A descent algorithm for constrained stochastic extrema.
Descent algorithm for finding stochastic extremum for situations not suited to optimal feedback control
Ho, Y. C.↗
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Incomplete state feedback for systems with parameter uncertainty and random disturbances
A unified design philosophy is presented for limited state feedback control problems with parameter uncertainty for both deterministic and stochastic problems. Two approaches are considered: linear compensator for the deterministic problem with parameter uncertainty, and for the single input-single output system with parameter uncertainty, a model on order equal to that of the system less the number of zeroes. The limitations of these approaches are discussed along with suggestions for further research.
Basuthakur, S.↗
Oxygen Ion Heat Rate within Alfvenic Turbulence in the Cusp
The role that the cleft/cusp has in ionosphere-magnetosphere coupling makes it a dynamic and important region. It is directly exposed to the solar wind, making it possible for the entry of electromagnetic energy and precipitating electrons and ions from dayside reconnection and other dayside events. It is also a significant source of ionospheric plasma, contributing largely to the mass loading of the magnetosphere with large fluxes of outflowing ions. Crossing the cusp/cleft near 5100 km, the Polar instruments observe the common correlation of downward Poynting flux, ion energization, soft electron precipitation, broadband extremely low-frequency (BB-ELF) emissions, and density depletions. The dominant power in the BB-ELF emissions is now identified to be from spatially broad, low frequency Alfv nic structures. For a cusp crossing, we determine using the Electric Field Investigation (EFI), that the electric and magnetic field fluctuations are Alfv nic and the electric field gradients satisfy the inequality for stochastic acceleration. With all the Polar 1996 horizontal crossings of the cusp, we determine the O+ heating rate using the Thermal Ion Dynamics Experiment (TIDE) and Plasma Wave Investigation (PWI). We then compare this heating rate to other heating rates assuming the electric field gradient criteria exceeds the limit for stochastic acceleration for the remaining crossings. The comparison suggests that a stochastic acceleration mechanism is operational and the heating is controlled by the transverse spatial scale of the Alfvenic waves.
Coffey, Victoria N.↗
H ∞ Control for Energy Dispatch in Autonomous Nanogrid With Communication Delays
This paper proposes an optimal controller and estimator for energy dispatch to balance the power supply and demand considering communication delays. The proposed algorithm involves modeling an autonomous nanogrid (ANG) consisting of distributed energy resources, energy storage systems, loads, an $H$ ∞ controller with a reference power modulation technique, and a state estimator. The ANG was developed to express the dynamic supply-demand energy balance of a nanogird system. Reference power modulation was designed to generate the desired ESS power based on the imbalanced energy. Random communication delays were modeled using a stochastic variable satisfying the Bernoulli random binary distribution. The optimal $H$ ∞ controller and estimator were developed using a linear matrix inequality approach to exponentially stabilize the closed-loop system. Simulations were performed using real daily demand forecasts obtained from the Korea Meteorological Administration to demonstrate the effectiveness of the proposed real-time optimization algorithm.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Real Time Predictive and Adaptive Hybrid Powertrain Control Development via Neuroevolution
The real-time application of powertrain-based predictive energy management (PrEM) brings the prospect of additional energy savings for hybrid powertrains. Torque split optimal control methodologies have been a focus in the automotive industry and academia for many years. Their real-time application in modern vehicles is, however, still lagging behind. While conventional exact and non-exact optimal control techniques such as Dynamic Programming and Model Predictive Control have been demonstrated, they suffer from the curse of dimensionality and quickly display limitations with high system complexity and highly stochastic environment operation. This paper demonstrates that Neuroevolution associated drive cycle classification algorithms can infer optimal control strategies for any system complexity and environment, hence streamlining and speeding up the control development process. Neuroevolution also circumvents the integration of low fidelity online plant models, further avoiding prohibitive embedded computing requirements and fidelity loss. This brings the prospect of optimal control to complex multi-physics system applications. The methodology presented here covers the development of the drive cycles used to train and validate the neurocontrollers and classifiers, as well as the application of the Neuroevolution process.
