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Results for “chance constrained optimization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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18 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2013

Mixed-Strategy Chance Constrained Optimal Control

This paper presents a novel chance constrained optimal control (CCOC) algorithm that chooses a control action probabilistically. A CCOC problem is to find a control input that minimizes the expected cost while guaranteeing that the probability of violating a set of constraints is below a user-specified threshold. We show that a probabilistic control approach, which we refer to as a mixed control strategy, enables us to obtain a cost that is better than what deterministic control strategies can achieve when the CCOC problem is nonconvex. The resulting mixed-strategy CCOC problem turns out to be a convexification of the original nonconvex CCOC problem. Furthermore, we also show that a mixed control strategy only needs to "mix" up to two deterministic control actions in order to achieve optimality. Building upon an iterative dual optimization, the proposed algorithm quickly converges to the optimal mixed control strategy with a user-specified tolerance.

Ono, Masahiro↗
DOE OSTI2024

An Empirical Quantile Estimation Approach for Chance-Constrained Nonlinear Optimization Problems

We investigate an empirical quantile estimation approach to solve chance-constrained nonlinear optimization problems. Our approach is based on the reformulation of the chance constraint as an equivalent quantile constraint to provide stronger signals on the gradient. In this approach, the value of the quantile function is estimated empirically from samples drawn from the random parameters, and the gradient of the quantile function is estimated via a finite-difference approximation on top of the quantile-function-value estimation. We establish a convergence theory of this approach within the framework of an augmented Lagrangian method for solving general nonlinear constrained optimization problems. The foundation of the convergence analysis is a concentration property of the empirical quantile process, and the analysis is divided based on whether or not the quantile function is differentiable. In contrast to the sampling-and-smoothing approach used in the literature, the method developed in this paper does not involve any smoothing function and hence the quantile-function gradient approximation is easier to implement and there are less accuracy-control parameters to tune. Furthermore, we demonstrate the effectiveness of this approach and compare it with a smoothing method for the quantile-gradient estimation. Numerical investigation shows that the two approaches are competitive for certain problem instances.

Applied Probability↗
NASA NTRS2008

Robust Path Planning and Feedback Design Under Stochastic Uncertainty

Autonomous vehicles require optimal path planning algorithms to achieve mission goals while avoiding obstacles and being robust to uncertainties. The uncertainties arise from exogenous disturbances, modeling errors, and sensor noise, which can be characterized via stochastic models. Previous work defined a notion of robustness in a stochastic setting by using the concept of chance constraints. This requires that mission constraint violation can occur with a probability less than a prescribed value.In this paper we describe a novel method for optimal chance constrained path planning with feedback design. The approach optimizes both the reference trajectory to be followed and the feedback controller used to reject uncertainty. Our method extends recent results in constrained control synthesis based on convex optimization to solve control problems with nonconvex constraints. This extension is essential for path planning problems, which inherently have nonconvex obstacle avoidance constraints. Unlike previous approaches to chance constrained path planning, the new approach optimizes the feedback gain as wellas the reference trajectory.The key idea is to couple a fast, nonconvex solver that does not take into account uncertainty, with existing robust approaches that apply only to convex feasible regions. By alternating between robust and nonrobust solutions, the new algorithm guarantees convergence to a global optimum. We apply the new method to an unmanned aircraft and show simulation results that demonstrate the efficacy of the approach.

autonomuys vehicles↗
DOE OSTI2026

Stochastic Microgrid Scheduling With Chance‐Constrained Resilience Consideration

Traditionally, it is assumed that microgrids transition seamlessly from grid‐connected operation to islanded mode in the event of sudden main grid outages. In reality, the islanding process, especially unintentional islanding, is rarely seamless. Instead, it is subject to voltage and frequency fluctuations caused by the instantaneous disconnection of the point of common coupling (PCC) switch, variations in loads and renewable generation output and even the protection tripping of distributed energy resources (DERs). To mitigate these fluctuations and facilitate a smooth islanding process, we propose a stochastic microgrid scheduling model that incorporates chance‐constrained resilience measures. Specifically, the resilience measure is defined as the probability of successful islanding (PSI), that is, the probability that a microgrid can mitigate the generation‐demand imbalance caused by the disconnection of the PCC switch, variations in load and renewable generation and DER tripping. This measure is modelled using chance constraints. Unlike existing reliability and resilience indices, which typically neglect the possibility of microgrid/DER failure under extreme events and assume their survival while primarily focussing on reducing impact duration or magnitude, the proposed PSI‐based framework explicitly addresses microgrid and DER survival during the islanding transition. The formulated nonlinear chance constraints are approximated using a multiinterval approach and equivalently represented as a mixed‐integer linear programming (MILP) formulation. Case study results validate the proposed method, showing that the PSI estimation error is reduced to less than 8%, compared to approximately 28% with existing methods. Various sensitivity analyses on the DER tripping rate and PSI settings were performed to validate the robustness of the proposed method. In particular, the necessity of accounting for DER tripping in the PSI calculation was demonstrated.

