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This work explores the dynamics of an epidemic considering an SIVIS (susceptible-infected-vaccinated-infected-susceptible) epidemiological model, accounting for heterogeneous susceptibility, governmental interventions, social behavioral dynamics and public reactions in both of autonomous and nonautonomous aspects. The study frames the system as an optimal control problem, considering time-dependent control strategies for strength of social behavior of public and pharmaceutical treatments. The emergence of a coexistence steady state is analyzed based on the basic reproduction number. The impact of model parameters on disease propagation is assessed through sensitivity analysis. Transcritical bifurcation-induced stability alteration is explored, and numerical simulations illustrate theoretical findings. The proposed system investigates the dynamical behavior in case of periodic transmission rate. It vividly highlights the profound impact of factors such as vaccination rates, frequency and amplitude of transmission on the enduring and evolving dynamic patterns exhibited by the disease.

This article explores the global properties of a generalized S I c I R S (susceptible-asymptomatically infected-symptomatically infected-recovered-susceptible) epidemic model, which takes into consideration the factors associated with government policies, public responses and social behavioural reactions. Essentially, this study centres on infectious diseases that can be propagated through asymptomatic carriers—individuals who are infected and contagious but do not exhibit any disease symptoms. Additionally, the analysis delves into the effects of environmental fluctuations on the dynamics of disease transmission. For the deterministic model, it has been observed that disease invasion occurs in the system when the basic reproduction number exceeds 1. On the other hand, if we raise the noise intensities in case of the stochastic model, the disease extinction happens quickly. Also, we have proved that the system undergoes transcritical bifurcation in the vicinity of the infection-free equilibrium. Also, two-parameter bifurcation provides the regions where stability of both the equilibrium points are analysed. This work, in particular, highlights the significance of nonlinear dynamic analyses on epidemic models. It also emphasizes the substantial impact that social behaviour and governmental action have on disease transmission by asymptomatically infected carriers and symptomatically infected individuals. The numerical data and simulations illustrate the critical role of government interventions in managing an epidemic, and the system tends to achieve an infection-free state more rapidly when the government takes early action during the onset of a disease outbreak.

The robust stabilization problem with respect to both dynamic and parametric uncertainty for linear deterministic systems is analyzed in the present article. The robust design methods consider either the dynamic modelling in frequency domain of the uncertainty or, its parametric representation in the state space realisation. Suitable analysis approaches for parametric uncertainty modelling are provided by Kharitonov and Edge-type theorems. Under some specific assumptions, these methods allow to determine the whole admissible domain of the uncertain parameters for which a system is stable. It shall describe a method that combines the advantages of the control techniques with ones given by the polytopic representation of parametric uncertainty. A modified ∞ loop-shaping approach allowing to solve control problems in which robust stabilization, sensitivity reduction, and model following design objectives are formulated is presented and it allows to handle tracking design specifications. The modified loop-shaping procedure allows to design a controller that provides a) robust stability with respect to the normalized left coprime factorization (NLCF); b) reduced sensitivity with respect to output disturbance on a specified range of frequencies, and c) tracking of the output of a given ideal model. The article is finished with a case study in which a two degrees-of-freedom control system with respect to the pitch angle for the longitudinal dynamics of a UAV (ARCHER V1.7) is designed using the modified ∞ loop-shaping procedure.

The central limit theorem states that, in the limits of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to attain a stable distribution. The condition of independence, however, only holds in real systems as an approximation. To extend the theorem to more general situations, previous studies have derived a version of the central limit theorem that also holds for variables that are not independent. Here, we present numerical results that characterize how convergence is attained when the variables being summed are deterministically related to one another through the recurrent application of an ergodic mapping. In all the explored cases, the convergence to the limit distribution is slower than for random sampling. Yet, the speed at which convergence is attained varies substantially from system to system, and these variations imply differences in the way information about the deterministic nature of the dynamics is progressively lost as the number of summands increases. Some of the identified factors in shaping the convergence process are the strength of mixing induced by the mapping and the shape of the marginal distribution of each variable, most particularly, the presence of divergences or fat tails.

