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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Convex Q-Learning in Continuous Time with Application to Dispatch of Distributed Energy Resources

Convex Q-learning is a recent approach to reinforcement learning, motivated by the possibility of a firmer theory for convergence, and the possibility of making use of greater a priori knowledge regarding policy or value function structure. This paper explores algorithm design in the continuous time domain, with a finite-horizon optimal control objective. The main contributions are (i) The new Q-ODE: a model-free characterization of the Hamilton-Jacobi-Bellman equation. (ii) A formulation of Convex Q-learning that avoids approximations appearing in prior work. The Bellman error used in the algorithm is defined by filtered measurements, which is necessary in the presence of measurement noise. (iii) Convex Q-learning with linear function approximation is a convex program. It is shown that the constraint region is bounded, subject to an exploration condition on the training input. (iv) The theory is illustrated in application to resource allocation for distributed energy resources, for which the theory is ideally suited.

Lu, Fan↗
DOE OSTI2025

Large Scale Bilevel Optimization for N-K SCOPF Using Adversarial Robustness

Ensuring a secure dispatch against multiple simultaneous outages has long been desired to maintain grid security in the presence of severe events, such as extreme weather phenomena. Traditionally denoted as N-k security constrained optimal power flow (N-k SCOPF), this problem is intractable to solve due to its size being combinatorial in the number of simultaneous outages and due to the non-convex nature of the AC network constraints. This hinders the use of N-k SCOPF for operating realistic-scale systems. In this paper, we introduce a methodology to scalably solve an AC-feasible dispatch that improves security over k simultaneous outages. Our methodology poses N-k SCOPF as a bilevel optimization problem and solves it using an adversarial robustness approach. We develop new efficient methods to solve each level of the bilevel optimization by employing knowledge of the physics of the underlying system. This yields significant improvements in speed and convergence that enable us to address the N-k SCOPF problem at scale. We demonstrate the effectiveness of our method by conducting a comprehensive analysis of an N-3 SCOPF for a 500-bus network. Furthermore, we emphasize the ability of our physics-driven techniques to handle larger systems by successfully scaling up to 12,000 buses.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Disjunctive linear separation conditions and mixed-integer formulations for aircraft conflict resolution

In this paper, we address the aircraft conflict resolution problem in air traffic control. We introduce new mixed-integer programming formulations for aircraft conflict resolution with speed, heading and altitude control which are based on disjunctive linear separation conditions. We first examine the two-dimensional aircraft conflict resolution problem with speed and heading control represented as continuous decision variables. We show that the proposed disjunctive linear separation conditions are equivalent to the classical nonlinear conditions for aircraft separation. Further, we characterise conflict-free trajectories based on aircraft velocity bounds and propose a simple pre-processing algorithm to identify aircraft pairs which are either always conflict-free, or which cannot be separated using speed and heading control only. We then incorporate altitude control and propose a lexicographic optimisation formulation that aims to minimise the number of flight level changes before resolving outstanding conflicts via two-dimensional velocity control. The proposed mixed-integer programming formulations are nonconvex, and we propose convex relaxations, decomposition methods and constraint generation algorithms to solve the two-dimensional and lexicographic optimisation formulations to guaranteed optimality. Numerical experiments on four types of conflict resolution benchmarking instances are conducted to test the performance of the proposed mixed-integer formulations. Further, the proposed method is compared against two benchmarks based on state-of-the-art approaches for the aircraft conflict resolution problem. Our numerical results show that the proposed method largely outperforms both benchmarks in terms of runtime and is able to solve significantly more instances to global optimality.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Alternating Direction Decomposition with Strong Bounding and Convexification (ADDSBC) for Solving Security Constrained AC Unit Commitment Problems