chance constrained optimization↗
NASA NTRS2011

Chance-Constrained Guidance With Non-Convex Constraints

Missions to small bodies, such as comets or asteroids, require autonomous guidance for descent to these small bodies. Such guidance is made challenging by uncertainty in the position and velocity of the spacecraft, as well as the uncertainty in the gravitational field around the small body. In addition, the requirement to avoid collision with the asteroid represents a non-convex constraint that means finding the optimal guidance trajectory, in general, is intractable. In this innovation, a new approach is proposed for chance-constrained optimal guidance with non-convex constraints. Chance-constrained guidance takes into account uncertainty so that the probability of collision is below a specified threshold. In this approach, a new bounding method has been developed to obtain a set of decomposed chance constraints that is a sufficient condition of the original chance constraint. The decomposition of the chance constraint enables its efficient evaluation, as well as the application of the branch and bound method. Branch and bound enables non-convex problems to be solved efficiently to global optimality. Considering the problem of finite-horizon robust optimal control of dynamic systems under Gaussian-distributed stochastic uncertainty, with state and control constraints, a discrete-time, continuous-state linear dynamics model is assumed. Gaussian-distributed stochastic uncertainty is a more natural model for exogenous disturbances such as wind gusts and turbulence than the previously studied set-bounded models. However, with stochastic uncertainty, it is often impossible to guarantee that state constraints are satisfied, because there is typically a non-zero probability of having a disturbance that is large enough to push the state out of the feasible region. An effective framework to address robustness with stochastic uncertainty is optimization with chance constraints. These require that the probability of violating the state constraints (i.e., the probability of failure) is below a user-specified bound known as the risk bound. An example problem is to drive a car to a destination as fast as possible while limiting the probability of an accident to 10(exp -7). This framework allows users to trade conservatism against performance by choosing the risk bound. The more risk the user accepts, the better performance they can expect.

FROM↗
NASA NTRS2013

Risk-Constrained Dynamic Programming for Optimal Mars Entry, Descent, and Landing

A chance-constrained dynamic programming algorithm was developed that is capable of making optimal sequential decisions within a user-specified risk bound. This work handles stochastic uncertainties over multiple stages in the CEMAT (Combined EDL-Mobility Analyses Tool) framework. It was demonstrated by a simulation of Mars entry, descent, and landing (EDL) using real landscape data obtained from the Mars Reconnaissance Orbiter. Although standard dynamic programming (DP) provides a general framework for optimal sequential decisionmaking under uncertainty, it typically achieves risk aversion by imposing an arbitrary penalty on failure states. Such a penalty-based approach cannot explicitly bound the probability of mission failure. A key idea behind the new approach is called risk allocation, which decomposes a joint chance constraint into a set of individual chance constraints and distributes risk over them. The joint chance constraint was reformulated into a constraint on an expectation over a sum of an indicator function, which can be incorporated into the cost function by dualizing the optimization problem. As a result, the chance-constraint optimization problem can be turned into an unconstrained optimization over a Lagrangian, which can be solved efficiently using a standard DP approach.

Ono, Masahiro↗
DOE OSTI2024

Multi-Factor-Coupled, Ahead-of-Time Aggregation of Power Flexibility Under Forecast Uncertainty