33 ADVANCED PROPULSION SYSTEMS↗
AEOLUS: Advances in Experimental Design, Optimal Control, and Learning for Uncertain Complex Systems
Sustained advances in the mathematics of modeling and simulation have resulted in the capability today for routine simulation of a number of large scale complex DOE-relevant systems. As remarkable as this capability for solving the so-called forward problem is, it is typically only the first step-an inner loop within an outer loop that explores the simulation model's parameter space and decision space to characterize uncertainty in the model's predictions, learn unknown model parameters from data, design the most informative experiments, determine optimal control strategies, and create optimal designs. Broadly, what unifies all of these outer loop problems is that they are, in one form or another, optimization problems over parameter/control/design space that are constrained by complex uncertain models. To fully realize the power of scientific simulation as a basis for scientific discovery, technological innovation, and rational decision-making, it is imperative to move beyond simulation to tackle the outer loop of optimization for learning from data, experimental design, and control with complex uncertain models. When the models under consideration are large-scale and complex, and when the optimization variable and uncertain parameter spaces are high (or infinite) dimensional, this constitutes a grand challenge of the highest order, and is intractable with conventional methods. To overcome these challenges, the AEOLUS Center was established to develop a unified mathematical, computational, and statistical framework for (1) Learning predictive models from complex data via Bayesian inference and optimization, and (2) Optimizing experiments, processes, and designs using the resulting uncertain models. These problems are intractable with conventional methods, for several reasons: (1) The simulation problems that govern the inner loops of the optimization problems are expensive to execute (due to severe nonlinearity, heterogeneity, multiphysics/multiscale coupling); (2) The optimization variable and uncertain parameter spaces are high dimensional, often stemming from discretizations of infinite dimensional fields such as initial conditions, sources, or material properties. We argue that the key to overcoming these challenges is to develop new mathematical, computational, and statistical methods that exploit the structure of the Bayesian inference and optimization problems mediated by their underlying complex uncertain models. This structure includes the regularity, sparsity, geometry, low intrinsic dimensionality, and multifidelity nature of the maps from uncertain parameter/optimization variable spaces to the specific objectives targeted: Bayesian inference, optimal experimental design, and optimal control design. Black box methods developed as generic tools are incapable of exploiting this structure. To be successful, we must create, integrate, and cross-fertilize ideas across multiple areas of applied math--including approximation theory, Bayesian inference, data science, experimental design, information theory, machine learning, model reduction, optimal control theory, parallel algorithms, PDE-constrained optimization, randomized algorithms, stochastic optimization, and uncertainty quantification--all while exploiting the structure of the problems at hand. With this goal in mind, we have marshaled a team of leading authorities in these areas. While the methods we develop will be broadly applicable across a wide spectrum of DOE problems in which experiments inform models and the systems those models describe must be optimized under uncertainty, we have chosen a specific area, advanced manufacturing and materials, to drive our work. AMM is characterized by complex models across multiple scales, and is a rich source of challenging problems in inference, experimental design, and optimal control, requiring multifaceted and integrated advances in applied mathematics. As such, AMM serves as an excellent vehicle to motivate and demonstrate the advances in applied mathematics developed by our center.
97 MATHEMATICS AND COMPUTING↗
Photoinduced correlations in stochastic dynamics of a solid-state ionic conductor
Photoexcitation by ultrashort laser pulses plays a crucial role in controlling reaction pathways, creating nonequilibrium material properties, and probing complex molecular dynamics. The photoresponse following a laser pulse is generally nonidentical between exposures due to spatiotemporal fluctuations or the stochastic nature of dynamical pathways. However, most ultrafast pump-probe experiments struggle to distinguish intrinsic sample fluctuations from extrinsic apparatus noise, often missing deviations from the averaged response. Leveraging the stability and high photon flux of time-resolved X-ray micro-diffraction at a synchrotron, we characterized stochastic photoinduced dynamics in a solid-state ionic conductor. By analyzing temporal evolutions of the lattice parameter of a single grain, we found that shot-to-shot fluctuations are not independent. Instead, correlations exist between nonequilibrium lattice trajectories following adjacent shots, with a characteristic correlation length of approximately 1500 shots, corresponding to an energy barrier of 0.4 ± 0.1 eV, close to the activation energy of lithium-ion diffusion.
