Optimal control of the sweeping process over polyhedral controlled sets

The paper addresses a new class of optimal control problems governed by the dissipative and discontinuous differential inclusion of the sweeping/Moreau process while using controls to determine the best shape of moving convex polyhedra in order to optimize the given Bolza-type functional, which depends on control and state variables as well as their velocities. Besides the highly non-Lipschitzian nature of the unbounded differential inclusion of the controlled sweeping process, the optimal control problems under consideration contain intrinsic state constraints of the inequality and equality types. All of this creates serious challenges for deriving necessary optimality conditions. We develop here the method of discrete approximations and combine it with advanced tools of first-order and second-order variational analysis and generalized differentiation. This approach allows us to establish constructive necessary optimality conditions for local minimizers of the controlled sweeping process expressed entirely in terms of the problem data under fairly unrestrictive assumptions. As a by-product of the developed approach, we prove the strong $W^{1,2}$-convergence of optimal solutions of discrete approximations to a given local minimizer of the continuous-time system and derive necessary optimality conditions for the discrete counterparts. The established necessary optimality conditions for the sweeping process are illustrated by several examples

Isogeometric analysis for functionally graded microplates based on modified couple stress theory

Analysis of static bending, free vibration and buckling behaviours of functionally graded microplates is investigated in this study. The main idea is to use the isogeometric analysis in associated with novel four-variable refined plate theory and quasi-3D theory. More importantly, the modified couple stress theory with only one material length scale parameter is employed to effectively capture the size-dependent effects within the microplates. Meanwhile, the quasi-3D theory which is constructed from a novel seventh-order shear deformation refined plate theory with four unknowns is able to consider both shear deformations and thickness stretching effect without requiring shear correction factors. The NURBS-based isogeometric analysis is integrated to exactly describe the geometry and approximately calculate the unknown fields with higher-order derivative and continuity requirements. The convergence and verification show the validity and efficiency of this proposed computational approach in comparison with those existing in the literature. It is further applied to study the static bending, free vibration and buckling responses of rectangular and circular functionally graded microplates with various types of boundary conditions. A number of investigations are also conducted to illustrate the effects of the material length scale, material index, and length-to-thickness ratios on the responses of the microplates.Comment: 57 pages, 14 figures, 18 table

On the stability function of functionally-fitted Runge--Kutta methods

Classical collocation Runge--Kutta methods are polynomially fitted in the sense that they integrate an ODE problem exactly if its solution is an algebraic polynomial up to some degree. Functionally fitted Runge--Kutta methods are collocation techniques that generalize this principle to solve an ODE problem exactly if its solution is a linear combination of a chosen set of arbitrary basis functions. Given for example a periodic or oscillatory ODE problem with a known frequency, it might be advantageous to tune a trigonometric functionally fitted Runge--Kutta method targeted at such a problem. However, functionally fitted Runge--Kutta methods lead to variable coefficients that depend on the parameters of the problem, the time, the step size, and the basis functions in a non-trivial manner that inhibits any in-depth analysis of the behavior of the methods in general. We present the class of so-called separable basis functions and show that it is possible to characterize the stability region of some special methods in this particular class. Explicit stability functions are given for some representative examples

Unsupervised deep learning-based reconfigurable intelligent surface aided broadcasting communications in industrial IoTs

This paper presents a general system framework which lays the foundation for Reconfigurable Intelligent Surface (RIS)-enhanced broadcast communications in Industrial Internet of Things (IIoTs). In our system model, we consider multiple sensor clusters co-existing in a smart factory where the direct links between these clusters and a central base station (BS) is blocked completely. In this context, an RIS is utilized to reflect signals broadcast from BS toward cluster heads (CHs) which act as a representative of clusters, where BS only has access to the statistical distribution of the channel state information (CSI). An analytical upper bound of the total ergodic spectral efficiency and an approximation of outage probability are derived. Based on these analytical results, two algorithms are introduced to control the phase shifts at RIS, which are the Riemannian conjugate gradient (RCG) method and the deep neural network (DNN) method. While the RCG algorithm operates based on the conventional iterative method, the DNN technique relies on unsupervised deep learning. Our numerical results show that the both algorithms achieve satisfactory performance based on only statistical CSI. In addition, compared to the RCG scheme, using deep learning reduces the computational latency by more than 10 times with an almost identical total ergodic spectral efficiency achieved. These numerical results reveal that while using conventional RCG method may provide unsatisfactory latency, DNN technique shows much promise for enabling RIS in ultra reliable and low latency communications (URLLC) in the context of IIoTs

