Costanzo Manes

• PhD
• Professor (Associate) at University of L'Aquila

This work deals with 1-moment stability for continuous-time Markov Jump Linear Systems under stationary and time-varying transition rates. The analysis leverages comparison systems to exploit stability results from the context of positive systems. For the case of stationary transition rates, we introduce novel sufficient conditions of 1-moment stab...

Brain–computer interfaces (BCIs) are pivotal in translating neural activities into control commands for external assistive devices. Non-invasive techniques like electroencephalography (EEG) offer a balance of sensitivity and spatial-temporal resolution for capturing brain signals associated with motor activities. This work introduces MOVING, a Mult...

This work focuses on linear continuous‐time systems with time‐varying delays, in the general case of time‐varying matrices. Initially, we explore the case of positive systems within this class and introduce two distinct delay‐independent conditions of exponential input‐to‐state stability. Moreover, we provide guaranteed exponential convergence rate...

In collaborative robotics, to improve human-robot interaction (HRI), it is necessary to avoid accidental impacts. In this direction, several works reported how to modify the trajectories of collaborative robots (cobots), monitoring the operator's position in the cobot workspace by industrial safety devices, cameras, or wearable tracking devices. Th...

The following work aims to improve the interaction between humans and collaborative robots (IURc) by limiting potential accidental collisions. The IURc can be enhanced by detecting decreases in the operator's concentration caused by emotional state alterations. Therefore, by modifying the trajectory and reducing the speed of the task, it is possibl...

This work introduces novel results on the stability of linear time-varying discrete-time delay systems, addressing both internal stability and input-to-state stability. We start from the special case of positive delay systems and provide conditions of global exponential stability, both delay-dependent and delay-independent. Moreover, we formulate a...

Target tracking represents a state estimation problem recurrent in many practical scenarios like air traffic control, autonomous vehicles, marine radar surveillance and so on. In a Bayesian perspective, when phenomena like clutter are present, the vast majority of the existing tracking algorithms have to deal with association hypotheses which can g...

The main subject of this work is the stability analysis of Switched Auto-Regressive models with eXogenous inputs (SARX), which constitute a reference class for switched and hybrid system identification. The work introduces novel conditions for the arbitrary switching stability of multiple-input multiple-output SARX models which exploit the peculiar...

In order to be properly addressed, many practical problems require an accurate stochastic characterization of the involved uncertainties. In this regard, a common approach is the use of mixtures of parametric densities which allow, in general, to arbitrarily approximate complex distributions by a sum of simpler elements. Nonetheless, in contexts li...

Recent advances in the Optimal Transport theory allow to rewrite several known problems in a neat way, while providing a more general perspective. When dealing with mixture densities, or in general with intensities, such a framework naturally induces composite dissimilarities, together with corresponding Greedy Reduction and Refinement algorithms....

In target tracking and sensor fusion contexts it is not unusual to deal with a large number of Gaussian densities that encode the available information (multiple hypotheses), as in applications where many sensors, affected by clutter or multimodal noise, take measurements on the same scene. In such cases reduction procedures must be implemented, wi...

The stability analysis of time-delay systems is a tough task even in the linear case, especially when time-varying delays are considered. In recent years, for the class of positive delay systems, a number of insightful works appeared in the literature, highlighting their peculiar stability properties, which lead to simple and easy to check necessar...

In many practical contexts, Gaussian Mixtures are used as density approximators due to their versatility and representation capabilities. In some scenarios, it might be convenient to approximate a set of Gaussian densities with a single one, according to criteria which aim to preserve information while reducing the model complexity. This task can b...

Gaussian Mixtures (GMs) are a powerful tool for approximating probability distributions across a variety of fields. In some applications the number of GM components rapidly grows with time, so that reduction algorithms are necessary. Given a GM with a large number of components, the problem of Gaussian Mixture Reduction (GMR) consists in finding a...

This work studies the stability properties of Switched AutoRegressive eXogenous (SARX) models subject to arbitrary switching sequences. We provide necessary and sufficient conditions for the arbitrary switching stability of multiple-input single-output SARX models under nonnegativity constraints, and sufficient-only conditions removing sign constra...

