Loop-Shaping ℋ∞ Control of an Aeropendulum Model

This work presents a mathematical model of an aeropendulum system with two sets of motors with propellers and the design and simulation of a loop-shaping ℋ∞ control for this system. In this plant, the objective is to control the angular position of the pendulum rod through the torque generated by the thrust of the motorized propellers at the end of the rod’s axis. The control design is obtained by first using feedback linearization and then designing the ℋ∞ controller using the resulting linear system. For the control strategy validation, simulations were conducted in the Matlab/Simulink® environment, and the weighting functions for the ℋ∞ controller were adjusted to obtain the desired performance and stability of the closed-loop system. The simulation results show the efficiency of the applied methodology.

A Practical Approach for Continuous In Situ Characterization of Radiation Quality Factors in Space

The space radiation environment is qualitatively different from Earth, and its radiation hazard is generally quantified relative to photons using quality factors that allow assessment of biologically-effective dose. Two approaches exist for estimating radiation quality factors in complex radiation environments: One is a fluence-based risk cross-section approach, which requires very detailed in silico characterization of the radiation field and biological cross sections, and thus cannot realistically be used for in situ monitoring. By contrast, the microdosimetric approach, using measured (or calculated) distributions of microdosimetric energy deposition together with empirical biological weighting functions, is conceptually and practically simpler. To demonstrate feasibility of the microdosimetric approach, we estimated a biological weighting function for one specific endpoint, heavy-ion-induced tumorigenesis in APC1638N/+ mice, which was unfolded from experimental results after a variety of heavy ion exposures together with corresponding calculated heavy-ion microdosimetric energy deposition spectra. Separate biological weighting functions were unfolded for targeted and non-targeted effects, and these differed substantially. We folded these biological weighting functions with microdosimetric energy deposition spectra for different space radiation environments, and conclude that the microdosimetric approach is indeed practical and, in conjunction with in-situ measurements of microdosimetric spectra, can allow continuous readout of biologically-effective dose during space flight.

Malliavin Calculus and the Optimal Weighting Function in a Pure Jump Lévy Setting

The paper is devoted to the problem of obtaining weighting functions for the Greeks of an option price written on a stock whose dynamics are of pure jump type. The problem is motivated by the work of Fourni\'e et al. [8, 9], who considered the price sensitivities of a frictionless market and proved that Greeks can be computed as the expectation of the product of the discounted payoff $\Phi$ and a suitable weighted function, i.e.Greek = E[Φ(XT)weight]. Since the weighting functions are random variables that need to be explicitly computed on each specific case, we establish necessary and sufficient conditions to be satisfied. The method used relied on the Malliavin calculus for Levy processes.

The Impact of Reflectivity Gradients on the Performance of Range-Oversampling Processing

Range-oversampling processing is a technique that can be used to lower the variance of radar-variable estimates, reduce radar update times, or a mixture of both. There are two main assumptions for using range-oversampling processing: accurate knowledge of the range correlation and uniform reflectivity in the radar resolution volume. The first assumption has been addressed in previous research; this work focuses on the uniform reflectivity assumption. Earlier research shows that significant reflectivity gradients can occur in storms; we utilized those results to develop realistic simulations of radar returns that include effects of reflectivity gradients in range. An important consideration when using range-oversampling processing is the resulting change in the range weighting function. The range weighting function can change for different types of range-oversampling processing and some techniques, such as adaptive pseudowhitening, can lead to different range weighting functions at each range gate. To quantify the possible effects of differing range weighting functions in the presence of reflectivity gradients, we developed simulations to examine varying types of range-oversampling processing with two receiver filters: a matched receiver filter and a wider-bandwidth receiver filter (as recommended for use with range oversampling). Simulation results show that differences in range weighting functions are the only contributor to differences in radar reflectivity measurements. Results from real weather data demonstrate that the reflectivity gradients that occur in typical severe storms do not cause significant changes in reflectivity measurements, and the benefits from range-oversampling processing outweigh the possible isolated effects from large reflectivity gradients.

Single and Multiobjective optimal control of epidemic models involving vaccination and treatment

Introduction: A rigorous multiobjective optimal control strategy (that does not require the use of weighting functions) of the epidemic models that consider vaccination and treatment strategies is presented. Modifications of the standard susceptible-infectious-removed, susceptible-exposed-infectious-removed, and the modified susceptible-infectious-removed models are dynamically optimized to minimize the number of infected individuals while, controlling the rate at which the individuals are vaccinated and treated. Method:The optimization program, Pyomo , where the differential equations are automatically converted to a Nonlinear Program using the orthogonal collocation method is used for performing the dynamic optimization calculations. The Lagrange-Radau quadrature with three collocation points and 10 finite elements are chosen. The resulting nonlinear optimization problem was solved using the solver BARON 19.3, accessed through the Pyomo-GAMS27.2 interface. Results: The computational results how that the multiobjective optimal control profiles generated by this strategy are very similar to those produced when weighting functions are used. Conclusion: The main conclusion of this work is to demonstrate that one can perform a rigorous dynamic optimization of epidemic models without the use of weighting functions that have the potential to produce some uncertainty and doubt in the results, in addition to dealing with unnecessary additional variables.

The Influence of the Weight Function on the Results Accuracy in Structural Analysis by EFG Method

The use of mesh free methods, including the EFG method, raises a number of user issues. For the best possible result, the user must choose both the weight function and a series of parameters of the method used. This paper presents a part of the research undertaken by the authors to substantiate, on the basis of numerical experiments, some conclusions that will lead the user as quickly as possible to a more accurate result, which can be validated by analytical results and often by experiment. The numerical experiments performed by the authors are based on the use of their own program, made in Matlab, which allowed the use of many weighting functions, in different conditions established by choosing several values of the internodal distance and the size of the support domain. The numerical experiment is performed on a simple structure, widely used in the technical literature under the name Timoshenko beam, for which there are analytical (exact) solutions for both the displacements and stresses. The obtained results are presented in graphical and tabular form, with the highlighting of the errors compared to the exact solution. The final conclusions provide valuable information for practical work with the EFG method, which are also valid for the use of other meshless methods.

Mixed Sensitivity-Based Robust H∞ Control Method for Real-Time Hybrid Simulation

Real-time hybrid simulation (RTHS), dividing the emulated structure into numerical substructures (NS) and physical substructures (PS), is a powerful technique to obtain responses and then to assess the seismic performance of civil engineering structures. A transfer system, a servo-hydraulic actuator or shaking table, is used to apply boundary conditions between the two substructures. However, the servo-hydraulic actuator is inherently a complex system with nonlinearities and may introduce time delays into the RTHS, which will decrease the accuracy and stability of the RTHS. Moreover, there are various uncertainties in RTHS. An accurate and robust actuator control strategy is necessary to guarantee reliable simulation results. Therefore, a mixed sensitivity-based H∞ control method was proposed for RTHS. In H∞ control, the dynamics and robustness of the closed-loop transfer system are realized by performance weighting functions. A form of weighting function was given considering the requirement in RTHS. The influence of the weighting functions on the dynamics was investigated. Numerical simulations and actual RTHSs were carried out under symmetric and asymmetric dynamic loads, namely sinusoidal and earthquake excitation, respectively. Results indicated that the H∞ control method used for RTHS is feasible, and it exhibits an excellent tracking performance and robustness.