POSITION      

POSITIONS SERVED           

EDUCATION

• Ph.D. in Electronic Engineering, Faculty of Engineering, University of L'Aquila, February 10, 2000. Supervisor: Prof. A. Germani. The thesis (in Italian) deals with the control of undamped flexible structure, by using a functional approach. Most important results concerns the implementation of a finite dimensional control law, whose performances converge to the ones of the infinite dimensional optimal control law, as the approximation index increases to infinity. Taking into account the stability properties of the proposed control law, they are robust with respect to the system physical parameters.

• Qualification to the profession of Engineer, 120/120, University of L'Aquila, December 1995.

• Laurea Degree in Electronic Engineering, 110/110 cum laude, University of L'Aquila, Engineering Faculty, July 20, 1995. The thesis (in Italian) deals with the optimal polynomial filtering for linear discrete-time non Gaussian systems. Supervisor: Prof. A. Germani.

• "G. Galilei" High School Scientific Degree, 60/60, Pescara, July 1989.

TEACHING ACTIVITY
UNIVERSITY OF L'AQUILA, A.A. 2008/09

MESSAGE: STUDENTS CAN CONTACT PROF. P. PALUMBO IN ROME AT:
06 7716436     (IASI - Viale Manzoni, 30)
06 30155389   (BioMatLab, c/o Policlinico Gemelli)

• Contract Professor of "Systems Biology", specialistic laurea degree in Mathematics Engineering (lessons  in English)

• Teaching Assistant in:
  •  "Teoria dei Sistemi", Prof. C. Manes, first level laurea degree in Computer Science and Control, Electronic, Telecommunication Engineering

• "Teoria dei Sistemi", Prof. P. Pepe, first level laurea degree in Magement Engineering
• "Identificazione dei Modelli e Analisi dei Dati", Prof. A. Germani, first level laurea degree in Telecommunication Engineering
• "Sistemi di Regolazione e Controllo", Prof. P. Pepe, first level laurea degree in Electrical Engineering
• "Complementi di Automatica", Prof. A. Germani, specialistic laurea degree in Computer Science and Control Engineering

• At the University of L'Aquila, Pasquale Palumbo has been Contract Professor of:
  • "Teoria dei Sistemi II", first level laurea degree in Computer Science and Control Engineering, A.A. 2003/04 - 2006/07;
  • "Controlli Automatici II", first level laurea degree in Computer Science and Control Engineering, A.A. 2002/03;
  • "Calcolo delle Probabilità e Statistica", first level laurea degree in Civil Engineering, A.A. 2001/02;
  • "Calcolo delle Probabilità", laurea degree in Civil and Environmental Engineering, A.A. 2000/01

• "ESERCIZI DI TEORIA DEI SISTEMI - PARTE I", Libreria Universitaria Benedetti, L'Aquila, September 2003, ISBN 88-87182-14-0
• ESERCIZI DI TEORIA DEI SISTEMI - II EDIZIONE", Libreria Universitaria Benedetti, L'Aquila, Settembre 2008, ISBN 978-88-87182-31-6

More than 100 exercises all endowed with solutions above time-invariant finite-dimensional linear systems:
1) continuous and discrete time evolution: time and frequency domain approach (Laplace and Z transforms)
2) representation of transfer functions: Bode and polar
 diagrams
3) time-invariant linear systems stability; continuous-time systems (Routh criterion), discrete-time systems (Jury criterion), feedback systems (Nyquist criterion)
NEW PARAGRAPH on nonlinear systems stability
4) NEW CHAPTER on
controllability, observability and Kalman decomposition

• Pasquale Palumbo can be found for explanations and theses assistance at the Automatic Control and Robotics Laboratory (LabAuRo), Faculty of Engineering, University of L'Aquila.

