Final-State Constrained Optimal Control via a Projection Operator Approach

In this paper we develop a numerical method to solve nonlinear optimal control problems with final-state constraints. Specifically, we extend the PRojection Operator based Netwon's method for Trajectory Optimization (PRONTO), which was proposed by Hauser for unconstrained optimal control problems. While in the standard method final-state constraints can be only approximately handled by means of a terminal penalty, in this work we propose a methodology to meet the constraints exactly. Moreover, our method guarantees recursive feasibility of the final-state constraint. This is an appealing property especially in realtime applications in which one would like to be able to stop the computation even if the desired tolerance has not been reached, but still satisfy the constraints. Following the same conceptual idea of PRONTO, the proposed strategy is based on two main steps which (differently from the standard scheme) preserve the feasibility of the final-state constraints: (i) solve a quadratic approximation of the nonlinear problem to find a descent direction, and (ii) get a (feasible) trajectory by means of a feedback law (which turns out to be a nonlinear projection operator). To find the (feasible) descent direction we take advantage of final-state constrained Linear Quadratic optimal control methods, while the second step is performed by suitably designing a constrained version of the trajectory tracking projection operator. The effectiveness of the proposed strategy is tested on the optimal state transfer of an inverted pendulum

Distributed Personalized Gradient Tracking with Convex Parametric Models

We present a distributed optimization algorithm for solving online personalized optimization problems over a network of computing and communicating nodes, each of which linked to a specific user. The local objective functions are assumed to have a composite structure and to consist of a known time-varying (engineering) part and an unknown (user-specific) part. Regarding the unknown part, it is assumed to have a known parametric (e.g., quadratic) structure a priori, whose parameters are to be learned along with the evolution of the algorithm. The algorithm is composed of two intertwined components: (i) a dynamic gradient tracking scheme for finding local solution estimates and (ii) a recursive least squares scheme for estimating the unknown parameters via user's noisy feedback on the local solution estimates. The algorithm is shown to exhibit a bounded regret under suitable assumptions. Finally, a numerical example corroborates the theoretical analysis

Hybrid near-optimum binary receiver with realistic photon-number-resolving detectors

We propose a near-optimum receiver for the discrimination of binary phase-shift-keyed coherent states employing photon-number-resolving detectors. The receiver exploits a discrimination strategy based on both the so-called homodyne-like and the direct detection, thus resulting in a hybrid scheme. We analyse the performance and the robustness of the proposed scheme under realistic conditions, namely, in the presence of inefficient detection and dark counts. We show that the present hybrid setup is near-optimum and beats both the standard-quantum-limit and the performance of the Kennedy receiver.Comment: 20 pages, 6 figure

The Relativistic Hopfield network: rigorous results

The relativistic Hopfield model constitutes a generalization of the standard Hopfield model that is derived by the formal analogy between the statistical-mechanic framework embedding neural networks and the Lagrangian mechanics describing a fictitious single-particle motion in the space of the tuneable parameters of the network itself. In this analogy the cost-function of the Hopfield model plays as the standard kinetic-energy term and its related Mattis overlap (naturally bounded by one) plays as the velocity. The Hamiltonian of the relativisitc model, once Taylor-expanded, results in a P-spin series with alternate signs: the attractive contributions enhance the information-storage capabilities of the network, while the repulsive contributions allow for an easier unlearning of spurious states, conferring overall more robustness to the system as a whole. Here we do not deepen the information processing skills of this generalized Hopfield network, rather we focus on its statistical mechanical foundation. In particular, relying on Guerra's interpolation techniques, we prove the existence of the infinite volume limit for the model free-energy and we give its explicit expression in terms of the Mattis overlaps. By extremizing the free energy over the latter we get the generalized self-consistent equations for these overlaps, as well as a picture of criticality that is further corroborated by a fluctuation analysis. These findings are in full agreement with the available previous results.Comment: 11 pages, 1 figur

Using Knowledge Analytics to Search and Characterize Mass Properties Aerospace Data

There is growing capability in the field of Big Data and Data Analytics which Mass Properties Engineers might like to take advantage of. This paper utilizes an implementation of the IBM Knowledge Analytics and Watson search capabilities to explore a corpus of material developed primarily with the interests of Mass Properties Engineers and vehicle concept developers at its forefront. The full collection of SAWE (Society of Allied Weight Engineers, Inc.) Technical Papers from 1939 through 2015 is a major portion of the knowledge content. Additional aerospace vehicle design information includes metadata from AIAA (American Institute for Aeronautics and Astronautics), and INCOSE (International Council on Systems Engineering) as well as author-provided personal search material. This data is processed with respect to certain expected content, data taxonomies and key words to become the core data in NASA Langley Research Centers Vehicle Analysis Analytics, IBM Watson Content. Processed data becomes the corpus of information which is interrogated to provide examples of finding data for mass regression analysis, technology impacts on MPE (Mass Properties Engineering), mass properties control, standards, and other aspects of interest

Tolerance of warmer temperatures does not confer resilience to heatwaves in an Alpine herb

