Structurally robust biological networks

Background: The molecular circuitry of living organisms performs remarkably robust regulatory tasks, despite the often intrinsic variability of its components. A large body of research has in fact highlighted that robustness is often a structural property of biological systems. However, there are few systematic methods to mathematically model and describe structural robustness. With a few exceptions, numerical studies are often the preferred approach to this type of investigation. Results: In this paper, we propose a framework to analyze robust stability of equilibria in biological networks. We employ Lyapunov and invariant sets theory, focusing on the structure of ordinary differential equation models. Without resorting to extensive numerical simulations, often necessary to explore the behavior of a model in its parameter space, we provide rigorous proofs of robust stability of known bio-molecular networks. Our results are in line with existing literature. Conclusions: The impact of our results is twofold: on the one hand, we highlight that classical and simple control theory methods are extremely useful to characterize the behavior of biological networks analytically. On the other hand, we are able to demonstrate that some biological networks are robust thanks to their structure and some qualitative properties of the interactions, regardless of the specific values of their parameters

Robust control strategies for multi-inventory systems with average flow constraints.

In this paper, we consider multi-inventory systems in the presence of uncertain demand. We assume that (i) demand is unknown but bounded in an assigned compact set and (ii) the control inputs (controlled flows) are subject to assigned constraints. Given a long-term average demand, we select a nominal flow that feeds such a demand. In this context, we are interested in a control strategy that meets at each time all possible current demands and achieves the nominal flow in the average. We provide necessary and sufficient conditions for such a strategy to exist and we characterize the set of achievable flows. Such conditions are based on linear programming and thus they are constructive. In the special case of a static flow (i.e. a system with 0-capacity buffers) we show that the strategy must be affine. The dynamic problem can be solved by a linear-saturated control strategy (inspired by the previous one). We provide numerical analysis and illustrative examples

Contracts as specifications for dynamical systems in driving variable form

This paper introduces assume/guarantee contracts on continuous-time control systems, hereby extending contract theories for discrete systems to certain new model classes and specifications. Contracts are regarded as formal characterizations of control specifications, providing an alternative to specifications in terms of dissipativity properties or set-invariance. The framework has the potential to capture a richer class of specifications more suitable for complex engineering systems. The proposed contracts are supported by results that enable the verification of contract implementation and the comparison of contracts. These results are illustrated by an example of a vehicle following system.Comment: 8 pages, 2 figures; minor changes in the final version, as accepted for publication in the Proceedings of the 2019 European Control Conference, Naples, Ital

Loop analysis of blood pressure/volume homeostasis

We performed a mathematical analysis of the dynamic control loops regulating the vasomotor tone of vascular smooth muscle, blood volume, and mean arterial pressure, which involve the arginine vasopressin (AVP) system, the atrial natriuretic peptide system (ANP), and the renin-angiotensin-aldosterone system (RAAS). Our loop analysis of the AVP-ANP-RAAS system revealed the concurrent presence of two different regulatory mechanisms, which perform the same qualitative function: one affects blood pressure by regulating vasoconstriction, the other by regulating blood volume. Both the systems are candidate oscillators consisting of the negative-feedback loop of a monotone system: they admit a single equilibrium that can either be stable or give rise to oscillatory instability. Also a subsystem, which includes ANP and AVP stimulation of vascular smooth muscle cells, turns out to be a candidate oscillator composed of a monotone system with multiple negative feedback loops, and we show that its oscillatory potential is higher when the delays along all feedback loops are comparable. Our results give insight into the physiological mechanisms ruling long-term homeostasis of blood hydraulic parameters, which operate based on dynamical loops of interactions

Enhancements on a saturated control for stabilizing a quadcopter: adaptive and robustness analysis in the flat output space

This paper extends our previous study on an explicit saturated control for a quadcopter, which ensures both constraint satisfaction and stability thanks to the linear representation of the system in the flat output space. The novelty here resides in the adaptivity of the controller's gain to enhance the system's performance without exciting its parasitic dynamics and avoid lavishing the input actuation with excessively high gain parameters. Moreover, we provide a thorough robustness analysis of the proposed controller when additive disturbances are affecting the system behavior. Finally, simulation and experimental tests validate the proposed controller

Temporal viability regulation for control affine systems with applications to mobile vehicle coordination under time-varying motion constraints

Controlled invariant set and viability regulation of dynamical control systems have played important roles in many control and coordination applications. In this paper we develop a temporal viability regulation theory for general dynamical control systems, and in particular for control affine systems. The time-varying viable set is parameterized by time-varying constraint functions, with the aim to regulate a dynamical control system to be invariant in the time-varying viable set so that temporal state-dependent constraints are enforced. We consider both time-varying equality and inequality constraints in defining a temporal viable set. We also present sufficient conditions for the existence of feasible control input for the control affine systems. The developed temporal viability regulation theory is applied to mobile vehicle coordination.Comment: 7 pages, 3 figures. Submitted to a conference for publicatio

A system-theoretic approach for image-based infectious plant disease severity estimation

The demand for high level of safety and superior quality in agricultural products is of prime concern. The introduction of new technologies for supporting crop management allows the efficiency and quality of production to be improved and, at the same time, reduces the environmental impact. Common strategies to disease control are mainly oriented on spraying pesticides uniformly over cropping areas at different times during the growth cycle. Even though these methodologies can be effective, they present a negative impact in ecological and economic terms, introducing new pests and elevating resistance of the pathogens. Therefore, consideration for new automatic and accurate along with inexpensive and efficient techniques for the detection and severity estimation of pathogenic diseases before proper control measures can be suggested is of great realistic significance and may reduce the likelihood of an infection spreading. In this work, we present a novel system-theoretic approach for leaf image-based automatic quantitative assessment of pathogenic disease severity regardless of disease type. The proposed method is based on a highly efficient and noise-rejecting positive non-linear dynamical system that recursively transforms the leaf image until only the symptomatic disease patterns are left. The proposed system does not require any training to automatically discover the discriminative features. The experimental setup allowed to assess the system ability to generalise symptoms detection beyond any previously seen conditions achieving excellent results. The main advantage of the approach relies in the robustness when dealing with low-resolution and noisy images. Indeed, an essential issue related to digital image processing is to effectively reduce noise from an image whilst keeping its features intact. The impact of noise is effectively reduced and does not affect the final result allowing the proposed system to ensure a high accuracy and reliability

Cascading Failures in the Global Financial System: A Dynamical Model

In this paper, we propose a dynamical model to capture cascading failures among interconnected organizations in the global financial system. Failures can take the form of bankruptcies, defaults, and other insolvencies. The network that underpins the financial interdependencies between different organizations constitutes the backbone of the financial system. A failure in one or more of these organizations can lead the propagation of the financial collapse onto other organizations in a domino effect. Paramount importance is therefore given to the mitigation of these failures. Motivated by the relevance of this problem and recent prominent events connected to it, we develop a framework that allows us to investigate under what conditions organizations remain healthy or are involved in the propagation of the failures in the network. The contribution of this paper is the following: i) we develop a dynamical model that describes the equity values of financial organizations and their evolution over time given an initial condition; ii) we characterize the equilibria for this model by proving the existence and uniqueness of these equilibria, and by providing an explicit expression for them; and iii) we provide a computational method via sign-space iteration to analyze the propagation of failures and the attractive equilibrium point