The increasing penetration of distributed energy resources (DERs) is significantly reshaping the role of distribution systems under active energy management. To aggregate the active-reactive power flexibility of DERs dispersed at the feeder and provide capacity support to the transmission system, it is essential to efficiently identify feasible substation power injection trajectories. This paper introduces a novel ahead-of-time flexibility characterization method to address it. First, a polyhedral non-feeder-level power flexibility region (PFR) is constructed, accounting for various time-dependent, power-coupled, and forecast error uncertainties. Then, a polyhedral feeder-level PFR is analytically derived through a coordinate transformation, which can reveal the uncertainty propagation path, i.e., how uncertainty applies to the feeder-level PFR. To facilitate the high-level application, a tractable chance-constrained Chebyshev centering optimization model is further developed to find a ball-shaped inner approximation of the feeder-level PFR. Finally, the proposed method is validated on a modified IEEE 123-bus test system. Here, both theoretical and experimental results show that, with appropriate robustness parameter settings, the proposed method can make the approximated PFR less conservative with abundant robustness against forecast error uncertainty.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Safe Reinforcement Learning-Based Transient Stability Control for Islanded Microgrids With Topology Reconfiguration

This paper proposes a safe reinforcement learning (RL)-based transient stability emergency control (TSEC) method for islanded microgrids. RL requires extensive interaction with the environment to learn control strategies, hence, a data-driven approach is used as a substitute for time-consuming time-domain simulation calculations. Deep sigma point processes (DSPP), which is a Gaussian process model, is utilized to predict the normal distribution of transient stability of microgrids and to construct a transient stability chance constraint. Reward-constrained policy optimization (RCPO) can simultaneously achieve objective prediction, policy learning, and constraint cost coefficient update across multiple timescales. RCPO interacts with the DSPP-based microgrid environment through a multi-process parallel manner, greatly increasing the training speed. Case studies on a real islanded microgrid demonstrate that the proposed method can efficiently and quickly obtain the optimal emergency control strategy while adhering to all hard constraints.

14 SOLAR ENERGY↗
NASA NTRS2012

A Risk-Constrained Multi-Stage Decision Making Approach to the Architectural Analysis of Mars Missions

This paper presents a novel risk-constrained multi-stage decision making approach to the architectural analysis of planetary rover missions. In particular, focusing on a 2018 Mars rover concept, which was considered as part of a potential Mars Sample Return campaign, we model the entry, descent, and landing (EDL) phase and the rover traverse phase as four sequential decision-making stages. The problem is to find a sequence of divert and driving maneuvers so that the rover drive is minimized and the probability of a mission failure (e.g., due to a failed landing) is below a user specified bound. By solving this problem for several different values of the model parameters (e.g., divert authority), this approach enables rigorous, accurate and systematic trade-offs for the EDL system vs. the mobility system, and, more in general, cross-domain trade-offs for the different phases of a space mission. The overall optimization problem can be seen as a chance-constrained dynamic programming problem, with the additional complexity that 1) in some stages the disturbances do not have any probabilistic characterization, and 2) the state space is extremely large (i.e, hundreds of millions of states for trade-offs with high-resolution Martian maps). To this purpose, we solve the problem by performing an unconventional combination of average and minimax cost analysis and by leveraging high efficient computation tools from the image processing community. Preliminary trade-off results are presented.

entry, descent, and landing (EDL)↗
DOE OSTI2025

Optimization problems governed by systems of PDEs with uncertainties

This paper reviews current theoretical and numerical approaches to optimization problems governed by partial differential equations (PDEs) that depend on random variables or random fields. Such problems arise in many engineering, science, economics and societal decision-making tasks. This paper focuses on problems in which the governing PDEs are parametrized by the random variables/fields, and the decisions are made at the beginning and are not revised once uncertainty is revealed. Examples of such problems are presented to motivate the topic of this paper, and to illustrate the impact of different ways to model uncertainty in the formulations of the optimization problem and their impact on the solution. A linear–quadratic elliptic optimal control problem is used to provide a detailed discussion of the set-up for the risk-neutral optimization problem formulation, study the existence and characterization of its solution, and survey numerical methods for computing it. Different ways to model uncertainty in the PDE-constrained optimization problem are surveyed in an abstract setting, including risk measures, distributionally robust optimization formulations, probabilistic functions and chance constraints, and stochastic orders. Furthermore, approximation-based optimization approaches and stochastic methods for the solution of the large-scale PDE-constrained optimization problems under uncertainty are described. Some possible future research directions are outlined.