In many contexts Gaussian Mixtures (GM) are used to approximate probability distributions, possibly time-varying. In some applications the number of GM components exponentially increases over time, and reduction procedures are required to keep them reasonably limited. The GM reduction (GMR) problem can be formulated by choosing different measures o...

This work introduces novel results on linear coupled differential-difference systems with multiple time-varying delays. First, necessary and sufficient conditions for the positivity and delay-independent asymptotic stability of such systems are introduced. Then, exploiting the Internally Positive Representation technique , we show how such stabilit...

Switched models whose dynamic matrices are in block companion form arise in theoretical and applicative problems such as representing switched ARX models in state-space form for control purposes. Inspired by some insightful results on the delay-independent stability of discrete-time systems with time-varying delays, in this work, the authors study...

In this paper we propose an observer for a class of Lipschitz nonlinear systems affected by time-varying and known measurement delays which is an improvement of the one presented in [9]. Under the assumption that the delay function is piece-wise continuous and differentiable we prove that exponential convergence to zero of the observation error can...

In this paper we extend the stability results of cascaded closed-loop predictors for deterministic systems to stochastic linear systems with additive noise and arbitrarily large time-varying input delay, under suitable hypothesis on the delay function. We propose an output-feedback controller design based on a set of differential delay equations wi...

Body weight control is gaining interest since its dysregulation eventually leads to obesity and metabolic disorders. An accurate mathematical description of the behavior of physiological variables in humans after food intake may help in understanding regulation mechanisms and in finding treatments. This work proposes a multi-compartment mathematica...

This work studies the stability properties of Switched AutoRegressive eXogenous (SARX) models subject to arbitrary switching sequences. We provide necessary and sufficient conditions for the arbitrary switching stability of multiple-input single-output SARX models under nonnegativity constraints, and sufficient-only conditions removing sign constra...

Inspired by some insightful results on the delay-independent stability of discrete-time systems with time-varying delays, in this work we study the arbitrary switching stability for some classes of discrete-time switched systems whose dynamic matrices are in block companion form. We start from the special family of block companion matrices whose fi...

Inspired by some insightful results on the delay-independent stability of discrete-time systems with time-varying delays, in this work we study the arbitrary switching stability for some classes of discrete-time switched systems whose dynamic matrices are in block companion form. We start from the special family of block companion matrices whose fi...

This note investigates the behavior of a population of interconnected irreversible switches, whose switching mechanism is triggered by a chaotic map. Motivation comes from the fact that many emergent properties of biological systems are ruled by the activation of a population of biochemical switches, whose timing and fluctuations may lead to differ...

This work studies linear coupled differential-difference systems, in the general case of multiple time-varying delays. The paper presents two main contributions: first, we formulate necessary and sufficient conditions for both the positivity and delay-independent asymptotic stability of this class of systems. Then, exploiting the Internally Positiv...

This paper describes a generalized internally positive representation of a diagonalizable matrix and proves that its stability is equivalent to the fact that its eigenvalues belong to the zone described by the Karpelevich Theorem. This in turn implies the minimality of the generalized internally positive representation of complex numbers.

This work introduces the Internally Positive Representation of linear coupled differential-difference systems with time-varying delays. Then a stability analysis is conducted on this class of systems: relying on results established under positivity assumptions, the IPR technique leads to a novel sufficient condition for the delay-independent asympt...

We consider the problem of state-feedback control of linear continuous-time stochastic systems with nonlinear diffusion terms affected by time-varying input delays or, equivalently, by time-varying state measurement delays. We propose a finite-dimensional control law based on closed-loop predictors and derive sufficient delay bounds for the exponen...

This work introduces the internally positive representation of linear time-varying delay differential systems, in the general case of multiple time-varying delays. The technique, previously established for the delay-free case and recently extended to various classes of linear delay systems, aims at building a positive representation of systems whos...

The characterization of the behavior that can be achieved by a plant when interconnected with a controller is a topic widely investigated in mathematical systems theory. In this regard, many results have been obtained for several classes of continuous systems, and also for discrete–event and hybrid systems. However, current literature is rather sca...

Ghrelin, a peptide hormone, occupies a crucial role in food intake control. Differently from other hormones contributing to energy homeostasis, usually exerting their regulating action by signaling satiety (e.g. leptin), ghrelin is known to stimulate appetite and, in general, to upsurge the propensity of animals to seek out food and start eating. M...