This project aims to develop efficient and robust computational methods for solving the security-constrained unit commitment and alternating current optimal power flow problem (SC-UC-ACOPF). The SC-UC-ACOPF problem is at the center of the short-term operation of the U.S. Power Grid. It is solved every week, every day, and every 10 minutes to plan for the optimal action of electricity generation and consumption by minimizing the generation cost and maintaining power system reliability against potential disruptions of equipment failures. In mathematical terms, SC-UC-ACOPF is a challenging large-scale mixed-integer nonlinear optimization model. This means that the decisions involve both discrete variables, e.g. the turning on and off of generators and switching of transmission lines and transformers, and continuous decisions, e.g. the amount of energy generated by each generator and the power flows in the power grid. The physics of the power flow is described by nonlinear equations involving real and reactive power and bus voltages. Another key feature is the large number of contingencies, i.e. the system needs to stay reliable in face of failure of any one equipment, such as transmission lines and generators. The U.S. power grids are extremely complicated and large scale with more than 5,000 generators, 50,000 buses, and 100,000 high-voltage transmission lines, making the SC-UC-ACOPF a very large-scale computation challenge. The research developed in this project aims to solve the SC-UC-ACOPF problems in the three timescales, i.e. weekly, daily, and every 10-min. The proposed computational methods are built on a principled algorithmic approach of decomposition and penalization. More specifically, the algorithm develops spatial and temporal decomposition by exploiting the strong temporal coupling and weak spatial coupling of the UC problem and the complementary feature, i.e. weak temporal coupling and strong spatial coupling of the ACOPF problem. The algorithm also leverages recent progresses in strong convex relaxation of ACOPF. A unique feature of the proposed approach is that it generates a valid, global upper bound on the optimal maximum profit. In this way, a global optimality gap is available to measure the quality of the solution. To further speed up computation, the research team has developed a plethora of effective heuristics to strengthen the iterative penalty-based decomposition framework. For instance, a heuristic is developed to construct inner approximations of the time coupling constraints within the time decoupled problems. Contingencies are pre-screened and low-rank matrix computation is exploited to find the almost unique solution to each contingency. A novel heuristic for line switching is proposed and tested with positive impacts on instances where line switching is beneficial. Taking a systematic approach and carefully handling every detail of the problem pays off. The TIM-GO’s performance throughout the trials and the final event was stellar. TIM-GO garnered the second highest total prize money and is ranked in the top three positions across all categories of comparison.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1976

Lagrange duality theory for convex control problems

The Lagrange dual to a control problem is studied. The principal result based on the Hahn-Banach theorem proves that the dual problem has an optimal solution if there exists an interior point for the constraint set. A complementary slackness condition holds, if the primal problem has an optimal solution. A necessary and sufficient condition for the optimality of solutions to the primal and the dual problem is also presented.

Hager, W. W.↗
DOE OSTI2024

Intelligent Partitioning based Fully Parallel AC Security-Constrained Optimal Power Flow

Today’s power grid is becoming more diverse and integrated with high-level distributed energy resources and smart control technologies that is creating a new set of grid management challenges in terms of large-scale, nonlinear, and non-convex problem modeling, complex and time-consuming computation, as well as difficult uncertainty handling. This project focused on solving a challenging multi-period security-constrained generation scheduling problem, which is of great importance for maximizing the social welfare of real-time dispatch, day-ahead market, as well as weekly planning of power systems. Our developed software explored parallel optimization algorithms for complex and realistic power system models, and develop fast, efficient, and robust grid optimization solutions on the high-performance computing platform that will enable increased grid economics, flexibility, resilience, as well as energy security in the United States.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

An adaptive sampling augmented Lagrangian method for stochastic optimization with deterministic constraints