• Ph.: ++39 0862 434453

• Fax: ++39 0862 434403

• Email: ppalumbo@ing.univaq.it
  

• Control of flexible systems, a functional approach: flexible structures can be accurately described by continuum models, i.e. dynamic systems with infinite-dimensional state space. Therefore, any finite-dimensional model necessarily neglects the higher order vibration modes. On the other hand, a control law can be implemented only if it admits a finite-dimensional representation. Two main approaches can be followed to obtain finite-dimensional control laws for infinite-dimensional systems, such as flexible structures: according to the classical approach, a finite-dimensional control law is designed on the basis of a finite-dimensional approximation of the flexible structure (finite elements, Galerkin projections, or other approximation schemes); however, such a classical approach neglects the higher order modes of vibration of the structure, so that in many cases the unmodeled modes can be excited by the control law itself, so inducing undesired and unexpected vibrations in the structure, phenomenon known as spillover. Because of the intrinsic infinite-dimensional nature of the mechanical structure, any control law designed on the basis of a finite-dimensional model may produce this undesired effect. On the other hand, according to a modern approach, a finite-dimensional control law is designed on the basis of a distributed parameter model of the flexible structure. Such a modern approach allows to overcome the drawbacks of the classical one, in that it provides feedback control laws suitably designed exploiting the infinite-dimensional model, where all the modes of vibration of the system are considered. With this approach, the spillover effects are avoided by ensuring the closed loop stability for the original flexible structure. When the regulator is achieved without taking its physical realizability into account, the resulting feedback control law may well be defined as an operator acting on an infinite-dimensional state space. In these cases, a finite-dimensional approximation scheme is needed in order to implement the control law. In order to make effective such a methodology, for any approximation index, the corresponding regulator has to ensure the modal stability of the system, in order to overcome the spillover. The paper R[7] (taken from the Ph.D. dissertation) deals with the LQG control of an undamped Euler-Bernoulli cantilever beam with a tip mass at the free end. The optimal solution to such a problem is available in the literature, and is achieved in an infinite-dimensional setting; also an approximate implementable transfer function is provided. However it is not clear how far the proposed approximate compensator is from the optimal solution. The idea of the paper is to present a sequence of approximate, physically implementable regulators converging to the optimal LQG solution. It is proved that, for any given finite time horizon, the evolution of the system state driven by the approximate control input converges in L2-norm to the evolution of the system state driven by the optimal control law, as the order of the approximation scheme increases. An interesting feature is that the transfer function of the approximated compensator monotonically approaches the shape of the transfer function of the optimal compensator, as it can be appreciated in the magnitude/phase Bode representation. Preliminary results have been presented in C[2]. In R[7] it is proved also that, for each order of the approximation, the closed loop system is strongly stable, and, moreover, the proposed compensator guarantees modal stability of the closed loop system also in the presence of stiffness/inertia uncertainties. Such performances are indeed achieved by means of a Galerkin approximation scheme, based on the complete set of the generalized eigenfunctions of the structure instead of the usual splines. In C[3], an implementable Luenberger-like observer has been proposed for a similar undamped flexible structure, whose measurements are acquired with a not negligible delay.

• Filtering of non Gaussian singular linear systems: it is well known that the optimal solution to the minimum variance filtering problem is given by the expectation value of the state conditioned by all the measurements up to the current time, that is the projection onto the linear space of all the Borel functions of the measurements. In the linear Gaussian case the optimal filter is given by the Kalman filter, which is a linear transformation of the measurements. Unfortunately, in the non Gaussian case, there is not a simple characterization of the conditional expectation, so that it is worthwhile to consider suboptimal estimates which have a simpler mathematical structure. The simplest suboptimal estimate is the optimal affine one. It consists in projecting the state onto the subspace of all the linear transformations of the output. For linear systems the optimal affine estimate is still achieved by the Kalman filter. Suboptimal estimates comprised between the optimal linear and the conditional expectation can be considered by projecting onto subspaces of polynomial transformations of the measurements. A quadratic filter has been implemented in C[1], for a digital linear system, whose measurements are affected by quantization noise. The optimal polynomial approach has been proposed for the filtering of linear singular systems (also known as descriptor systems). Pubblications in this field use the measurements in order to overcome the lack of knowledge coming from the singular model. According to non restrictive hypotheses, a regular system is associated to the singular model, whose state, filtered by using a polynomial estimate, univocally identify the descriptor vector. In R[2], the polynomial filter has been proposed in the discrete-time framework (a preliminar version has been presented in C[12]). It has been proved that the linear version C[4], gives back the maximum likelihood estimate, in the Gaussian case. In C[5] a Kalman-Bucy-like filter is achieved for a singular stochastic differential system, in the Ito formulation.