This paper presents a solution of the problem of designing a stabilizing state feedback for a linear multivariable discrete-time stationary system based on the data of the system’s behavior. It is assumed that the system’s matrices are unknown. An algorithm for directly designing a feedback matrix based on the Sylvester matrix equation without solving the identification problem is considered. The conditions for the existence of a solution of the design problem are obtained. A numerical example is considered.

The problem of the approach of a tether system with an uncontrolled space object (space debris, cargo, etc.) in an almost circular near-Earth orbit is considered. An approach method is proposed that consists of the preliminary transfer of an active spacecraft to an orbit whose parameters are selected so that in its relative motion it moves along a trajectory close to an ellipse relative to a passive space object. Next, the tether system is deployed with a gripper device in the radial direction, and the length of the tether approximately corresponds to half of the small semiaxis of the ellipse of relative motion. After the end of the tether’s deployment, the entire system continues to rotate around the passive space object. In this case, there is a possibility of additional correction of the length of the tether in order to reduce the minimum distance between the gripper device and the load. To control the movement of an active spacecraft, jet engines are used, the components of the continuous thrust of which are directed along the transversal and binormal orbits. The results of end-to-end modeling in a geocentric fixed coordinate system of the considered stages of pointing the gripper device at a passive space object in the spatial case are presented, including an assessment of the impact of the gripper process on the subsequent movement of the entire system with cargo during its transportation.

In the context of deterministic discrete-time control systems, we examined the implementation of value iteration (VI) and policy (PI) algorithms in Markov decision processes (MDPs) situated within Borel spaces. The deterministic nature of the system's transfer function plays a pivotal role, as the convergence criteria of these algorithms are deeply interconnected with the inherent characteristics of the probability function governing state transitions. For VI, convergence is contingent upon verifying that the cost difference function stabilizes to a constant$ k $ensuring uniformity across iterations. In contrast, PI achieves convergence when the value function maintains consistent values over successive iterations. Finally, a detailed example demonstrates the conditions under which convergence of the algorithm is achieved, underscoring the practicality of these methods in deterministic settings.

The motion of two interacting bodies along a straight line in a medium with quadratic resistance is considered. The force of interaction between the bodies is a control action, on which no restrictions are imposed. The problem of moving each of the bodies of the system over the given distance is solved, provided that the bodies are at rest at the beginning and at the end of the movement. In the constructed motion, moments of time at which the interaction force instantly changes the velocities of the bodies alternate with time intervals in which the interaction force is zero or provides the equality of the velocities of the bodies.

This paper has two purposes. One is to demonstrate contextuality analysis of systems of epistemic random variables. The other is to evaluate the performance of a new, hierarchical version of the measure of (non)contextuality introduced in earlier publications. As objects of analysis we use impossible figures of the kind created by the Penroses and Escher. We make no assumptions as to how an impossible figure is perceived, taking it instead as a fixed physical object allowing one of several deterministic descriptions. Systems of epistemic random variables are obtained by probabilistically mixing these deterministic systems. This probabilistic mixture reflects our uncertainty or lack of knowledge rather than random variability in the frequentist sense.

In transportation modeling, after defining a road network and its origin-destination (OD) matrix, the next important question is how to assign traffic among OD-pairs. Nowadays, advanced traveler information systems (ATIS) make it possible to realize the user equilibrium solution. Simultaneously, with the advent of the Cooperative Intelligent Transport Systems (C-ITS), it is possible to solve the traffic assignment problem in a system optimum way. As a potential traffic assignment method in the future transportation system for automated cars, the deterministic system optimum (DSO) is modeled and simulated to investigate the potential changes it may bring to the existing traditional traffic system. In this paper, stochastic user equilibrium (SUE) is used to simulate the conventional traffic assignment method. This work concluded that DSO has considerable advantages in reducing trip duration, time loss, waiting time, and departure delay under the same travel demand. What is more, the SUE traffic assignment has a more dispersed vehicle density distribution. Moreover, DSO traffic assignment helps the maximum vehicle density of each alternative path arrive almost simultaneously. Furthermore, DSO can significantly reduce or avoid the occurrence of excessive congestion.