The analysis and control of time-delay systems has gained increasing interest in the last decades due to the effectiveness of delay differential equations (DDEs) in modeling a wide range of physical and engineering frameworks, such as ecological systems, industrial processes, telerobotic systems, earth-controlled satellite devices, and biomedical e...

Ghrelin, a peptide hormone, occupies a crucial role in food intake control. Differently from other hormones contributing to energy homeostasis, usually exerting their regulating action by signaling satiety (e.g. leptin), ghrelin is known to stimulate appetite and, in general, to upsurge the propensity of animals to seek out food and start eating. M...

The subject of this paper is the identification of closed-loop continuous-time systems, with delayed feedback action, from sampled input-output measurements. In particular, a method for the identification of both forward and feedback subsystems is presented that requires only the knowledge of their orders and of the time-delay introduced in the fee...

This work introduces the Internally Positive Representation of linear continuous-time difference systems with multiple delays. The technique, originally developed for delay-free linear systems, and recently extended to differential systems with multiple delays, proved to be a useful tool to exploit results available for positive systems also for sy...

Type-2 Diabetes Mellitus (T2DM) is a metabolic syndrome characterized by low insulin sensitivity, so that higher amounts of insulin are required in order to keep glycemia in a safe range (approximately, 60 ~ 110 mg/dl or, equivalently, 3.33 ~ 6.11 mM). Although insulin resistance and T2DM are often treated without exogenous insulin administration,...

Ghrelin, a peptide hormone, occupies a crucial role in food intake control. Differently from other hormones contributing to energy homeostasis, usually exerting their regulating action by signaling satiety (e.g. leptin), ghrelin is known to stimulate appetite and, in general, to upsurge the propensity of animals to seek out food and start eating. M...

Timing and synchronization mechanisms are ubiquitous in living systems, and in many cases involve switch-like regulators that control complex molecular pathways and cellular functions. The switching of such regulators is often irreversible and controlled by the co-activation of a set of concurrent independent enabling events. Despite the random nat...

Artificial Pancreas (AP) is an expression referred to a set of techniques for the closed-loop control of the plasma glucose concentration by means of exogenous insulin administration in diabetic patients. Diabetes comprises a group of metabolic disorders characterized by high blood sugar levels over a prolonged period, due to pancreas failure to pr...

This chapter introduces the Internally Positive Representation of linear systems with multiple time-varying state delays. The technique, previously introduced for the undelayed case, aims at building a positive representation of systems whose dynamics is, in general, indefinite in sign. As a consequence, stability criteria for positive time-delay s...

This paper concerns the filtering problem of stochastic nonlinear systems that depend either on some external input (open-loop system) or on the system output (closed-loop system), through a controller. Such systems are denoted feedback systems. The following result is proven: for feedback systems, the minimum variance estimator belonging to a spec...

In this paper we propose definitions of equivalence via stochastic bisimulation and of equivalence of stochastic external behavior for the class of discrete-time stochastic linear control systems with possibly degenerate normally distributed disturbances. The first notion is inspired by the notion of probabilistic bisimulation for probabilistic cha...

In this paper we propose definitions of equivalence via stochastic bisimulation and of equivalence of stochastic external behavior for the class of discrete-time stochastic linear control systems with possibly degenerate normally distributed disturbances. The first notion is inspired by the notion of probabilistic bisimulation for probabilistic cha...

Abstract Ghrelin is a quite powerful hormone discovered in the end of the 1990s that controls appetite and energy homeostasis, alongside leptin and other hormones still to be investigated in depth by the medical sciences literature. On this poster we provide a simple mathematical model, consisting of a set of ordinary differential equations detaili...

In budding yeast, overcoming of a critical size to enter S phase and the mitosis/mating switch - two central cell fate events - take place in the G 1 phase of the cell cycle. Here we present a mathematical model of the basic molecular mechanism controlling the G 1 /S transition, whose major regulatory feature is multisite phosphorylation of nuclear...

Supplementary Figures 1-19, Supplementary Tables 1-10, Supplementary Notes 1-24 and Supplementary References

Role of functional and decoy phosphosites in the control of timing and coherence of multi-target regulatory events in cell cycle progression. Upper and lower left panels of the movie show a schematic cell nucleus containing SBF-Whi5-controlled G1/S regulon genes. Open circles represent non-transcribed genes, while green circle transcribed genes. Ri...

