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Results for “Optimal Control Problem”

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 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
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 OSTI2022

Learning Stochastic Parametric Differentiable Predictive Control Policies

We present a scalable unsupervised learning-based method for obtaining explicit control policies for model predictive control problems for stochastic linear systems with additive uncertainties subject to nonlinear chance constraints. We call the proposed method stochastic parametric differentiable predictive control (SP-DPC), which extends the recently proposed deterministic DPC policy optimization algorithm. We formulate the SP-DPC as a deterministic approximation to the stochastic parametric constrained optimal control problem via independent sampling of the problem's parameters and uncertainties. This formulation allows us to directly compute the policy gradients via automatic differentiation of the problem's value function, evaluated over sampled parameters and uncertainties. In particular, the computed expectation of the problem's value function is backpropagated through the finite-time closed-loop system rollouts parametrized by a known nominal system dynamics model and neural control policy. We also provide theoretical probabilistic guarantees on closed-loop stability and chance constraints satisfaction for systems controlled by learned neural policies. We demonstrate the computational efficiency and scalability of the proposed policy optimization algorithm in three numerical examples, including systems with a large number of states or subject to nonlinear constraints.

Drgona, Jan↗
NASA NTRS1988

Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures

An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.

Gibson, J. S.↗
NASA NTRS1972

Control of linear uncertain systems utilizing mismatched state observers

The control of linear continuous dynamical systems is investigated as a problem of limited state feedback control. The equations which describe the structure of an observer are developed constrained to time-invarient systems. The optimal control problem is formulated, accounting for the uncertainty in the design parameters. Expressions for bounds on closed loop stability are also developed. The results indicate that very little uncertainty may be tolerated before divergence occurs in the recursive computation algorithms, and the derived stability bound yields extremely conservative estimates of regions of allowable parameter variations.

Goldstein, B.↗
NASA NTRS2006

Singular-Arc Time-Optimal Trajectory of Aircraft in Two-Dimensional Wind Field

This paper presents a study of a minimum time-to-climb trajectory analysis for aircraft flying in a two-dimensional altitude dependent wind field. The time optimal control problem possesses a singular control structure when the lift coefficient is taken as a control variable. A singular arc analysis is performed to obtain an optimal control solution on the singular arc. Using a time-scale separation with the flight path angle treated as a fast state, the dimensionality of the optimal control solution is reduced by eliminating the lift coefficient control. A further singular arc analysis is used to decompose the original optimal control solution into the flight path angle solution and a trajectory solution as a function of the airspeed and altitude. The optimal control solutions for the initial and final climb segments are computed using a shooting method with known starting values on the singular arc The numerical results of the shooting method show that the optimal flight path angle on the initial and final climb segments are constant. The analytical approach provides a rapid means for analyzing a time optimal trajectory for aircraft performance.

Nguyen, Nhan↗
NASA NTRS2024

Optimal Control Allocation for Distributed Electric Propulsion in a Series/Parallel Partial Hybrid Powertrain

The SUbsonic Single Aft eNgine (SUSAN) Electrofan is a NASA concept jet transport aircraft with a 2040 entry-into-service date. It utilizes electrified aircraft propulsion (EAP) to enable propulsive and aerodynamic benefits to reduce fuel usage, emissions, and cost. The powertrain consists of a single thrust producing, boundary layer-ingesting (BLI) turbofan gas turbine engine (GTE) with generators driving a series/parallel partial hybrid EAP system. The architecture includes 16 underwing contrarotating BLI fans, eight on each side, in a mailslot configuration. The 16 fans run on power extracted from the GTE through four 5 MW motor/generators connected to the Low-Pressure Spool, and a single 1 MW motor/generator on the High-Pressure Spool. The distributed fans can be used by the flight control to augment or replace the rudder function. At top of climb, the power extracted from the GTE for the fans is boosted by batteries. The design provides redundancy, and the capacity for boost means that the fans are designed to be able to provide additional thrust when necessary. These features can be leveraged in case of a fan or generator failure. This paper sets up the optimal control problem of setpoint determination for individual fans in the distributed propulsion system, accounting for electrical string efficiencies, saturations, and failures. The solution minimizes power consumption while maintaining thrust and torque on the airframe for maneuvering. Additionally, thrust that would have been lost due to temporary fan speed or power saturation is optimally redistributed to maintain overall desired thrust and torque on the aircraft. The power extraction range constraints derive from the gas turbine engine design and the small amount of variation allowed for the engine to maintain operability. The problem formulation allows the number and location of fan failures for which the thrust and torque can be maintained to be investigated, which has implications for certification. Simulations of a coordinated turn utilizing the distributed electric propulsion for yaw rate control under different failure scenarios demonstrate the robustness of the powertrain design to failures and help define its limitations.