• Filtering and identification of variable structure systems: the research activity investigates the problem of state etimation and system identification for the general class of stochastic uncertain systems, in the discrete time framework. A very interesting case is the one of switching systems, that is systems whose matrices switch according to an unknown parameter. Taking into account the case of a Markovian switching parameter, a suitable state space realization has been proposed. It has been proved that the minimum variance linear approach C[7] (or the others available in literature) is not enough to simultaneously estimate both the state and the unknown parameter, unless a known input suitably excites the system. On the contrary, a polynomial approach C[10] is able also to identify the system even in complete absence of a known input. Such a polynomial approach has been applied to a digital telecommunication system, providing in real-time both system identification and channel estimation. In R[4], the case of absence of any stochastic or deterministic characterization of the switching parameter has been investigated. Such a loss of knowledge has been modeled by using an extended singular system, driven by bounded covariance extended noises, whose second order moments are not completely known. Then the minimax criterion is adopted (a preliminary version of the paper has been presented in C[6]). Simulations reported in R[4] show the effectiveness of the proposed approach, compared with other robust filters, such has the ones based on LMIs, or on the maximum entropy criterion. Moreover, in R[4], the asymptotic properties of the filter have been investigated. In C[11, 13] the uncertainties of the model deal with one or more unknown constant (or even slowly time-varying) parameters, taking values in a suitably defined discrete C[11] or continuous C[13] range. An extended state is defined, containing among its components the uncertain parameters and, then, is filtered by using the polynomial approach. The same problem of simultaneous parameter identification and filtering has been investigated in C[18], for a generic class of interval nonlinear systems. Analogously to the linear case, the approach is based on a suitably defined extended state, including the unknown parameters among its components: the extended state estimate is then achieved by means of the Polynomial EKF (PEKF), R[3].

• Filtering of stochastic nonlinear systems: taking into account the field of continuous time systems, the state estimate problem has been investigated in R[1] for a bilinear stochastic differential system, driven by unknown inputs. According to the Ito formulation, the measurements overcome the loss of knowledge concerning the unknown input, so that the optimal linear state estimate is achieved. In the discrete time framework, the case of stochastic linear systems driven by unknown nonlinearities has been investigated in C[8]: an extended singular system is considered, in order to model the uncertainties, and the state is filtered by using the minimum variance criterion. In R[3] the polynomial version of the Extended Kalman Filter (EKF), so widely used in many engineering frameworks, has been developed. According to the linear approximation of the system, the EKF performs well if the initial estimation error and the disturbing noises are small enough. On the other hand, the Polynomial-EKF (PEKF) is based on the Carleman stochastic bilinearization of the system, whose extended state is filtered by means of the minimum variance estimate; a preliminary version of R[3] has been presented in C[9]. A double index version of the PEKF has been proposed in C[15], where the first index is related to the degree of approximation of the nonlinear system, while the other is related to the order of the polynomial estimate adopted. The Carleman approximation has been also used in R[10], in order to estimate the state of a nonlinear stochastic differential system: the algorithm consists of the optimal linear filter applied to the bilinear differential system approximating the original model (a preliminary version had been presented in C[19]).  In C[23] a polynomial filtering approach has been used in a telecommunication framework: a recursive filtering algorithm is proposed for log-Rice signals generated by the envelope of noisy narrow band Gaussian signals through noisy logarithmic amplifiers. A class of filters is considered, and within this class the filter providing the optimal estimate is computed. A polynomial filtering approach has been used also in a robotic framework C[24], where a new analytical algorithm performs the localization of a mobile robot using odometry and laser readings. The algorithm provides the optimal affine filter in a class of suitably defined estimators. The comparison with the standard Extended Kalman Filter shows the efficiency of the proposed filter also in critical situations where the system nonlinearities cause a bad behavior of the EKF.

• State observers for deterministic nonlinear systems: in C[14] a state observer for continuous-time deterministic systems characterized by linear input-state dynamics and polynomial state-output function. The observer design is based on the embedding of the original dynamics into a higher order system, with time-varying linear state dynamics and linear state-output maps. The interest in this observer is in its capability of state reconstruction also in cases in which the original system is not drift-observable (observable from zero-inputs) nor uniformly observable (observable from any input). In C[22] the same methodology has been applied for systems characterized by output functions that are ratios of polynomials of the state. The case of linear and bilinear input-state dynamics is considered. Both C[14] and C[22] provide conditions for exponential error decay. From an applicative point of view, in C[16] an asymptotic observer for nonlinear systems (previously published by part of the authors) has been implemented in order to estimate the insulin flow from pure glucose measurements, taking into account a dynamical model of the glucose/insulin homeostasis.