We present a state observer for a class of nonlinear systems with variable measurement delays, based on a modular design. An array of elementary high-gain observers with exponential decaying dynamics of the error are arranged to compensate arbitrarily large delays. We derive the relationship between the error decay rate, the observer gain and the b...

This chapter deals with the problem of output feedback control of nonlinear systems affected by time-varying measurement delay. A control law is presented, which is made of an observer-controller cascade where the controller is a classic state-linearizing scheme, and the observer is a high-gain observer of chain-type. It is shown that under suitabl...

Amongst the entire potential spectrum of expansion of the engineering sciences as an omnipresent field, we might point out the studies of drugs, applied pharmacology, as a good candidate for receiving attention. The common problematic encountered in the literature faced by the industry of drugs is the high cost for drug development and systematic a...

Interval observers are dynamic systems that provide upper and lower bounds of the true state trajectories of systems. In this work we introduce a technique to design interval observers for linear systems affected by state and measurement disturbances, based on the Internal Positive Representations (IPRs) of systems, that exploits the order preservi...

This paper presents an observer with exponential error decay for systems described by bilinear input-state dynamics and output functions that are ratios of polynomials in the state. It is shown that such kind of systems can be immersed into systems of higher dimension, with time-varying linear state dynamics and linear output map. The observer here...

This paper deals with the LQG control problem of flexible structures. Since the solution to this problem is given by infinite dimension equations, an approximation scheme is necessary to find an implementable control law. Here a Galerkin approach is used. The novelty of the paper is the successful use of the eigenfunctions of the system instead of...

The problem of state observation for nonlinear systems in which the output measurement is accessible after some time delay is studied in this paper, and an observer is proposed for the unforced case. On this matter no results, to our knowledge, are available in literature. The proposed observer is a nonlinear delay system and is an identity observe...

On this work it is discussed on the optimal control theory as supplementary and complementary methodological procedure to operations researches. Accordingly, it is disserted on the importance of optimal control theory as an essential tool for supporting operations research on its chases for enhancing processes by means of optimization. Here two cas...

We develop a positive observer for general (i.e. non necessarily positive) linear time varying systems, in both the continuous and discrete time cases. A nice feature of the approach is that no change of coordinates is needed. The observer size is twice the size of the observed system and it is stable whenever the observed system is stable. The des...

This paper presents a method for designing state observers with exponential error decay for nonlinear systems whose output measurements are affected by known time-varying delays. A modular approach is followed, where subobservers are connected in cascade to achieve a desired exponential convergence rate (chain observer). When the delay is small, a...

An Internally Positive Representation (IPR) of a non-positive system is a positive system that, under suitable input, state and output transformations, exactly replicates the behavior of the original system. Any construction method of an IPR necessarily introduces additional natural modes, which in some cases are unstable. In a previous paper the a...

This paper concerns the problem of the control of linear systems by means of feedback from delayed output, where the delay is known and time-varying. The main advantage of the approach is that it can be applied to systems with any delay bound, i.e. not only small delays. The predictor is based on a combination of finite-dimensional elementary predi...

We consider the problem of controlling a linear system when the state is available with a known time-varying delay (delayed-state feedback control) or the actuator is affected by a delay. The solution proposed in this paper consists in partially assigning the spectrum of the closed-loop system to guarantee the exponential zero-state stability with...

Motivated by a practical problem, in this work we investigate the problem of simultaneous estimation of state and parameters of an Hidden Markov Model with a particular structure. The motivating application is the problem of automatic counting of bubbles or droplets flowing into a microfluidic channel, where the noisy output of a photodiode has to...

Sensors providing only quantized or binary measurements are present in several automation contexts. A remarkable example is the Radio Frequency IDentification technology when only the detection of the tags is used as information for robot localization. In this paper we propose an algorithm which merges some concepts of the Unscented Kalman Filter (...

This paper presents a method for designing state observers with exponential error decay for nonlinear systems whose output measurements are affected by known time-varying delays. A modular approach is followed, where sub-observers are connected in cascade to achieve a desired exponential convergence rate (chain observer). The observer employs delay...