The primary goal of this paper is to provide an efficient solution algorithm based on the augmented Lagrangian framework for optimization problems with a stochastic objective function and deterministic constraints. Our main contribution is combining the augmented Lagrangian framework with adaptive sampling, resulting in an efficient optimization methodology validated with practical examples. To achieve the presented efficiency, here we consider inexact solutions for the augmented Lagrangian subproblems, and through an adaptive sampling mechanism, we control the variance in the gradient estimates. Furthermore, we analyze the theoretical performance of the proposed scheme by showing equivalence to a gradient descent algorithm on a Moreau envelope function, and we prove sublinear convergence for convex objectives and linear convergence for strongly convex objectives with affine equality constraints. The worst-case sample complexity of the resulting algorithm, for an arbitrary choice of penalty parameter in the augmented Lagrangian function, is $\mathscr{O}$(ϵ -3-δ ) , where ϵ > 0 is the expected error of the solution and δ > 0 is a user-defined parameter. If the penalty parameter is chosen to be $\mathscr{O}$(ϵ -1 ), we demonstrate that the result can be improved to $\mathscr{O}$(ϵ -2 ) , which is competitive with the other methods employed in the literature. Moreover, if the objective function is strongly convex with affine equality constraints, we obtain $\mathscr{O}$(ϵ -1 log(1/ϵ)) complexity. Finally, we empirically verify the performance of our adaptive sampling augmented Lagrangian framework in machine learning optimization and engineering design problems, including topology optimization of a heat sink with environmental uncertainty.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1971

A stochastic constrained optimization technique and its application to detector array processing.

A stochastic projected gradient algorithm is proposed which can be used for finding a constrained optimum point for a concave or convex objective function subject to nonlinear constraints which form a connected region even when only a noisy estimate of the objective function is available. For a constraint described by a single linear equation, convergence to the constrained optimum value is proved, and the rate of convergence of the algorithm to the constrained optimum value is determined. The algorithm is applied to the nonlinear problem of obtaining automatically an array of detectors which forms a beam in a desired direction in space in the presence of interfering noise so as to maximize the SNR subject to a constraint on the super-gain ratio.

Winkler, L. P.↗
NASA NTRS1991

On convexity of H-infinity Riccati solutions

The authors revealed several important eigen properties of the stabilizing solutions of the two H-infinity Riccati equations and their product. Among them, the most prominent one is that the spectral radius of the product of these two Riccati solutions is a continuous, nonincreasing, convex function of gamma in the domain of interest. Based on these properties, quadratically convergent algorithms are developed to compute the optimal H-infinity norm. Two examples are used to illustrate the algorithms.

Li, X. P.↗
DOE OSTI2025

Efficient Neural Network Approaches for Conditional Optimal Transport with Applications in Bayesian Inference

In this work, we present two neural network approaches that approximate the solutions of static and dynamic conditional optimal transport (COT) problems. Both approaches enable conditional sampling and conditional density estimation, which are core tasks in Bayesian inference—particularly in the simulation-based (“likelihood-free”) setting. Our methods represent the target conditional distribution as a transformation of a tractable reference distribution. Obtaining such a transformation, chosen here to be an approximation of the COT map, is computationally challenging even in moderate dimensions. To improve scalability, our numerical algorithms use neural networks to parameterize candidate maps and further exploit the structure of the COT problem. Our static approach approximates the map as the gradient of a partially input convex neural network. It uses a novel numerical implementation to increase computational efficiency compared to state-of-the-art alternatives. Our dynamic approach approximates the conditional optimal transport via the flow map of a regularized neural ODE; compared to the static approach, it is slower to train but offers more modeling choices and can lead to faster sampling. We demonstrate both algorithms numerically, comparing them with competing state-of-the-art approaches, using benchmark datasets and simulation-based Bayesian inverse problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Reliability-based hull geometry optimisation of a point-absorber wave energy converter with power take-off structural reliability objectives