36 MATERIALS SCIENCE↗
A Novel Deep Reinforcement Learning Approach to Traffic Signal Control with Connected Vehicles
The advent of connected vehicle (CV) technology offers new possibilities for a revolution in future transportation systems. With the availability of real-time traffic data from CVs, it is possible to more effectively optimize traffic signals to reduce congestion, increase fuel efficiency, and enhance road safety. The success of CV-based signal control depends on an accurate and computationally efficient model that accounts for the stochastic and nonlinear nature of the traffic flow. Without the necessity of prior knowledge of the traffic system’s model architecture, reinforcement learning (RL) is a promising tool to acquire the control policy through observing the transition of the traffic states. In this paper, we propose a novel data-driven traffic signal control method that leverages the latest in deep learning and reinforcement learning techniques. By incorporating a compressed representation of the traffic states, the proposed method overcomes the limitations of the existing methods in defining the action space to include more practical and flexible signal phases. The simulation results demonstrate the convergence and robust performance of the proposed method against several existing benchmark methods in terms of average vehicle speeds, queue length, wait time, and traffic density.
42 ENGINEERING↗
Volt-Var Curve Reactive Power Control Requirements and Risks for Feeders with Distributed Roof-Top Photovoltaic Systems
The benefits and risks associated with Volt-Var Curve (VVC) control for management of voltages in electric feeders with distributed, roof-top photovoltaic (PV) can be defined using a stochastic hosting capacity analysis methodology. Although past work showed that a PV inverter’s reactive power can improve grid voltages for large PV installations, this study adds to the past research by evaluating the control method’s impact (both good and bad) when deployed throughout the feeder within small, distributed PV systems. The stochastic hosting capacity simulation effort iterated through hundreds of load and PV generation scenarios and various control types. The simulations also tested the impact of VVCs with tampered settings to understand the potential risks associated with a cyber-attack on all of the PV inverters scattered throughout a feeder. The simulation effort found that the VVC can have an insignificant role in managing the voltage when deployed in distributed roof-top PV inverters. This type of integration strategy will result in little to no harm when subjected to a successful cyber-attack that alters the VVC settings.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Stochastic boundary condition effects on supersonic leading edge blowing
The present manuscript studies the robustness of leading edge blowing for active control of the upstream bow shock and overall aerothermal characteristics of a supersonic airfoil subject to variability in the injection conditions. The injection boundary conditions were considered stochastic and their randomness was propagated to the flow topology and aerothermal quantities of interest by means of non-intrusive Polynomial Chaos Expansions. The evaluations needed to build these expansions were carried out via steady two-dimensional Reynolds-Averaged Navier Stokes simulations. Two different injection port sizes were considered, with the smallest promoting a Coanda effect that gives rise to non-symmetric flow topologies. The uncertain boundary conditions lead to significant variations in the flow topology, particularly at the injection exit and the bow shock position, with variations of up to 75% of the nominal value. Here this study identifies the key operating conditions to ensure the optimal application of leading-edge injection for active control of supersonic airfoils.
97 MATHEMATICS AND COMPUTING↗
Stochasticity in microbiology: managing unpredictability to reach the Sustainable Development Goals
Pure (single) cultures of microorganisms and mixed microbial communities (microbiomes) have been important for centuries in providing renewable energy, clean water and food products to human society and will continue to play a crucial role to pursue the Sustainable Development Goals. To use microorganisms effectively, microbial engineered processes require adequate control. Microbial communities are shaped by manageable deterministic processes, but also by stochastic processes, which can promote unforeseeable variations and adaptations. Here, we highlight the impact of stochasticity in single culture and microbiome engineering. First, we discuss the concepts and mechanisms of stochasticity in relation to microbial ecology of single cultures and microbiomes. Second, we discuss the consequences of stochasticity in relation to process performance and human health, which are reflected in key disadvantages and important opportunities. Third, we propose a suitable decision tool to deal with stochasticity in which monitoring of stochasticity and setting the boundaries of stochasticity by regulators are central aspects. Stochasticity may give rise to some risks, such as the presence of pathogens in microbiomes. We argue here that by taking the necessary precautions and through clever monitoring and interpretation, these risks can be mitigated.