Distributed Electric Propulsion↗
NASA NTRS1987

Guidance and control strategies for aerospace vehicles

A simplified method of matched asymptotic expansions was developed where the common part in composite solution is generated as a polynomial in stretched variable instead of actually evaluating the same from the outer solution. This methodology was applied to the solution of the exact equations for three dimensional atmospheric entry problems. Compared to previous works, the present simplified methodology yields explicit analytical expressions for various components of the composite solution without resorting to any type of transcendental equations to be solved only by numerical methods. The optimal control problem arising in the noncoplanar orbital transfer employing aeroassist was also addressed.

Hibey, Joseph L.↗
NASA NTRS1989

A variable-gain output feedback control design approach

A multi-model design technique to find a variable-gain control law defined over the whole operating range is proposed. The design is formulated as an optimal control problem which minimizes a cost function weighing the performance at many operating points. The solution is obtained by embedding into the Multi-Configuration Control (MCC) problem, a multi-model robust control design technique. In contrast to conventional gain scheduling which uses a curve fit of single model designs, the optimal variable-gain control law stabilizes the plant at every operating point included in the design. An iterative algorithm to compute the optimal control gains is presented. The methodology has been successfully applied to reconfigurable aircraft flight control and to nonlinear flight control systems.

Haylo, Nesim↗
DOE OSTI2019

An Efficient Parallel-in-Time Method for Optimization with Parabolic PDEs

To solve optimization problems with parabolic PDE constraints, often methods working on the reduced objective functional are used. They are computationally expensive due to the necessity of solving both the state equation and a backward-in-time adjoint equation to evaluate the reduced gradient in each iteration of the optimization method. In this study, we investigate the use of the parallel-in-time method PFASST in the setting of PDE-constrained optimization. In order to develop an efficient fully time-parallel algorithm, we discuss different options for applying PFASST to adjoint gradient computation, including the possibility of doing PFASST iterations on both the state and the adjoint equations simultaneously. Here, we also explore the additional gains in efficiency from reusing information from previous optimization iterations when solving each equation. Numerical results for both a linear and a nonlinear reaction-diffusion optimal control problem demonstrate the parallel speedup and efficiency of different approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Juqbox.jl

The Juqbox.jl package implements functionality for solving the quantum optimal control problem for realizing logical gates in closed quantum systems. The dynamics of the quantum system is modeled by Schroedinger's equation, which takes to form of a linear system of ordinary differential equations (ODE). Juqbox.jl solves this ODE by numerical time stepping and applies a gradient-based optimization technique to determine control pulses for driving an initial state to a final state, according to the desired logical gate transformation. To evaluate the gradient, Juqbox.jl applies the ``first discretize, then optimize'' approach based on a discrete adjoint time stepping technique. The actual optimization is performed by the open source Ipopt libaray. Juqbox.jl is written in the Julia programming language which, among many other features, provides a convenient interface to the Ipopt library.

