Most of the existing techniques for palmprint recognition rely on metrics, typically based on static functions, which evaluate the distance between a pair of features. In this paper, we propose a new technique for palmprint verification based on a dynamical system approach for principal palm lines matching. The proposed dynamic algorithm is recursive and involves a positive linear dynamical system, whose evolution depends on the matching level between the two input images. In a preprocessing phase, the procedure iteratively erodes both of the images to be compared, by eliminating points in each image that do not have enough close neighboring points both in the image itself and the comparison image. As a result of the iterations, only the points that have enough neighboring points in both the image itself and in the comparison image can survive. Thus, the output of the dynamical system converges either to zero, when a deep mismatch exists between the two images, or to a high value, when a good matching is observed. The results, in terms of verification, are in line with the state-of-the-art results in the current literature. The main advantage of the approach is its robustness when dealing with low-resolution and noisy images. The impact of noise (e.g., salt and pepper noise) is effectively reduced: images corrupted with such noise are easily recognized, while a randomly generated image is rejected even when compared with itself.@en

We formulate a control problem for positive compartmental systems formed by nodes (buffers) and arcs (flows). Our main result is that, on a finite horizon, we can solve the Pontryagin equations in one shot without resorting to trial and error via shooting. As expected, the solution is bang–bang and the switching times can be easily determined. We are also able to find a cost-to-go-function, in an analytic form, by solving a simple nonlinear differential equation. On an infinite horizon, we consider the Hamilton–Jacobi–Bellman theory and we show that the HJB equation can be solved exactly. Moreover, we show that the optimal solution is constant and the cost-to-go function is linear and copositive. This function is the solution of a nonlinear equation. We propose an iterative scheme for solving this equation, which converges in finite time. We also show that an exact solution can be found if there is a positive external disturbance affecting the process and the problem is formulated in a minsup framework. We finally provide illustrative examples related to flood control and epidemiology.@en

Despite their complexity, biological systems are able to endure huge parameter fluctuations and survive in the most diverse environmental conditions. Mathematical tools from graph theory and systems and control theory are naturally well-suited to understand the functioning of biological systems and reveal that their tremendous robustness is often rooted in their peculiar interconnection structure. This survey considers a wide class of ordinary-differential-equation biological models, including chemical reaction networks, and provides an overview of structural approaches proposed in the literature to assess whether a system structure enjoys fundamental qualitative properties, yielding specific types of dynamic or steady-state behaviours, regardless of the precise parameter values.@en

Introduction: Mal de Debarquement Syndrome (MdDS) is a poorly understood neurological disorder affecting mostly perimenopausal women. MdDS has been hypothesized to be a maladaptation of the vestibulo-ocular reflex, a neuroplasticity disorder, and a consequence of neurochemical imbalances and hormonal changes. Our hypothesis considers elements from these theories, but presents a novel approach based on the analysis of functional loops, according to Systems and Control Theory. Hypothesis: MdDS is characterized by a persistent sensation of self-motion, usually occurring after sea travels. We assume the existence of a neuronal mechanism acting as an oscillator, i.e., an adaptive internal model, that may be able to cancel a sinusoidal disturbance of posture experienced aboard, due to wave motion. Thereafter, we identify this mechanism as a multi-loop neural network that spans between vestibular nuclei and the flocculonodular lobe of the cerebellum. We demonstrate that this loop system has a tendency to oscillate, which increases with increasing strength of neuronal connections. Therefore, we hypothesize that synaptic plasticity, specifically long-term potentiation, may play a role in making these oscillations poorly damped. Finally, we assume that the neuromodulator Calcitonin Gene-Related Peptide, which is modulated in perimenopausal women, exacerbates this process thus rendering the transition irreversible and consequently leading to MdDS. Conclusion and Validation: The concept of an oscillator that becomes noxiously permanent can be used as a model for MdDS, given a high correlation between patients with MdDS and sea travels involving undulating passive motion, and an alleviation of symptoms when patients are re-exposed to similar passive motion. The mechanism could be further investigated utilizing posturography tests to evaluate if subjective perception of motion matches with objective postural instability. Neurochemical imbalances that would render individuals more susceptible to developing MdDS could be investigated through hormonal profile screening. Alterations in the connections between vestibular nuclei and cerebellum, notably GABAergic fibers, could be explored by neuroimaging techniques as well as transcranial magnetic stimulation. If our hypothesis were tested and verified, optimal targets for MdDS treatment could be found within both the neural networks and biochemical factors that are deemed to play a fundamental role in loop functioning and synaptic plasticity.@en