Recent studies have focused on optimising wave energy converter (WEC) designs, maximising their power performance and techno-economic feasibility. Reliability has yet to be fully considered in these formulations, despite its impact on cost and performance. In this study, this gap is addressed by developing a reliability-based design optimisation framework for WEC hull geometries to explore the trade-off between power performance and power take-off (PTO) system damage equivalent loading (DEL). Optimised hull geometries for two sites are considered (from the centre of the North Sea and off the west coast of Norway), and two directions of motions (heave and surge). Results indicate that site characteristics affect the potential power production and DEL for an optimal WEC design. These are also affected by the direction of motion for power extraction, which also significantly changes optimal hull shape characteristics. Optimal surging WEC designs have edges facing oncoming wave directions, while heaving WECs have pointed bottoms, both to streamline movement. Larger, more convex WECs result in greater power production and DEL, while smaller, more concave WECs result in lesser power production and DEL. These findings underline the importance of considering WEC hull geometry in early design processes to optimise cost, power production, and reliability.

16 TIDAL AND WAVE POWER↗
DOE OSTI2023

Rethinking the Price Formation Problem–Part 1: Participant Incentives under Uncertainty

Operators of organized wholesale electricity markets attempt to form prices in such a way that the private incentives of market participants are consistent with a socially optimal commitment and dispatch schedule. In the U.S. context, several competing price formation schemes have been proposed to address the non-convex production cost functions characteristic of most generation technologies. Here, this paper considers how the design and analysis of price formation policies for non-convex markets are affected by the uncertainty inherent in electricity demand and supply. We argue that by excluding uncertainty, the analytical framework underlying existing policies mischaracterizes the incentives of market participants, leading to inefficient price formation and poor incentives for flexibility. We establish favorable theoretical properties of a new construct, ex ante convex hull pricing , and demonstrate the difference between this idealized benchmark and existing methods on a large-scale test system. Given increased operational uncertainty with a transition to wind and solar generation, distortions caused by poor incentives for flexibility are likely to grow without improved price formation in organized wholesale markets.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS2013

Smart-Divert Powered Descent Guidance to Avoid the Backshell Landing Dispersion Ellipse

A smart-divert capability has been added into the Powered Descent Guidance (PDG) software originally developed for Mars pinpoint and precision landing. The smart-divert algorithm accounts for the landing dispersions of the entry backshell, which separates from the lander vehicle at the end of the parachute descent phase and prior to powered descent. The smart-divert PDG algorithm utilizes the onboard fuel and vehicle thrust vectoring to mitigate landing error in an intelligent way: ensuring that the lander touches down with minimum- fuel usage at the minimum distance from the desired landing location that also avoids impact by the descending backshell. The smart-divert PDG software implements a computationally efficient, convex formulation of the powered-descent guidance problem to provide pinpoint or precision-landing guidance solutions that are fuel-optimal and satisfy physical thrust bound and pointing constraints, as well as position and speed constraints. The initial smart-divert implementation enforced a lateral-divert corridor parallel to the ground velocity vector; this was based on guidance requirements for MSL (Mars Science Laboratory) landings. This initial method was overly conservative since the divert corridor was infinite in the down-range direction despite the backshell landing inside a calculable dispersion ellipse. Basing the divert constraint instead on a local tangent to the backshell dispersion ellipse in the direction of the desired landing site provides a far less conservative constraint. The resulting enhanced smart-divert PDG algorithm avoids impact with the descending backshell and has reduced conservatism.

Carson, John M.↗
DOE OSTI2020

Extremum seeking for optimal control problems with unknown time-varying systems and unknown objective functions

We consider the problem of optimal feedback control of an unknown, noisy, time-varying, dynamic system that is initialized repeatedly. Examples include a robotic manipulator which must perform the same motion, such as assisting a human, repeatedly and accelerating cavities in particle accelerators which are turned on for a fraction of a second with given initial conditions and vary slowly due to temperature fluctuations. In this paper, we present an approach that applies to systems of practical interest. The method presented here is model independent; does not require knowledge of the objective function; is robust to measurement noise; is applicable for any set of initial conditions; is applicable to simultaneously controlling an arbitrary number of parameters; and may be implemented with a broad range of continuous or discontinuous functions such as sine or square waves. For systems with convex cost functions we prove that our algorithm will produce controllers that approach the minimal cost. For linear systems we reproduce the cost minimizing linear quadratic regulator optimal controller that could have been designed analytically had the system and cost function been known. We demonstrate the effectiveness of the algorithm with simulation studies of noisy and time-varying systems.

