance principle, which is widely used in the frequency analysis of nonlinear control systems, two practical methods are presented for predicting the existence and the location of...

The paper proposes a practical engineering approach for predicting chaotic dynamics in an important class of nonlinear systems. The aim of this approach is to provide a heuristic method of analysis which can give reasonably accurate answers but is far simpler to apply than other more rigorous methods based on nonlinear dynamics. Our approach is fou...

Investigates the chaotic behaviour of nonlinear feedback systems. A heuristic model of this phenomenon is proposed and applied. Conditions for the existence and the location of chaotic motions are derived in terms of simple relations among the parameters of the system. Two examples show the application of the method and its approximation is discuss...

A n-order quadratic system is considered and an analysis of the domain of attraction of its origin is developed in the paper. The presented method selects a quadratic Lyapunov function V on the basis of the linear part of the system under study and of possible information about the field where such a system holds. In particular, this field is defin...

The problem of the existence and of the uncertainty of limit cycles in nonlinear feedback systems is examined. If approximate solution obtained using the describing function method is assumed to be known for a class of multiloop polynomial systems then sufficient conditions are derived to ensure in the neighborhood the existence of a true periodic...

A quite general approach to the problem of stabilizing a SISO (single-input single-output) bilinear system by output feedback is presented. Following a Lyapunov-like method, a family of admissible controls is defined and an easy way for deriving its general features is proposed. Previous results can be obtained as special cases of this approach. Nu...

This note presents a method for designing the linear feedback of a single-input single-output (SISO) bilinear system. By using the concept of matrix measure guaranteed estimations are obtained for the main characteristics of the control system. These results allow a quite simple selection of the feedback gain according to the design specifications.

Some considerations on the stability robustness of a state space description for perturbed linear systems are presented. On the basis of a determinantal criterion the two problems of the stability domain and of checking in the parameter space are considered and a number of computationally simple results are derived. An extension to a general pole p...

The presence of limit cycles in feedback bilinear systems is investigated. Using a procedure quite similar to the sinusoidal describing function method, an approximable solution is derived. The existence and the uncertainty of an actual solution using techniques based on a continuation principle are than stated

This paper presents some results obtained in time series forecasting using two nonstandard approaches and compares them with those obtained by usual statistical techniques. In particular, a new method based on recent results of the General Theory of Optimal Algorithm is considered. This method may be useful when no reliable statistical hypotheses c...

This paper deals with the problem of the estimation of regions of asymptotic stability for continuous, autonomous, nonlinear systems. The first part of the work provides a comprehensive survey of the existing methods and of their applications in engineering fields. In the second part certain topological considerations are first developed and the "t...

A revised version of the Group Method of Data Handling (GMDH) specifically oriented to nonlinear modelling and forecasting of time series is presented. Particular attention is devoted to the problems of partial models optimal structure determination and selection of intermediate variables, both affecting the final choice of the model. In particular...

This paper specifically analyses the problem of on-line prediction (with a lead time from 1 min to 30 min) of the residual load obtained after the removal of a base load determined by using standard techniques. It is shown that the Zadeh-Ragazzini method and the ARMA model method are both well suited for the on-line forecasting of the electric load...

This note gives some stability results concerning second-order systems dot{x} = f(x) , where f(x) contains either linear and quadratic or linear and cubic terms in x . Following a Lyapunov-like approach, a closed-form estimate for asymptotic stability regions of such systems is derived in terms of quadratic functions and then it is optimized with r...

The paper deals with the problem of the estimation of regions of asymptotic stability for continuous, autonomous, nonlinear systems. After an outline of the main approaches available in the literature, the "trajectory reversing method" is presented as a. powerful numerical technique for low order systems. Then, an analytical procedure based on the...

On-line prediction of electric load in the buses of the EHV grid of a power generation and transmission system is basic information required by on-line procedures for centralized advanced dispatching of power generation. This paper presents two alternative approaches to on-line short term forecasting of the residual component of the load obtained a...

An approach is proposed to the study of the electric arc near current zero by means of mathematical models. The approach is based on Lyapunov's stability theory and allows a qualitative analysis of the nonlinear differential equations describing the phenomenon. The main results concern the determination of the set of conditions leading to arc extin...

The "classic" approaches to the class selection problem (essentially founded on statistical hypothesis testing or on realization theory) are based on the assumption that the available data are actually generated by one of the considered structures, and the aim is to select this structure by processing such data. On the contrary, in these last years...

In view of the particular interest in the problem of reduced-order modeling in recent years, some considerations not sufficiently investigated in current literature are pointed out and a comprehensive set of references is given.

A linear time-varying stochastic system described in terms of input-output data corrupted by noise is given and an optimal, time-invariant, low-order approximating model is required. After the problem statement, the paper introduces an input-independent criterion and then considers the problem of its evaluation from the available data. A procedure...

The identification of the Italian power network, which is interconnected within the European system, is examined. A simplified linear model is assumed, which approximates nonlinearities for small perturbations occurring under normal operating conditions. The load variations in different networks are assumed not to be correlated; cross correlations...