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Results for “stochastic optimal control”

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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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

A Stochastic Gradient Descent Approach for Stochastic Optimal Control

In this work, we introduce a stochastic gradient descent approach to solve the stochastic optimal control problem through stochastic maximum principle. The motivation that drives our method is the gradient of the cost functional in the stochastic optimal control problem is under expectation, and numerical calculation of such an expectation requires fully computation of a system of forward backward stochastic differential equations, which is computationally expensive. By evaluating the expectation with single-sample representation as suggested by the stochastic gradient descent type optimisation, we could save computational efforts in solving FBSDEs and only focus on the optimisation task which aims to determine the optimal control process.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

A Multiobjective Optimization Framework for Online Stochastic Optimal Control in Hybrid Electric Vehicles

The increasing urgency to extract additional efficiency from hybrid propulsion systems has led to the development of advanced power management control algorithms. In this paper we address the problem of online optimization of the supervisory power management control in parallel hybrid electric vehicles (HEVs). We model HEV operation as a controlled Markov chain and we show that the control policy yielding the Pareto optimal solution minimizes online the long-run expected average cost per unit time criterion. The effectiveness of the proposed solution is validated through simulation and compared to the solution derived with dynamic programming using the average cost criterion. Both solutions achieved the same cumulative fuel consumption demonstrating that the online Pareto control policy is an optimal control policy.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2016

A duality framework for stochastic optimal control of complex systems

In this study, we address the problem of minimizing the long-run expected average cost of a complex system consisting of interactive subsystems. We formulate a multiobjective optimization problem of the one-stage expected costs of the subsystems and provide a duality framework to prove that the control policy yielding the Pareto optimal solution minimizes the average cost criterion of the system. We provide the conditions of existence and a geometric interpretation of the solution. For practical situations having constraints consistent with those studied here, our results imply that the Pareto control policy may be of value when we seek to derive online the optimal control policy in complex systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Centralized Stochastic Optimal Control of Complex Systems

In this paper we address the problem of online optimization of the supervisory power management control in parallel hybrid electric vehicles (HEVs). We model HEV operation as a controlled Markov chain using the long-run expected average cost per unit time criterion, and we show that the control policy yielding the Pareto optimal solution minimizes the average cost criterion online. The effectiveness of the proposed solution is validated through simulation and compared to the solution derived with dynamic programming using the average cost criterion.

complex systems↗
DOE OSTI2015

Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost

This work is concerned with stochastic optimal control for a running maximum cost. A direct approach based on dynamic programming techniques is studied leading to the characterization of the value function as the unique viscosity solution of a second order Hamilton–Jacobi–Bellman (HJB) equation with an oblique derivative boundary condition. A general numerical scheme is proposed and a convergence result is provided. Error estimates are obtained for the semi-Lagrangian scheme. These results can apply to the case of lookback options in finance. Moreover, optimal control problems with maximum cost arise in the characterization of the reachable sets for a system of controlled stochastic differential equations. Some numerical simulations on examples of reachable analysis are included to illustrate our approach.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

A Multiobjective Optimization Framework for Stochastic Control of Complex Systems

This paper addresses the problem of minimizing the long-run expected average cost of a complex system consisting of subsystems that interact with each other and the environment. We treat the stochastic control problem as a multiobjective optimization problem of the one-stage expected costs of the subsystems, and we show that the control policy yielding the Pareto optimal solution is an optimal control policy that minimizes the average cost criterion for the entire system. For practical situations with constraints consistent to those we study here, our results imply that the Pareto control policy may be of value in deriving online an optimal control policy in complex systems.

Complex systems↗
DOE OSTI2016

Optimal Control for Stochastic Delay Evolution Equations

In this paper, we investigate a class of infinite-dimensional optimal control problems, where the state equation is given by a stochastic delay evolution equation with random coefficients, and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation. We first prove the continuous dependence theorems for stochastic delay evolution equations and anticipated backward stochastic evolution equations, and show the existence and uniqueness of solutions to anticipated backward stochastic evolution equations. Then we establish necessary and sufficient conditions for optimality of the control problem in the form of Pontryagin’s maximum principles. To illustrate the theoretical results, we apply stochastic maximum principles to study two examples, an infinite-dimensional linear-quadratic control problem with delay and an optimal control of a Dirichlet problem for a stochastic partial differential equation with delay. Further applications of the two examples to a Cauchy problem for a controlled linear stochastic partial differential equation and an optimal harvesting problem are also considered.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

An Efficient Numerical Algorithm for Solving Data Driven Feedback Control Problems

The goal of this paper is to solve a class of stochastic optimal control problems numerically, in which the state process is governed by an Itô type stochastic differential equation with control process entering both in the drift and the diffusion, and is observed partially. The optimal control of feedback form is determined based on the available observational data. In this work, we call this type of control problems the data driven feedback control. The computational framework that we introduce to solve such type of problems aims to find the best estimate for the optimal control as a conditional expectation given the observational information. To make our method feasible in providing timely feedback to the controlled system from data, we develop an efficient stochastic optimization algorithm to implement our computational framework.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A backward SDE method for uncertainty quantification in deep learning

Here, we develop a backward stochastic differential equation based probabilistic machine learning method, which formulates a class of stochastic neural networks as a stochastic optimal control problem. An efficient stochastic gradient descent algorithm is introduced with the gradient computed through a backward stochastic differential equation. Convergence analysis for stochastic gradient descent optimization and numerical experiments for applications of stochastic neural networks are carried out to validate our methodology in both theory and performance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Discrete Time McKean–Vlasov Control Problem: A Dynamic Programming Approach