Heinkenschloss, Matthias [Rice Univ., Houston, TX ↗
DOE OSTI2024

Analytic Neural Network Gaussian Process Enabled Chance-Constrained Voltage Regulation for Active Distribution Systems with PVs, Batteries and EVs

This paper proposes an analytic neural network Gaussian process (NNGP)-based chance-constrained real-time voltage regulation method for active distribution systems with photovoltaics (PVs), batteries, and electric vehicles (EVs). NNGP can utilize historical measurement data to achieve real-time probabilistic node voltage estimation through Bayesian inference. Then, NNGP is fully analytically embedded into the optimal power flow model to perform voltage regulation and adapt to various topological changes. The uncertainties of voltage estimations are easily considered via the chance constraint, and it has been shown that the adoption of this chance constraint can significantly improve the reliability of voltage regulation under various scenarios. The comparison results with other methods, carried out on a real 759-node distribution system located in western Colorado, U.S., show that the proposed method can achieve accurate voltage estimation across different topologies and reliably perform voltage regulation considering PVs, batteries, and EVs.

active distribution systems↗
NASA NTRS2003

Stochastic Control Synthesis of Systems with Structured Uncertainty

This paper presents a study on the design of robust controllers by using random variables to model structured uncertainty for both SISO and MIMO feedback systems. Once the parameter uncertainty is prescribed with probability density functions, its effects are propagated through the analysis leading to stochastic metrics for the system's output. Control designs that aim for satisfactory performances while guaranteeing robust closed loop stability are attained by solving constrained non-linear optimization problems in the frequency domain. This approach permits not only to quantify the probability of having unstable and unfavorable responses for a particular control design but also to search for controls while favoring the values of the parameters with higher chance of occurrence. In this manner, robust optimality is achieved while the characteristic conservatism of conventional robust control methods is eliminated. Examples that admit closed form expressions for the probabilistic metrics of the output are used to elucidate the nature of the problem at hand and validate the proposed formulations.

Padula, Sharon L.↗
NASA NTRS2012

Joint Chance-Constrained Dynamic Programming

This paper presents a novel dynamic programming algorithm with a joint chance constraint, which explicitly bounds the risk of failure in order to maintain the state within a specified feasible region. A joint chance constraint cannot be handled by existing constrained dynamic programming approaches since their application is limited to constraints in the same form as the cost function, that is, an expectation over a sum of one-stage costs. We overcome this challenge by reformulating the joint chance constraint into a constraint on an expectation over a sum of indicator functions, which can be incorporated into the cost function by dualizing the optimization problem. As a result, the primal variables can be optimized by a standard dynamic programming, while the dual variable is optimized by a root-finding algorithm that converges exponentially. Error bounds on the primal and dual objective values are rigorously derived. We demonstrate the algorithm on a path planning problem, as well as an optimal control problem for Mars entry, descent and landing. The simulations are conducted using a real terrain data of Mars, with four million discrete states at each time step.

Ono, Masahiro↗
NASA NTRS2016

Fermi GBM Observations of LIGO Gravitational-Wave Event Gw150914

With an instantaneous view of 70% of the sky, the Fermi Gamma-ray Burst Monitor (GBM) is an excellent partner in the search for electromagnetic counterparts to gravitational-wave (GW) events. GBM observations at the time of the Laser Interferometer Gravitational-wave Observatory (LIGO) event GW150914 reveal the presence of a weak transient above 50 keV, 0.4 s after the GW event, with a false-alarm probability of 0.0022 (2.9(sigma)). This weak transient lasting 1 s was not detected by any other instrument and does not appear to be connected with other previously known astrophysical, solar, terrestrial, or magnetospheric activity. Its localization is ill-constrained but consistent with the direction of GW150914. The duration and spectrum of the transient event are consistent with a weak short gamma-ray burst (GRB) arriving at a large angle to the direction in which Fermi was pointing where the GBM detector response is not optimal. If the GBM transient is associated with GW150914, then this electromagnetic signal from a stellar mass black hole binary merger is unexpected. We calculate a luminosity in hard X-ray emission between 1 keV and 10 MeV of 1.8(sup +1.5, sub -1.0) x 10(exp 49) erg/s. Future joint observations of GW events by LIGO/Virgo and Fermi GBM could reveal whether the weak transient reported here is a plausible counterpart to GW150914 or a chance coincidence, and will further probe the connection between compact binary mergers and short GRBs.

gamma-ray burst: general – gravitational waves↗
NASA NTRS2020

Revisiting the Effectiveness Of HCHO/NO2 Ratios for Inferring Ozone Sensitivity to Its Precursors Using High Resolution Airborne Remote Sensing Observations in A High Ozone Episode During the KORUS-AQ Campaign