Force‐sensing catheters during pediatric radiofrequency ablation: The FEDERATION Study

Background Based on data from studies of atrial fibrillation ablations, optimal parameters for the TactiCath (TC; St. Jude Medical, Inc) force‐sensing ablation catheter are a contact force of 20 g and a force‐time integral of 400 g·s for the creation of transmural lesions. We aimed to evaluate TC in pediatric and congenital heart disease patients undergoing ablation. Methods and Results Comprehensive chart and case reviews were performed from June 2015 to March 2016. Of the 102 patients undergoing electrophysiology study plus ablation, 58 (57%) underwent ablation initially with a force‐sensing catheter. Patients had an average age of 14 (2.4–23) years and weight of 58 (18–195) kg with 15 patients having abnormal cardiac anatomy. Electrophysiology diagnoses for the + TC group included 30 accessory pathway–mediated tachycardia, 24 atrioventricular nodal reentrant tachycardia, and 7 other. Baseline generator settings included a power of 20 W, temperature of 40°, and 6 cc/min flow during lesion creation with 11 patients (19%) having alterations to parameters. Seventeen patients (30%) converted to an alternate ablation source. A total of 516 lesions were performed using the TC with a median contact force of 6 g, force‐time integral of 149 g·s, and lesion size index of 3.3. Median‐term follow‐up demonstrated 5 (10%) recurrences with no acute or median‐term complications. Conclusions TactiCath can be effectively employed in the treatment of pediatric patients with congenital heart disease with lower forces than previously described in the atrial fibrillation literature. Patients with atrioventricular nodal reentrant tachycardia or atrioventricular reciprocating tachycardia may not require transmural lesions and the TC may provide surrogate markers for success during slow pathway ablation. </jats:sec

Sulfur management strategies to improve partial sulfur balance with irrigated peanut production on deep sands

Sands have favourable physical properties for harvesting peanut, but improving S and water use efficiency on these soils remains a challenge. We studied partial S balance in irrigated peanut crops on sands of Central Vietnam to identify key factors of S fertiliser management affecting S inputs and outputs. Field trials were conducted in the spring seasons of 2015 and 2016 to determine the effects of S application rates (0, 15, 30, 45 kg ha−1) on peanut yield and partial S balance. Sulfur balances were negative (-28.3 to 5.6 kg S ha−1) at rates < 30 kg S ha−1, while at higher rates of S fertiliser application that produced maximum pod yield (30 - 45 kg S ha−1), three of four sites showed neutral to slightly positive S balance (1.5 - 5.6 kg S ha−1). The negative partial S balance decreased with increasing S rates but was mostly attributable to the large S removal in peanut shoots (9.7 - 22.3 kg S ha−1) which are used on farms for animal feed. The negative partial S balance results in depletion of soil S reserves and hence efficient recycling of S on farms is critical for sustainable crop production on sands of VN

Severe cholestasis and bile acid nephropathy from anabolic steroids successfully treated with plasmapheresis

Severe cholestasis with anabolic androgenic steroids is well-known to cause acute liver injury. Treatment is usually supportive after withdrawal of the offending agent. Acute kidney injury (AKI) frequently occurs in acute liver injury and may complicate management and prognosis. We highlight the use of plasmapheresis resulting in rapid improvement in cholestatic jaundice with resolution of AKI. Plasmapheresis should be considered in special cases in which there is progressive clinical decline despite supportive care

Optimal control of the sweeping process

We formulate and study an optimal control problem for the sweeping (Moreau) process, where control functions enter the moving sweeping set. To the best of our knowledge, this is the first study in the literature devoted to optimal control of the sweeping process. We first establish an existence theorem of optimal solutions and then derive necessary optimality conditions for this optimal control problem of a new type, where the dynamics is governed by discontinuous differential inclusions with variable right-hand sides. Our approach to necessary optimality conditions is based on the method of discrete approximations and advanced tools of variational analysis and generalized differentiation. The final results obtained are given in terms of the initial data of the controlled sweeping process and are illustrated by nontrivial examples