59 BASIC BIOLOGICAL SCIENCES↗
Impact of model predictive control-enabled home energy management on large-scale distribution systems with photovoltaics
Residential customers use more than one-quarter of the electricity in the world. Optimally managing home energy consumption is an effective way of easing the operational challenges facing the electric grid with increasing solar photovoltaics (PV). This paper studies the impact of the future proliferation of home energy management systems (HEMS) in the presence of PV on large-scale distribution systems. First, we present a stochastic HEMS model that minimizes residential customers' thermal discomfort and energy costs under uncertainty. The HEMS model schedules the optimal operations of residential appliances in the presence of PV within a mixed-integer linear programming-based model predictive control framework that links the proposed HEMS to a quasi-steady-state time-series simulation tool. Additionally, extensive simulations are conducted for a stand-alone residential home using two tariff structures and for 1977 homes on an 8,500-node distribution feeder. Simulation results quantify the impact of the future proliferation of HEMS on the large-scale distribution system with PV.
14 SOLAR ENERGY↗
Compensator design for stability enhancement with collocated controllers
A continuum model rather than a finite element model is used. The optimal compensator design is formulated as a stochastic regulator problem and is shown to be solvable by the general infinite-dimensional theory developed by the author despite the lack of exponential stabilizability. Infinite-dimensional steady-state Riccati equations characterizing the feedback control gain and the Kalman filter gain operators can be solved explicitly. The associated performance indexes including the mean-square control-effort are calculated in closed form. As a first approximation, the compensator transfer function can be realized as a bank of bandpass filters in parallel centered at the undamped mode frequencies. Numerical calculations for the gain and bandwidths for a typical configuration are presented. The performance of the compensator is evaluated when in fact in the true model there is no actuator noise. The theoretical problem involved is to show that the infinite-dimensional stochastic process is asymptotically stationary. It is possible to calculate the steady-state covariance in closed form and thereby calculate performance indexes of interest explicitly, facilitating the choice of optimal design parameters.
Balakrishnan, A. V.↗
Analysis of leading edge protection application on wind turbine performance through energy and power decomposition approaches
Abstract Wind power production is driven by, and varies with, the stochastic yet uncontrollable wind and environmental inputs. To compare a wind turbine's performance, a direct comparison on power outputs is always confounded by the stochastic effect of weather inputs. It is therefore crucial to control for the weather and environmental influence. Toward that objective, our study proposes an energy decomposition approach. We start with comparing the change in the total energy production and refer to the change in total energy as delta energy. On this delta energy, we apply our decomposition method, which is to separate the portion of energy change due to weather effects from that due to the turbine itself. We derive a set of mathematical relationships allowing us to perform this decomposition and examine the credibility and robustness of the proposed decomposition approach through extensive cross‐validation and case studies. We then apply the decomposition approach to Supervisory Control and Data Acquisition data associated with several wind turbines to which leading‐edge protection was carried out. Our study shows that the leading‐edge protection applied on blades may cause a small decline to the power production efficiency in the short term, although we expect the leading‐edge protection to benefit the blade's reliability in the long term.
17 WIND ENERGY↗
Time-Sequenced Flow Field Prediction in an Optima Spark-Ignition Direct-Injection Engine Using Bidirectional Recurrent Neural Network (bi-RNN) with Long Short-Term Memory
To further improve the energy conversion efficiency of internal combustion engine, the transient and complex air flow movement inside the cylinder needs to be better understood and controlled. Although the in-cylinder flow fields are highly stochastic with strong cycle-to-cycle fluctuations, machine learning can still provide an efficient way to learn and regress the complex flow movement process inside the cylinder. In this work, a bidirectional recurrent neural network (bi-RNN) model with long short-term memory was applied to predict the in-cylinder flow fields at different time steps using training data from mull-cycle particle image velocimetry (PIV) measurements. To evaluate the agreement between the true and predicted flow fields, structure and magnitude comparison indices are calculated both globally and locally. The comparison results show that the bi-RNN model can accurately predict the bulk flow and vortex motions from early intake stroke to compression stroke. This work demonstrates that the machine learning model has the potential to predict the underlying dynamics of the interaction between in-cylinder flows and provides a reliable way to improve temporal resolution in PIV flow data to better reveal transient in-cylinder flow features.