We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that dynamic programming principle holds in its general form. We apply our method for solving explicitly the mean-variance portfolio selection and the multivariate linear-quadratic McKean–Vlasov control problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Stochastic Framework for Optimal Control of Planetary Reentry Trajectories Under Multilevel Uncertainties

We present a novel stochastic optimal control framework that accounts for various types of uncertainties, with application to reentry trajectory planning. The formulation of the optimal trajectory control problem is presented in the context of an indirect method where a functional objective associated with the terminal vehicle speed is to be minimized. Uncertain input parameters in the optimal trajectory control model, including aerodynamic parameters and initial and terminal conditions, are modeled as aleatory random variables, while the statistical parameters of these aleatory distributions are themselves random variables. The parametric and model uncertainties are simultaneously propagated through an extended polynomial chaos expansion (EPCE) formalism. Several metrics are described to evaluate response statistics and presented as insightful tools for robust decision making. Specifically, the response probability density function (PDF) reflecting influence of both epistemic and aleatory uncertainties is obtained. By sampling over the random variables representing model error, an ensemble of response PDFs is generated and the associated failure probability is estimated as a random variable with its own polynomial chaos expansion. Besides, the sensitivity index functions of response PDF with respect to the statistical parameters are evaluated. Coupling parametric and model uncertainties within the EPCE framework leads to a robust and efficient paradigm for multilevel uncertainty propagation and PDF characterization in general optimal control problems.

Engineering↗
DOE OSTI2026

Near-Optimal Performance of Stochastic Model Predictive Control

Here, this article presents a regret analysis for stochastic model predictive control (SMPC) in linear systems with quadratic performance index and additive and multiplicative uncertainties. Under a finite support assumption, the problem can be cast as a finite-dimensional quadratic program, but the problem becomes quickly intractable as the problem size grows exponentially in the horizon length. SMPC aims to compute approximate solutions by solving a sequence of problems with truncated prediction horizons and committing the solution in a receding-horizon fashion. Although this approach is widely used in practice, its performance relative to the optimal solution is not well understood. This article reports for the first time a rigorous near-optimal performance guarantee of SMPC: under stabilizability and detectability conditions, the regret of SMPC is exponentially small in the prediction horizon length, allowing SMPC to achieve near-optimal performance at a substantially reduced computational expense.

93E20, 93B45↗
DOE OSTI2020

Modeling and Control Using Stochastic Distribution Control Theory for Intersection Traffic Flow

In this work, we investigated stochastic distribution control theory-based traffic signal optimization to achieve a smooth and uniform flow of vehicles through signalized intersections. In this context, the static and linear dynamic stochastic distribution models were developed to express the relationship between the signal timing and the traffic queue length together with its probability density function. Two stochastic distribution control algorithms were designed to control the signal timing at intersections such that the probability density function of the traffic queue of each intersection road segment is made as narrow and as small as possible. Also, a recursive input-output traffic queue estimation model was proposed, which is data-driven and dynamic in nature, to calculate real-time traffic queue length using traffic signal timings and loop-detector data. The control algorithms were evaluated for a one-signal corridor, two-signal corridor, and 2 x 2 network of signalized intersections. MATLAB simulation examples are provided to demonstrate the use of the proposed algorithms and comparison to the existing widely-used semi-actuated control has been made. Desired results were obtained.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Application of Optimal Production Control theory for Home Energy Management in a Micro Grid

We consider the optimal stochastic control problem for home energy systems with solar and energy storage devices when the demand is realized from the grid. The demand is subject to Brownian motions with both drift and variance parameters modulated by a continuous-time Markov chain that represents the regime of electricity price. We model the systems as pure stochastic differential equation models, and then we follow the completing square technique to solve the stochastic home energy management problem. The effectiveness of the efficiency of the proposed approach is validated through a simulation example. For practical situations with constraints consistent to those studied here, our results imply the proposed framework could reduce the electricity cost from short-term purchase in peak hour market.

Malikopoulos, Andreas↗
DOE OSTI2022

Next-Cycle Optimal Dilute Combustion Control via Online Learning of Cycle-to-Cycle Variability Using Kernel Density Estimators

Dilute combustion using exhaust gas recirculation (EGR) presents a cost-effective method for increasing the efficiency of spark-ignition (SI) engines. However, the maximum amount of EGR that can be used at a given condition is limited by a rapid increment of cycle-to-cycle variability (CCV). This study describes a methodology to design a model-based stochastic optimal controller to adjust the cycle-to-cycle fuel injection quantity in order to reduce CCV and further extend the dilute limit. Given the complexity and chaotic nature of combustion events, the controller was enhanced with online learning in order to identify the statistical properties of combustion efficiency, which are needed to generate predictions for next-cycle events. This study showed that a kernel density estimator (KDE) can be used to learn the combustion properties in real time and can be incorporated into the feedback policy in order to calculate the optimal control command. Experimental results suggested that the dilute limit can be extended from 18.5% to 21% EGR fraction at an operating condition relevant for highway cruising. Additionally, the proposed controller can achieve a large CCV reduction with less fuel enrichment compared to previous methods, overall contributing to an increase in 0.2% indicated fuel conversion efficiency.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2015

Weak Necessary and Sufficient Stochastic Maximum Principle for Markovian Regime-Switching Diffusion Models

In this paper we prove a weak necessary and sufficient maximum principle for Markovian regime switching stochastic optimal control problems. Instead of insisting on the maximum condition of the Hamiltonian, we show that 0 belongs to the sum of Clarke’s generalized gradient of the Hamiltonian and Clarke’s normal cone of the control constraint set at the optimal control. Under a joint concavity condition on the Hamiltonian and a convexity condition on the terminal objective function, the necessary condition becomes sufficient. We give four examples to demonstrate the weak stochastic maximum principle.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