PETERSSON, NILSA.↗
DOE OSTI2021

Data-driven optimized control of the COVID-19 epidemics

Optimizing the impact on the economy of control strategies aiming at containing the spread of COVID-19 is a critical challenge. We use daily new case counts of COVID-19 patients reported by local health administrations from different Metropolitan Statistical Areas (MSAs) within the US to parametrize a model that well describes the propagation of the disease in each area. We then introduce a time-varying control input that represents the level of social distancing imposed on the population of a given area and solve an optimal control problem with the goal of minimizing the impact of social distancing on the economy in the presence of relevant constraints, such as a desired level of suppression for the epidemics at a terminal time. We find that with the exception of the initial time and of the final time, the optimal control input is well approximated by a constant, specific to each area, which contrasts with the implemented system of reopening ‘in phases’. For all the areas considered, this optimal level corresponds to stricter social distancing than the level estimated from data. Proper selection of the time period for application of the control action optimally is important: depending on the particular MSA this period should be either short or long or intermediate. We also consider the case that the transmissibility increases in time (due e.g. to increasingly colder weather), for which we find that the optimal control solution yields progressively stricter measures of social distancing. We finally compute the optimal control solution for a model modified to incorporate the effects of vaccinations on the population and we see that depending on a number of factors, social distancing measures could be optimally reduced during the period over which vaccines are administered to the population.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1997

Optimal Trajectories for the Helicopter in One-Engine-Inoperative Terminal-Area Operations

This paper presents a summary of a series of recent analytical studies conducted to investigate one-engine-inoperative (OEI) optimal control strategies and the associated optimal trajectories for a twin engine helicopter in Category-A terminal-area operations. These studies also examine the associated heliport size requirements and the maximum gross weight capability of the helicopter. Using an eight states, two controls, augmented point-mass model representative of the study helicopter, continued takeoff (CTO), rejected takeoff (RTO), balked landing (BL), and continued landing (CL) are investigated for both vertical-takeoff-and-landing (VTOL) and short-takeoff-and-landing (STOL) terminal-area operations. The formulation of the non-linear optimal control problems with considerations for realistic constraints, solution methods for the two-point boundary-value problem, a new real-time generation method for the optimal OEI trajectories, and the main results of this series of trajector optimization studies are presented. In particular, a new balanced-weight concept for determining the takeoff decision point for VTOL Category-A operations is proposed, extending the balanced-field length concept used for STOL operations.

Chen, Robert T. N.↗
NASA NTRS1996

Optimal Trajectories for the Helicopter in One-Engine-Inoperative Terminal-Area Operations

This paper presents a summary of a series of recent analytical studies conducted to investigate One-Engine-Inoperative (OEI) optimal control strategies and the associated optimal trajectories for a twin engine helicopter in Category-A terminal-area operations. These studies also examine the associated heliport size requirements and the maximum gross weight capability of the helicopter. Using an eight states, two controls, augmented point-mass model representative of the study helicopter, Continued TakeOff (CTO), Rejected TakeOff (RTO), Balked Landing (BL), and Continued Landing (CL) are investigated for both Vertical-TakeOff-and-Landing (VTOL) and Short-TakeOff-and-Landing (STOL) terminal-area operations. The formulation of the nonlinear optimal control problems with considerations for realistic constraints, solution methods for the two-point boundary-value problem, a new real-time generation method for the optimal OEI trajectories, and the main results of this series of trajectory optimization studies are presented. In particular, a new balanced- weight concept for determining the takeoff decision point for VTOL Category-A operations is proposed, extending the balanced-field length concept used for STOL operations.

Zhao, Yiyuan↗
NASA NTRS2005

Discrete Event Supervisory Control Applied to Propulsion Systems

The theory of discrete event supervisory (DES) control was applied to the optimal control of a twin-engine aircraft propulsion system and demonstrated in a simulation. The supervisory control, which is implemented as a finite-state automaton, oversees the behavior of a system and manages it in such a way that it maximizes a performance criterion, similar to a traditional optimal control problem. DES controllers can be nested such that a high-level controller supervises multiple lower level controllers. This structure can be expanded to control huge, complex systems, providing optimal performance and increasing autonomy with each additional level. The DES control strategy for propulsion systems was validated using a distributed testbed consisting of multiple computers--each representing a module of the overall propulsion system--to simulate real-time hardware-in-the-loop testing. In the first experiment, DES control was applied to the operation of a nonlinear simulation of a turbofan engine (running in closed loop using its own feedback controller) to minimize engine structural damage caused by a combination of thermal and structural loads. This enables increased on-wing time for the engine through better management of the engine-component life usage. Thus, the engine-level DES acts as a life-extending controller through its interaction with and manipulation of the engine s operation.