The nonlinear chemical processes involved in ozone production (P(O3)) have necessitated using proxy indicators to convey information about the primary dependence of P(O3) on volatile organic compounds (VOCs) or nitrogen oxides (NOx). In particular, the ratio of remotely sensed columns of formaldehyde (HCHO) to nitrogen dioxide (NO2) has been widely used for studying O3 sensitivity. Previous studies found that the errors in retrievals and the incoherent relationship between the column and the near-surface concentrations are a barrier in applying the ratio in a robust way. In addition to these obstacles, we provide calculational-observational evidence, using an ensemble of 0-D photochemical box models constrained by DC-8 aircraft measurements on an ozone event during the Korea-United States Air Quality (KORUS-AQ) campaign over Seoul, to demonstrate the chemical feedback of NO2 on the formation of HCHO is a controlling factor for the transition line between NOx-sensitive and NOx-saturated regimes. A fixed value (~2.7) of the ratio of the chemical loss of NOx (LNOx) to the chemical loss of HO2+RO2 (LROx) perceptibly differentiates the regimes. Following this value, data points with a ratio of HCHO/NO2 less than 1 can be safely classified as NOx-saturated regime, whereas points with ratios between 1 and 4 fall into one or the other regime. We attribute this mainly to the HCHO-NO2 chemical relationship causing the transition line to occur at larger (smaller) HCHO/NO2 ratios in VOC-rich (VOC-poor) environments. We then redefine the transition line to LNOx/LROx~2.7 that accounts for the HCHO-NO2 chemical relationship leading to HCHO = 3.7 × (NO2 – 1.14 × 1016 molec.cm-2). Although the revised formula is locally calibrated (i.e., requires for readjustment for other regions), its mathematical format removes the need for having a wide range of thresholds used in HCHO/NO2 ratios that is a result of the chemical feedback. Therefore, to be able to properly take the chemical feedback into consideration, the use of HCHO = a × (NO2 – b) formula should be preferred to the ratio in future works. We then use the Geostationary Trace gas and Aerosol Sensor Optimization (GeoTASO) airborne instrument to study O3 sensitivity in Seoul. The unprecedented spatial (250 × 250 m2) and temporal (~every 2 h) resolutions of HCHO and NO2 observations form the sensor enhance our understanding of P(O3) in Seoul; rather than providing a crude label for the entire city, more in-depth variabilities in chemical regimes are observed that should be able to inform mitigation strategies correspondingly.

KORUS-AQ; formaldehyde; NOx; VOC; OMI; GeoTASO; oz↗
NASA NTRS2019

Design of P-3 Nadir Port

This project details the design and analysis of a structure to replace the interface of the P-3B nadir port with an optimized interface for science installations. A new nadir port plug has been designed to replace the OEM (Original Equipment Manufacturer) plug (Lockheed PN 910169) currently used in Nadir ports 1 and 2 on the NASA P-3B aircraft. The plug consists of a milled frame that can be outfitted with customizable flat plates to meet a broad range of science needs. The frame slides into place using the existing P-3B rail system using a lever and tie-rod assembly. The seal interface will contact the Fuselage skin of the aircraft and consists of a bulb E-seal that is riveted around the perimeter of the frame. The flat plate (20 inches x 31 inches) provides a large profile that can be outfitted based on science mission goals and requirements to attach multiple instruments. This is a significant increase to the aircraft capability. Previously, the OEM plug had to be modified to hold very small plates, windows, or instruments limiting the use of the ports.There were several challenges for this project that included a constrained schedule, lack of historical references, and reverse engineering. The unusually tight schedule for design, manufacture, and install limited potential approaches. In addition, design of a new interface to replace the existing plug, on an aircraft designed in the 1960's by Lockheed for the Navy with little to no documentation, required substantial reverse engineering. In order to accomplish this, a suitable method to determine interface requirements with the aircraft had to be solved. After several iterations, the solution was to implement laser scanning techniques to scan the aircraft and the OEM plug and generate a 3D model to capture the design envelope. The structure is designed to maintain a positive margin of safety when subjected to the inertial, pressure, and aerodynamic load requirements for an external installation on the P-3B, as described in the Wallops' P-3B Design Requirements 548-RQMT-0001 Rev. A . A finite element model is created in FEMAP (Finite Element Modeling And Postprocessing) and is run through NX Nastran solver to analyze the structure. After several iterations of analysis, the structure was enveloped to hold 115 pounds evenly distributed on the plate.

Chance, Monica↗