• Control of stochastic systems: in C[25] the optimal control problem has been investigated for a linear stochastic system affected by disturbances generated by a nonlinear stochastic exosystem. The approach followed is based on the Carleman approximation of a stochastic nonlinear system [R3], and provides a real-time algorithm to design an implementable control law.
  

• Modeling and control of the glucose/insulin homeostasis (research activity developed at the BioMatLab of IASI, located at the Policlinico Gemelli Hospital): the homeostasis of glucose, involving the secretion of its controlling hormone insulin by pancreas is the object of several mathematical models over the past thirty years. One of the goals of this modeling effort is the measurement of the degree to which a given subject is able to accomodate a load of glucose (for instance administred as an intra-venous bolus, the well knwon Intra-Venous Glucose Tolerance Test, IVGTT). The fact that several attempts at modeling the glucose-insulin system have been made in the past points to the actual difficulty in constructing a model which is at the same time mathematically coherent, statistically robust and physiologically meaningful. In other words, the model should exhibit satisfactory properties of the solutions, its parameters should be statistically estimable with sufficient precision from data sets obtained from standard experimental procedures, and it should conform to established physiological concepts. So far, indeed, no single model exhibiting simultaneously all of these features has been proposed. In R[8] a family of delay-differential models of the glucose-insulin system is presented, whose members represent adequately the Intra-Venous Glucose Tolerance Test and allied experimental procedures of diabetological interest. Different models of the family have been identified from IVGTT data R[9], providing excellent results in terms of parameter estimation. These models, then, appear statistically and physiologically promising. In R[8] the mathematical analysis has been performed. All the models in the family admit positive bounded unique solutions for any positive initial condition and are persistent. The models agree with the physics underlying the experiments, and they all present a unique positive equilibrium point. Local stability is investigated in a pair of interesting member models: one, a discrete-delays differential system (a preliminar version of the model is presented in C[20]); the other, a distributed-delay system reducing to an ordinary differential system evolving on a suitably defined extended state space. In both cases conditions are given on the physical parameters in order to ensure the local asymptotic stability of the equilibrium point. These conditions are always satisfied, given the actual parameter estimates obtained experimentally. A study of the global stability properties is also performed. The modeling of insulin absorption from a subcutaneous infusion has been investigated in R[5], where a pair of time-varying periodic models have been proposed, both taking into account the fact that different absorption rates are associated with different times of a 24 hour period (a preliminary version of the paper has been presented in C[17]). In B[1] and C[21] the problem of tracking a desired level of plasma glycemia has considered, by means of continuous intravenous injection. Based on a single-distributed delay model which allows to properly take into account also a pancreatic insulin production , the closed loop control law is performed according to the feedback linearization theory: a state feedback is designed in order to exactly linearize the model w.r.t. a suitably defined change of coordinates. Then, the tracking of the deired level is achieved. In C[21] such a task is obtained by means of the minimization of a suitably defined performance index, which takes into account a desired glycemic profile. Of course, the parameter identification and the aim of a closed loop control are strictly related to the capability and quality of both glucose and insulin concentration measurements in plasma. At the present time, the former measurement is accurately achieved with low cost devices, while the latter is expensive and not immediate. In C[16] an asymptotic observer for nonlinear systems has been implemented in order to estimate the insulin flow from pure glucose measurements, taking into account a recent dynamical model of the glucose/insulin kinetics.

• Higher order methods for the solution of nonlinear equations: it is well known that, looking for the solution of nonlinear equations, the Newton's method has local quadratic convergence, according to a set of non restrictive convergence conditions. In R[6] a new iterative method for the scalar case is proposed, based on a suitable polynomial model derived from the Taylor series expansion. Providing the same Newton's convergence conditions, it achieves a convergence rate increasing with the approximation degree. Moreover, an easy implementable scheme is obtained, according to a specific matrix factorization, achieved in a closed form (i.e. no further numerical computation), by using the Jordan decomposition.