Introduction: Mal de Debarquement Syndrome (MdDS) is a poorly understood neurological disorder affecting mostly perimenopausal women. MdDS has been hypothesized to be a maladaptation of the vestibulo-ocular reflex, a neuroplasticity disorder, and a consequence of neurochemical imbalances and hormonal changes. Our hypothesis considers elements from these theories, but presents a novel approach based on the analysis of functional loops, according to Systems and Control Theory. Hypothesis: MdDS is characterized by a persistent sensation of self-motion, usually occurring after sea travels. We assume the existence of a neuronal mechanism acting as an oscillator, i.e., an adaptive internal model, that may be able to cancel a sinusoidal disturbance of posture experienced aboard, due to wave motion. Thereafter, we identify this mechanism as a multi-loop neural network that spans between vestibular nuclei and the flocculonodular lobe of the cerebellum. We demonstrate that this loop system has a tendency to oscillate, which increases with increasing strength of neuronal connections. Therefore, we hypothesize that synaptic plasticity, specifically long-term potentiation, may play a role in making these oscillations poorly damped. Finally, we assume that the neuromodulator Calcitonin Gene-Related Peptide, which is modulated in perimenopausal women, exacerbates this process thus rendering the transition irreversible and consequently leading to MdDS. Conclusion and Validation: The concept of an oscillator that becomes noxiously permanent can be used as a model for MdDS, given a high correlation between patients with MdDS and sea travels involving undulating passive motion, and an alleviation of symptoms when patients are re-exposed to similar passive motion. The mechanism could be further investigated utilizing posturography tests to evaluate if subjective perception of motion matches with objective postural instability. Neurochemical imbalances that would render individuals more susceptible to developing MdDS could be investigated through hormonal profile screening. Alterations in the connections between vestibular nuclei and cerebellum, notably GABAergic fibers, could be explored by neuroimaging techniques as well as transcranial magnetic stimulation. If our hypothesis were tested and verified, optimal targets for MdDS treatment could be found within both the neural networks and biochemical factors that are deemed to play a fundamental role in loop functioning and synaptic plasticity.@en

We consider the flow control problem for a general class of compartmental nonlinear systems, which can be associated with a graph whose nodes represent subsystems with their own internal dynamics, and whose arcs represent flow links among them. We consider a network-decentralized control: each agent controls a link between two nodes and decides its actions based on the states of these nodes only. We first provide general necessary and sufficient stabilizability conditions, proving that suitable network-decentralized strategies assure robust stability. We also show that, if all the subsystems at the nodes are marginally stable, a proper network-decentralized strategy asymptotically assures the minimum-norm flow, without requiring communication among agents.@en

This paper presents the mathematical conditions and the associated design methodology of an active fault diagnosis technique for continuous-Time linear systems. Given a set of faults known a priori, the system is modeled by a finite family of linear time-invariant systems, accounting for one healthy and several faulty configurations. By assuming bounded disturbances and using a residual generator, an invariant set and its projection in the residual space (i.e., its limit set) are computed for each system configuration. Each limit set, related to a single system configuration, is parameterized with respect to the system input. Thanks to this design, active fault isolation can be guaranteed by the computation of a test input, either constant or periodic, such that the limit sets associated with different system configurations are separated, and the residual converges toward one limit set only. In order to alleviate the complexity of the explicit computation of the limit set, an implicit dual representation is adopted, leading to efficient procedures, based on quadratic programming, for computing the test input. The developed methodology offers a competent continuous-Time solution to the optimization-based computation of the test input via Hahn-Banach duality. Simulation examples illustrate the application of the proposed active fault diagnosis methods and its efficiency in providing a solution, even in relatively large state-dimensional problems.@en

Due to the intrinsic uncertainty and variability affecting biochemical reaction networks, it is fundamental to assess their structural stability, i.e., to establish if all the networks having a given structure are stable independent of specific parameter values. For basic motifs in biochemical networks, we show that stability cannot be structurally proved by quadratic Lyapunov functions. However, structural stability of these motifs can be shown resorting to piecewise-linear Lyapunov functions, based on the results by Blanchini and Giordano (2014), who provide a theoretical framework and efficient numerical methods to evaluate structural stability of biochemical reaction networks with monotone reaction rates.@en