Climate change is generating both sustained trends in average temperatures and higher frequency and intensity of extreme events. This poses a serious threat to biodiversity, especially in vulnerable environments, like alpine systems. Phenotypic plasticity is considered to be an adaptive mechanism to cope with climate change in situ, yet studies of the plastic responses of alpine plants to high temperature stress are scarce. Future weather extremes will occur against a background of warmer temperatures, but we do not know whether acclimation to warmer average temperatures confers tolerance to extreme heatwaves. Nor do we know whether populations on an elevational gradient differ in their tolerance or plasticity in response to warming and heatwave events. We investigated the responses of a suite of functional traits of an endemic Australian alpine herb, Wahlenbergia ceracea, to combinations of predicted future (warmer) temperatures and (relative) heatwaves. We also tested whether responses differed between high- vs. low-elevation populations. When grown under warmer temperatures, W. ceracea plants showed signs of acclimation by means of higher thermal tolerance (Tcrit, T50, and Tmax). They also invested more in flower production, despite showing a concurrent reduction in photosynthetic efficiency (Fv/Fm) and suppression of seed production. Heatwaves reduced both photosynthetic efficiency and longevity. However, we found no evidence that acclimation to warmer temperatures conferred tolerance of the photosynthetic machinery to heatwaves. Instead, when exposed to heatwaves following warmer growth temperatures, plants had lower photosynthetic efficiency and underwent a severe reduction in seed production. High- and low-elevation populations and families exhibited limited genetic variation in trait means and plasticity in response to temperature. We conclude that W. ceracea shows some capacity to acclimate to warming conditions but there is no evidence that tolerance of warmer temperatures confers any resilience to heatwaves.This research was supported by the Australian Research Council (DP170101681), an International Ph.D. Scholarship to RN and an ARC Future Fellowship FT110100453 to LK. Research grants funded all research related costs (such as renting growth chambers or buying equipment), while the scholarship paid a stipend to RN

New Variant of the Treatment of Acromion-Clavicular Dislocation With TightRope ® System in a Mini - Open Approach: A Preliminary Clinical Study

Background: Many different surgical techniques have been described to stabilize the acromion-clavicular (AC) dislocations. So far many of these procedures are performed only in arthroscopy. Objectives: In this study, we describe a new technique that utilizes the tightrope with a mini-invasive open approach for the acute stabilization of the acromion-clavicular joint (ACJ) dislocation. Patients and Methods: We set an prospective study aimed to verify the efficacy of this new surgical technique. We treated 28 patients with acute ACJ dislocation with ACJ TightRope ® System with dual mini access. We retrospectively reviewed the data of 34 patients treated with arthroscopic technique. They were considered as the control group. Results: At 6 month’s follow-up, all the 28 patients showed a stable joint during clinical examination and obtained an average Constant score of 98.62/100, with a complete recovery of ROM and strength in abduction. The mean operation time was of 33.7 minutes. The mean recovery duration was 102.8 days. No significant difference was found between the experimental and control groups (P > 0.05). Conclusions: Results of this trial suggest the effectiveness of this new mini-invasive surgical technique in producing clinical and functional recovery in patients with ACJ dislocations

Methylsulfonylmethane and boswellic acids versus glucosamine sulfate in the treatment of knee arthritis: Randomized trial

Until now glucosamine sulfate (GS) has been the most widely used supplement and has been shown to be efficacious in the treatment of osteoarthritis (OA). Methylsulfonylmethane (MSM) and boswellic acids (BA) are new effective supplements for the management of inflammation and joint degeneration, according to previous experimental studies. The aim of our study is to test the effectiveness of association of MSM and BA in comparison with GS in knee arthritis.In this prospective randomized clinical trial, MEBAGA (Methylsulfonylmethane and Boswellic Acids versus Glucosamine sulfate in the treatment of knee Arthritis), 120 participants affected by arthritis of the knee were randomly assigned to an experimental group (MB group) or a control group (GS group) treated for 60 days with 5 g of MSM and 7.2 mg of BA or with 1500 mg of GS daily, respectively. At the 2-month (T1) and 6-months (T2) follow-up , the efficacy of these two nutraceuticals was assessed using the visual analog pain scale (VAS) and the Lequesne Index (LI) for joint function, along with the use of anti-inflammatory drugs (non-steroidal anti-inflammatory drugs and anti-cyclooxygenase-2).The repeated measures ANOVA analysis shows that for VAS, LI, and the use of anti-inflammatory drugs scores there are improvements due to the time in the two groups (respectively, F=26.0; P<0.0001; F=4.15; P=0.02; F=3.38; P=0.04), with a tendency to better values for the MB group at T2.On the basis of these preliminary data, we could support the efficacy of the MSM in association with BA in the treatment of OA. These results are consistent with the anti-inflammatory and chondroprotective effects previously occurred in experimental studies. This new combination of integration (MSM and BS) has presented good results and satisfactory in comparison with GS, until now the cornerstone of the treatment of arthritis in according to guidelines