We consider the problem of controlling a linear system when the state is available with a non-negligible delay (delayed-state-feedback control). In such conditions, the resulting closed-loop system is always a time-delay-system. The solution proposed in this paper consists in partially assigning the spectrum of the closed-loop system while ensuring...

In this work we consider the problem of training a linear classifier by assuming that the number of data is huge (in particular, data may be larger than the memory capacity). We propose to adopt a linear least-squares formulation of the problem and an incremental recursive algorithm which requires to store a square matrix (whose dimension is equal...

The problem of realizing arbitrary transfer functions as combinations of positive filters, or, more in general, of representing arbitrary systems by means of Internally Positive Representations (IPRs), has been widely investigated in the discrete-time framework. An IPR is a positive state-space representation, endowed with input, state and output t...

This paper presents a state observer for drift observable nonlinear systems when output measurements are affected by a known and bounded time varying delay. The proposed observer is an improvement over our previous work in [15] and it includes a delay-dependent gain to attain exponential convergence to zero of the estimation error. The result is il...

Two families of observers for discrete-time nonlinear systems are presented in this paper, whose design is based on the Taylor approximation of the inverse of the observation map. Semiglobal convergence results are provided under the assumption that the system observation map is a globally analytic diffeomorphism. The performances of the observers...

Stabilizing cascade observer-controller schemes for a class of nonlinear retarded systems are presented in this chapter. Conditions for the local and global asymptotic stability of the closed loop system are provided. Such conditions allow the separate design of the observer and of the controller subsystems (separation theorems).

The problem of representing linear systems through combination of positive systems is relevant when signal processing schemes, such as filters, state observers, or control laws, are to be implemented using “positive” technologies, such as Charge Routing Networks and fiber optic filters. This problem, well investigated in the SISO case, can be recas...

This paper presents a new technique for the construction of Internal Positive Representations (IPRs) of discrete time linear systems. The proposed method overcomes the limitations of a previously proposed technique, which provides stable IPRs of systems under a restrictive assumption on the position of the eigenvalues in the complex plane. The new...

The concept of Internally Positive Realization (IPR) of a system generalizes the idea of realization of a generic transfer function through combination of positive filters: an IPR is a positive state space representation, endowed with input, state and output transformations, that realizes the dynamics of a given generic (i.e. with no positivity con...

An original approach for the construction of state observers for dynamic systems is presented in this article. New notions of observability (delay-observability and delay-drift-observability), useful for the development of the observer equations and for the convergence proof, are introduced and compared with other standard observability concepts. I...

In some technological frame-works, such as Charge Routing Networks (CRNs), or fiber-optic filters, only positive state–space realizations of digital signal processing algorithms, such as filters or control laws, can be implemented. On the other hand, the imposition of an a priori positivity constraint on the processing algorithm is a too strong des...

This paper presents an improved version of a semiglobal state observer for nonlinear analytic discrete-time systems, proposed by the authors in a recent work . The method is based on the Taylor approximation of the inverse of the system observability map. In this work the performances of the improved observer are compared with those of the old vers...

In this paper global and local separation theorems for a class of retarded nonlinear systems are investigated.

The state estimation problem is here investigated for a class of stochastic linear switching-output systems, in which the output matrix switches in a finite set of possible values according to a not directly measured discrete Markov sequence. This note presents a real-time algorithm, based on the optimal polynomial filtering approach, which achieve...

In several technological frameworks only positive state space realizations of signal processing algorithms (filters or control laws) can be implemented. On the other hand, the imposition of an a priori positivity constraint on the processing algorithm is a too strong design limitation. For this reason, many authors studied the problem of state-spac...

This paper presents some results on the local exponential convergence of the Polynomial Extended Kalman Filter (PEKF, see [14]) used as a state observer for deterministic nonlinear discrete-time systems (Polynomial Extended Kalman Observer, PEKO). A new compact formalism is introduced for the representation of the so called Carleman linearization o...

The problem of asymptotic state reconstruction of systems characterized by nonlinear state-output maps is investigated in this paper. The approach here presented is based on the approximation of output maps by means of polynomials or by ratios of polynomials, also named rational functions (RF). In previous papers the authors showed that when the in...