Complex dynamical networks can often be analyzed as the interconnection of subsystems: This allows us to considerably simplify the model and better understand the global behavior. Some biological networks can be conveniently analyzed as aggregates of monotone subsystems. Yet, monotonicity is a strong requirement; it relies on the knowledge of the state representation and imposes a severe restriction on the Jacobian (which must be a Metzler matrix). Systems with a monotonic step response (MSR), which include input-output monotone systems as a special case, are a broader class and still have interesting features. The property of having a monotonically increasing step response (or, equivalently, in the linear case, a positive impulse response) can be evinced from experimental data, without an explicit model of the system. We consider networks that can be decomposed as aggregates of MSR subsystems and we provide a structural (parameter-free) classification of oscillatory and multistationary behaviors. The classification is based on the exclusive or concurrent presence of negative and positive cycles in the system aggregate graph, whose nodes are the MSR subsystems. The result is analogous to our earlier classification for aggregates of monotone subsystems. Models of biomolecular networks are discussed to demonstrate the applicability of our classification, which helps build synthetic biomolecular circuits that, by design, are well suited to exhibit the desired dynamics.@en

To simplify the analysis of complex dynamical networks, we have recently proposed an approach that decomposes the overall system into the sign-definite interconnection of subsystems with a Positive Impulse Response (PIR). PIR systems include and significantly generalise input-output monotone systems, and the PIR property (or equivalently, for linear systems, the Monotonic Step Response property) can be evinced from experimental data, without an explicit model of the system. An aggregate of PIR subsystems can be associated with a signed matrix of interaction weights, hence with a signed graph where the nodes represent the subsystems and the arcs represent the interactions among them. In this paper, we prove that stability is structurally ensured (for any choice of the PIR subsystems) if a Metzler matrix depending on the interaction weights is Hurwitz; this condition is non-conservative. We also show how to compute an influence matrix that represents the steady-state effects of the interactions among PIR subsystems.@en

This paper proposes a decentralised explicit (closed-form) iterative formula that solves convex programming problems with linear equality constraints and interval bounds on the decision variables. In particular, we consider a team of decision agents, each setting the value of a subset of the variables, and a team of information agents, in charge of ensuring that the equality constraints are fulfilled. The structure of the constraint matrix imposes a communication pattern between decision and information agents, which can be represented as a bipartite graph. We associate each information agent with an integral variable and each decision agent with a saturated function, which takes the interval bounds into account, and we design a decentralised dynamic mechanism that globally converges to the optimal solution. Under mild conditions, the convergence is shown to be exponential. We also provide a discrete-time algorithm, based on the Euler system, and we give an upper bound for the step parameter to ensure convergence. Although the considered optimisation problem is static, we show that the proposed scheme can be successfully applied to find the optimal solution of network-decentralised dynamic control problems.@en

We present a revised analysis of Negative Capacitance (NC) in ferroelectric-insulator capacitors, and particularly of the difference between systems with and without a metal interlayer. We develop a model accounting for the three-dimensional electrostatics and report analytical and numerical results based on Landau-Ginzburg equations. Our results explain the lack of NC operation in capacitors having an interlayer metal, compare well with recent experiments and enlighten the role of traps at the ferroelectric-oxide interface.@en

The authors regret that the value of ß in the caption of Fig. 4 was incorrectly given as 4.5 × 109 m5 C-2 F-1. The correct value of ß is 2.25 × 1010 m5 C-2 F-1. Fig. 4, along with the full corrected caption, is displayed below. The Royal Society of Chemistry apologises for these errors and any consequent inconvenience to authors and readers. (Figure Presented).@en

The authors regret that the value of ß in the caption of Fig. 4 was incorrectly given as 4.5 × 109 m5 C-2 F-1. The correct value of ß is 2.25 × 1010 m5 C-2 F-1. Fig. 4, along with the full corrected caption, is displayed below. The Royal Society of Chemistry apologises for these errors and any consequent inconvenience to authors and readers. (Figure Presented).@en