Bi-RNN model↗
A computer vision algorithm for interpreting lacustrine carbonate textures at Searles Valley, USA
Investigations of the paleohydrologies of pluvial lake systems have often employed lake carbonate deposits called “tufa” that grow subaqueously and can be preserved long after the drying of the lake. For this reason, tufa have been used as a proxy for minimum lake level. However, they exhibit a variety of textures that hold the potential to reveal richer paleoclimatological information. With the goal of determining if tufa texture can be used as a proxy for lake environment, this study investigates the textures of tufa at Mono Lake, California in comparison to the fossil tufa in Searles Valley, California. While observations in the last century suggest that the tufa in the Mono basin grew in waters similar to the modern, the tufa at Searles formed during the last glacial period, when the Great Basin contained a system of pluvial lakes on the scale of the modern Great Lakes. The tufa at both basins have been observed to have a range of classifiable textures, and new methods of inspecting visual data could be informative about what factors control these textures. To this end, a t-Distributed Stochastic Neighbor Embedding (t-SNE) algorithm is used to project images of the tufa at Searles and Mono into a coordinate space, allowing for simple, quantitative comparisons of the visual similarity of textures. In this work, the textures of tufa at Searles are compared to each other, as well as to the tufa at Mono. This study performs a robust assessment of the feasibility of Mono Lake as a modern analogue for Searles Valley. It finds that there is a justifiable basis for the comparison of certain fossil facies at Searles to the tufa at Mono, significant progress towards the goal of using texture as a metric for the environment in which tufa formed.
58 GEOSCIENCES↗
A Non-Cooperative Game-Based Distributed Beam Scheduling Framework for 5G Millimeter-Wave Cellular Networks
Here, this paper studies the problem of distributed beam scheduling for 5G millimeter-Wave (mm-Wave) cellular networks where base stations (BSs) belonging to different operators share the same spectrum without centralized coordination among them. Our goal is to design efficient distributed scheduling algorithms to maximize the network utility, which is a function of the achieved throughput by the user equipment (UEs), subject to the average and instantaneous power consumption constraints of the BSs. We propose a Media Access Control (MAC) and a power allocation/adaptation mechanism utilizing the Lyapunov stochastic optimization framework and non-cooperative games. In particular, we first decompose the original utility maximization problem into two sub-optimization problems for each time frame, which are a convex optimization problem and a non-convex optimization problem, respectively. By formulating the distributed scheduling problem as a non-cooperative game where each BS is a player attempting to optimize its own utility, we provide a distributed solution to the non-convex sub-optimization problem via finding the Nash Equilibrium (NE) of the game whose weights are determined optimally by the Lyapunov optimization framework. Finally, we conduct simulation under various network settings to show the effectiveness of the proposed game-based beam scheduling algorithm in comparison to that of several reference schemes.
42 ENGINEERING↗
Modeling and measurement of fault-tolerant multiprocessors
The workload effects on computer performance are addressed first for a highly reliable unibus multiprocessor used in real-time control. As an approach to studing these effects, a modified Stochastic Petri Net (SPN) is used to describe the synchronous operation of the multiprocessor system. From this model the vital components affecting performance can be determined. However, because of the complexity in solving the modified SPN, a simpler model, i.e., a closed priority queuing network, is constructed that represents the same critical aspects. The use of this model for a specific application requires the partitioning of the workload into job classes. It is shown that the steady state solution of the queuing model directly produces useful results. The use of this model in evaluating an existing system, the Fault Tolerant Multiprocessor (FTMP) at the NASA AIRLAB, is outlined with some experimental results. Also addressed is the technique of measuring fault latency, an important microscopic system parameter. Most related works have assumed no or a negligible fault latency and then performed approximate analyses. To eliminate this deficiency, a new methodology for indirectly measuring fault latency is presented.
Shin, K. G.↗