Litt, Jonathan S.↗
DOE OSTI2020

A General Framework for Bounding Approximate Dynamic Programming Schemes

For years, there has been interest in approximation methods for solving dynamic programming problems, because of the inherent complexity in computing optimal solutions characterized by Bellman’s principle of optimality. A wide range of approximate dynamic programming (ADP) methods now exists. It is of great interest to guarantee that the performance of an ADP scheme be at least some known fraction, say ß , of optimal. This letter introduces a general approach to bounding the performance of ADP methods, in this sense, in the stochastic setting. The approach is based on new results for bounding greedy solutions in string optimization problems, where one has to choose a string (ordered set) of actions to maximize an objective function. This bounding technique is inspired by submodularity theory, but submodularity is not required for establishing bounds. Instead, the bounding is based on quantifying certain notions of curvature of string functions; the smaller the curvatures the better the bound. The key insight is that any ADP scheme is a greedy scheme for some surrogate string objective function that coincides in its optimal solution and value with those of the original optimal control problem. The ADP scheme then yields to the bounding technique mentioned above, and the curvatures of the surrogate objective determine the value ß of the bound. The surrogate objective and its curvatures depend on the specific ADP.

discrete event systems↗
DOE OSTI2022

Optimization Modeling for Advanced Syngas to Olefin Reactive Systems

Reactor designs with mixed catalysts play an important role in transforming a multiple reactor system to single-shot reactors. In addition to savings in capital and ease of implementation, single-shot reactors are useful to break equilibrium limitations, thereby increasing the yield and selectivity of desired product as shown in previous studies. However, the nonlinear and highly exothermic nature of mixed-catalyst systems makes it difficult for commercial process simulation and optimization tools to optimize these systems. This study describes the development and application of optimization strategies for mixed-catalyst, single-shot reactors for syngas to olefin (STO) processes. Finding the optimal catalyst distribution is challenging and requires advanced solution strategies for singular optimal control problems, which are poorly conditioned and often lead to flat response surfaces. The graded bed and partial-moving finite-element approaches are used to find the optimal catalyst distribution that maximizes the olefins yield. A 1.3% increase in the yield is observed from one zone to three zones. The yield further improves from three zones to the exact infinite dimensional solution by 0.2%. This improvement can be realized in practice by changing only the catalyst distribution, without any extra investment. Lastly, the results suggest that a mixed-catalyst single shot reactor bed can be applied to other reaction mechanisms to increase reactor performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2001

Making the EZ Choice

Analytical Mechanics Associates, Inc. (AMA), of Hampton, Virginia, created the EZopt software application through Small Business Innovation Research (SBIR) funding from NASA's Langley Research Center. The new software is a user-friendly tool kit that provides quick and logical solutions to complex optimal control problems. In its most basic form, EZopt converts process data into math equations and then proceeds to utilize those equations to solve problems within control systems. EZopt successfully proved its advantage when applied to short-term mission planning and onboard flight computer implementation. The technology has also solved multiple real-life engineering problems faced in numerous commercial operations. For instance, mechanical engineers use EZopt to solve control problems with robots, while chemical plants implement the application to overcome situations with batch reactors and temperature control. In the emerging field of commercial aerospace, EZopt is able to optimize trajectories for launch vehicles and perform potential space station- keeping tasks. Furthermore, the software also helps control electromagnetic devices in the automotive industry.

Source record↗
NASA NTRS1990

Optimal stabilization of discrete event systems

An optimal stabilization problem for discrete event systems (DES) is addressed. A class of not necessarily finite state 'logical' DES models is utilized which can also model the costs for events to occur. Let P and A denote two such models. Suppose that P characterizes the valid behavior of a dynamical system and A represents certain design objectives which specify the allowable DES behavior which is 'contained in' the valid behavior. An optimal control problem for P and A is how to choose the sequence of inputs to P so that the DES behavior lies in A (i.e., it is allowable) and so that a performance index defined in terms of the costs of the events is minimized. Two solutions are provided to an optimal stabilization problem, i.e. how to find a sequence of inputs that results in an optimal state trajectory which cycles in a pre-specified set.

Passino, Kevin M.↗