We consider a class of epidemiological models in which a compartmental linear system, including various categories of infected individuals (e.g. asymptomatic, symptomatic, quarantined), is fed back by a positive feedback, representing contagion. The positive feedback gain decreases (in a sort of negative feedback) as the epidemic evolves, due to the decrease in the number of susceptible individuals. We first propose a convergence result based on a special copositive Lyapunov function. Then, we address a major problem for this class of systems: the deep uncertainty affecting parameter values. We face the problem adopting techniques from optimal and robust control theory to assess the sensitivity of the model. For this class of systems, the optimal control solution has a peculiar decoupling property that no shooting procedure is required. Finally, we exploit the obtained bounds to assess the effectiveness of possible epidemic control strategies, including intermittent restrictions adopted during the COVID-19 pandemic. @en

We consider the problem of tuning the output of a static plant whose model is unknown, under the only information that the input-output function is monotonic in each component or, more in general, that its Jacobian belongs to a known polytope of matrices. As a main result, we show that, if the polytope is robustly non-singular (or has full rank, in the non-square case), then a suitable tuning scheme drives the output to a desired point. The proof is based on the application of a well known theorem concerning the existence of a saddle point for a min-max zero-sum game. Some application examples are suggested.@en

A novel approach to the problem of inverse kinematics for redundant manipulators has been recently introduced: by considering the joints as point masses in a fictitious gravity field, and by adding proper constraints to take into account the length of the links, the kinematic inversion may be cast as a convex programming problem. Such a problem can be solved in an efficient way and may be easily modified to include constraints due to obstacles. Here we present further developments of the idea. In particular, for the case of planar robots, we show (i) how to impose hard constraints on the joint angles while preserving the convexity of the problem, and (ii) how to add constraints due to objects (for instance, a load carried by the robot) that are rigidly attached to some part of the robot.@en

This paper discusses the problem of tracking a moving target by means of a cluster of mobile agents that is able to sense the acoustic emissions of the target, with the aim of improving the target localization and tracking performance with respect to conventional fixed-array acoustic localization. We handle the acoustic part of the problem by modeling the cluster as a sensor network, and we propose a centralized control strategy for the agents that exploits the spatial sensitivity pattern of the sensor network to estimate the best possible cluster configuration with respect to the expected target position. In order to take into account the position estimation delay due to the frame-based nature of the processing, the possible positions of the acoustic target in a given future time interval are represented in terms of a compatible set, that is, the set of all possible future positions of the target, given its dynamics and its present state. A frame-by-frame cluster reconfiguration algorithm is presented, which adapts the position of each sensing agent with the goal of pursuing the maximum overlap between the region of high acoustic sensitivity of the entire cluster and the compatible set of the sound-emitting target. The tracking scheme iterates, at each observation frame, the computation of the target compatible set, the reconfiguration of the cluster, and the target acoustic localization. The reconfiguration step makes use of an opportune cost function proportional to the difference of the compatibility set and the acoustic sensitivity spatial pattern determined by the mobile agent positions. Simulations under different geometric configurations and positioning constraints demonstrate the ability of the proposed approach to effectively localize and track a moving target based on its acoustic emission. The Doppler effect related to moving sources and sensors is taken into account, and its impact on performance is analyzed. We compare the localization results with conventional static-array localization and positioning of acoustic sensors through genetic algorithm optimization, and results demonstrate the sensible improvements in terms of localization and tracking performance. Although the method is discussed here with respect to acoustic target tracking, it can be effectively adapted to video-based localization and tracking, or to multimodal information settings (e.g., audio and video).@en

For a vast class of dynamical networks, including chemical reaction networks (CRNs) with monotonic reaction rates, the existence of a polyhedral Lyapunov function (PLF) implies structural (i.e., parameter-free) local stability. Global structural stability is ensured under the additional assumption that each of the variables (chemical species concentrations in CRNs) is subject to a spontaneous infinitesimal dissipation. This paper solves the open problem of global structural stability in the absence of the infinitesimal dissipation, showing that the existence of a PLF structurally ensures global convergence if and only if the system Jacobian passes a structural non-singularity test. It is also shown that, if the Jacobian is structurally non-singular, under positivity assumptions for the system partial derivatives, the existence of an equilibrium is guaranteed. For systems subject to positivity constraints, it is shown that, if the system admits a PLF, under structural non-singularity assumptions, global convergence within the positive orthant is structurally ensured, while the existence of an equilibrium can be proven by means of a linear programming test and the computation of a piecewise-linear-in-rate Lyapunov function.@en