42 ENGINEERING↗
DOE OSTI2025

The origin of the Stokes–Einstein relation in simple dense liquids

Here, we investigate the origin of the universal relation between structural relaxation and diffusion in simple dense liquids, known as the Stokes–Einstein (SE) relation. The fact that this relation, originally derived from a hydrodynamic model of a macroscopic particle in a viscous medium, can describe the microscopic-scale liquid dynamics still eludes understanding. We introduce a new universal measure of structural relaxation in a system of N identical particles based on an explicit decomposition of the configuration space into N! congruent convex polyhedra. This measure makes it possible to quantify the correlation between two distinct particle configurations in terms of their minimal Euclidean distance, optimized with respect to particle permutations. Using this measure alongside a model of independent random walkers under the single-occupancy constraint, we derive a master equation that quantifies the SE relation. It allows us to demonstrate that the universal relation between structural relaxation and diffusion in simple dense liquids is caused by two conditions: (a) the confinement of the dominant density fluctuations to the first coordination shell, manifested by de Gennes narrowing, and (b) Gaussianity of the diffusion process; the former is shown to be violated in low-density fluids, and the latter is known to be violated in supercooled liquids.

Physics - Condensed matter physics↗
DOE OSTI2024

Optimal Control of SOEC-Based Hydrogen Production Systems for Demand Response Using Deep Reinforcement Learning in Smart Grids

Solid oxide electrolysis cell (SOEC) hydrogen production technology can range in size from small, appliance-size equipment to large-scale, central production facilities that can be tied directly to renewable or non-greenhouse-gas-emitting forms of electricity production, making it an ideal resource for demand response (DR). The SOEC hydrogen production system is a complex integrated system that encompasses fluid dynamics, electrical dynamics, and electrochemical and thermal dynamics, all of which involve non-linearity and non-convexity. Proper control of the SOEC hydrogen production system is crucial to enable its participation in the DR program. Here, to overcome the difficulty of designing an explicit control law for such nonlinear systems with nonconvex optimization features in DR applications, deep reinforcement learning (DRL) is explored to achieve the optimal control of the SOEC system for DR participation. Specifically, a twin delayed deterministic policy gradient (TD3) control framework is applied to achieve optimal response performance during DR events by considering power tracking error and hydrogen production efficiency with a suitable reward function. Two case studies with grid connections for tracking different DR commands were investigated. The first case study involved operating conditions reaching the boundaries, while the second involved operating conditions within the boundaries. The results showed that the proposed DRL-based control for SOEC can track the DR signal in a timely manner while maintaining high energy efficiency.

08 HYDROGEN↗
DOE OSTI2022

A proximal trust-region method for nonsmooth optimization with inexact function and gradient evaluations

Many applications require minimizing the sum of smooth and nonsmooth functions. For example, basis pursuit denoising problems in data science require minimizing a measure of data misfit plus an $\ell^1$-regularizer. Similar problems arise in the optimal control of partial differential equations (PDEs) when sparsity of the control is desired. Here, we develop a novel trust-region method to minimize the sum of a smooth nonconvex function and a nonsmooth convex function. Our method is unique in that it permits and systematically controls the use of inexact objective function and derivative evaluations. When using a quadratic Taylor model for the trust-region subproblem, our algorithm is an inexact, matrix-free proximal Newton-type method that permits indefinite Hessians. We prove global convergence of our method in Hilbert space and demonstrate its efficacy on three examples from data science and PDE-constrained optimization.

97 MATHEMATICS AND COMPUTING↗