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 Primal Decomposition for Large-Scale MILPs

This paper deals with a distributed Mixed-Integer Linear Programming (MILP) set-up arising in several control applications. Agents of a network aim to minimize the sum of local linear cost functions subject to both individual constraints and a linear coupling constraint involving all the decision variables. A key, challenging feature of the considered set-up is that some components of the decision variables must assume integer values. The addressed MILPs are NP-hard, nonconvex and large-scale. Moreover, several additional challenges arise in a distributed framework due to the coupling constraint, so that feasible solutions with guaranteed suboptimality bounds are of interest. We propose a fully distributed algorithm based on a primal decomposition approach and an appropriate tightening of the coupling constraint. The algorithm is guaranteed to provide feasible solutions in finite time. Moreover, asymptotic and finite-time suboptimality bounds are established for the computed solution. Montecarlo simulations highlight the extremely low suboptimality bounds achieved by the algorithm

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

Effects of warming temperatures on germination responses and trade-offs between seed traits in an alpine plant

1. Climate warming may affect multiple aspects of plant life history, including important factors such as germination responses and the key trade-off between offspring size and number. As a case study to address these concepts, we used an alpine plant (waxy bluebell, Wahlenbergia ceracea; Campanulaceae) that shows plasticity to warming in seed traits and in which seed dormancy status regulates germination. We chose an alpine species because alpine environments are ecosystems particularly under threat by climate change. 2. We conducted germination assays under cool and warm temperatures using seeds produced by individuals that were grown under historical (cooler) and future (warmer) temperature scenarios. We assessed the presence of a seed size vs number trade-off, and then examined the effects of seed number and size on germination percentage, the fractions of dormant and viable seeds, and germination velocity. Further, we examined whether warming during parental growth and during germination affected these relationships. 3. We found evidence for a seed size vs number trade-off only under historical parental temperatures. Indeed, under future growth temperatures, parental plants produced fewer and smaller seeds and there was no evidence of a trade-off. However, the reductions in both seed traits under warming did not affect germination, despite correlations of seed size and number with germination traits. Warming increased germination, particularly of larger seeds, but overall it resulted in more than fourfold reductions in parental fitness. 4. Synthesis. Our study shows the importance of growth conditions when evaluating the seed size vs number trade-off. Stressful conditions, such as warmer temperatures, can restrain the ability of plants to reach optimal investment in reproduction, masking the trade-off. By analysing responses across the whole life cycle, we show here an overall detrimental effect of warming, highlighting the potential risk of climate change for W. ceracea, and, potentially, for alpine plant communities more widely.Files can be opened using Excel and analysed using R.Funding provided by: Australian Research CouncilCrossref Funder Registry ID: http://dx.doi.org/10.13039/501100000923Award Number: DP170101681Experiments were conducted using the plant species Wahlnebrgia ceracea (waxy bluebells). Two datasets were used in this manuscript. 1) Seed size vs number trade-off: Parental individuals from a total of 30 lines ('Line') were grown in growth chambers for 191 days under temperature conditions of a historical/cooler (1960–1970) or a projected future/warmer (2090–2100) climate ('Parental_Temperature'). The parental individuals were randomly assigned to one of three blocks, which corresponded to positions inside the chambers, and each block was equivalent in all chambers ('Block'). Day and night temperatures during the experiment were changed every 15 days to mimic seasonality, with the maximum day temperatures during the peak of summer being 24°C and 29°C for the historical and future parental temperatures, respectively. After 100 days since the imposition of the temperature treatments (during the peak of the summer), half of the plants were moved for 5 days to new chambers, where the temperature was 5°C above the respective treatments, i.e., 29°C and 34°C ('Heatwave'). After this time, the parental individuals were moved back to their respective historical or future temperature treatments. We collected the seeds throughout the 191 days of parental growth, and we stored them in desiccators for at least 11 weeks. After this time, we calculated seed size ('Seed_Size') as the average mass of three lots of 50 seeds divided by 50. We calculated seed number ('Seed_Number') as the ratio between the cumulative mass of the seeds produced by each parental individual and seed size. The 30 lines of the parental individuals were obtained by crossing plants that originated from seeds that were collected at the same elevation, either high or low elevation ('Elevation') in sites within Kosciuszko National Park, NSW, Australia. Therefore, 14 lines originated from high elevations and 14 lines from low elevations. 2) Germination responses - seed traits correlations: The seeds were harvested from the parental individuals grown under historical/cooler or projected future/warmer temperatures ('Parental_Temperature') (see above) from a subset of 14 lines ('Line'). These seeds were used in germination assays in the glasshouse under cool (25°C) or warm temperatures (30°C) ('Germination_Temperature'). We measured seed size ('Seed_Size') as the average mass of three lots of 50 seeds; then these seeds were sowed in agar dishes (25 seeds per dish, 2 dishes per temperature treatment from each parental individual). Seed number ('Seed_Number') was the same as above. Dishes were left under temperature treatments for 4 weeks to allow germination of the non-dormant fraction of the seeds ('Not_Dormant_Seeds') and germination was checked once per week. Then, all the dishes were moved to a cold room at 4–5°C in the dark for 4 weeks to allow cold stratification. After this time, dishes were moved back to the glasshouse under the same temperature treatments as before to allow germination of the dormant seeds. We considered seeds to be dormant ('Dormant_seeds') if they germinated during or after cold stratification or if they did not germinate at all but were still determined to be viable at the end of the experiment. We considered seed to be viable ('Viable_Seeds') if they germinated ('Germinated_Seeds') as well as the seeds that contained an endosperm but still did not germinate ('Not_Germinated_Seeds'), while we considered empty seeds as non-viable ('Not_Viable_Seeds'). Germinated and not germinated seeds (as above) were used to calculate the germination percentage. We calculated germination velocity ('Germination_Velocity') as the reciprocal of the mean germination time (germination velocity (germination (%) week-1) GV = (G1 + G2 +…+ Gn) / (G1 x T1 + G2 x T2 +…+ Gn x Tn), where Gn is the number of new germinating seeds at each sampling point, and Tn is the time between each sampling point (= one week). The files provided present the datasets in their first sheet and keys with the definitions of each term in the second sheet