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All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Optimal Control Problems with Switching Points

The main idea of this report is to give an overview of the problems and difficulties that arise in solving optimal control problems with switching points. A brief discussion of existing optimality conditions is given and a numerical approach for solving the multipoint boundary value problems associated with the first-order necessary conditions of optimal control is presented. Two real-life aerospace optimization problems are treated explicitly. These are altitude maximization for a sounding rocket (Goddard Problem) in the presence of a dynamic pressure limit, and range maximization for a supersonic aircraft flying in the vertical, also in the presence of a dynamic pressure limit. In the second problem singular control appears along arcs with active dynamic pressure limit, which in the context of optimal control, represents a first-order state inequality constraint. An extension of the Generalized Legendre-Clebsch Condition to the case of singular control along state/control constrained arcs is presented and is applied to the aircraft range maximization problem stated above. A contribution to the field of Jacobi Necessary Conditions is made by giving a new proof for the non-optimality of conjugate paths in the Accessory Minimum Problem. Because of its simple and explicit character, the new proof may provide the basis for an extension of Jacobi's Necessary Condition to the case of the trajectories with interior point constraints. Finally, the result that touch points cannot occur for first-order state inequality constraints is extended to the case of vector valued control functions.

Seywald, Hans↗
NASA NTRS1996

Observations Regarding Use of Advanced CFD Analysis, Sensitivity Analysis, and Design Codes in MDO

Observations regarding the use of advanced computational fluid dynamics (CFD) analysis, sensitivity analysis (SA), and design codes in gradient-based multidisciplinary design optimization (MDO) reflect our perception of the interactions required of CFD and our experience in recent aerodynamic design optimization studies using CFD. Sample results from these latter studies are summarized for conventional optimization (analysis - SA codes) and simultaneous analysis and design optimization (design code) using both Euler and Navier-Stokes flow approximations. The amount of computational resources required for aerodynamic design using CFD via analysis - SA codes is greater than that required for design codes. Thus, an MDO formulation that utilizes the more efficient design codes where possible is desired. However, in the aerovehicle MDO problem, the various disciplines that are involved have different design points in the flight envelope; therefore, CFD analysis - SA codes are required at the aerodynamic 'off design' points. The suggested MDO formulation is a hybrid multilevel optimization procedure that consists of both multipoint CFD analysis - SA codes and multipoint CFD design codes that perform suboptimizations.

Newman, Perry A.↗
NASA NTRS2001

Free-form Airfoil Shape Optimization Under Uncertainty Using Maximum Expected Value and Second-order Second-moment Strategies

Free-form shape optimization of airfoils poses unexpected difficulties. Practical experience has indicated that a deterministic optimization for discrete operating conditions can result in dramatically inferior performance when the actual operating conditions are different from the - somewhat arbitrary - design values used for the optimization. Extensions to multi-point optimization have proven unable to adequately remedy this problem of "localized optimization" near the sampled operating conditions. This paper presents an intrinsically statistical approach and demonstrates how the shortcomings of multi-point optimization with respect to "localized optimization" can be overcome. The practical examples also reveal how the relative likelihood of each of the operating conditions is automatically taken into consideration during the optimization process. This is a key advantage over the use of multipoint methods.

Huyse, Luc↗
NASA NTRS1998

Geospace Magnetospheric Dynamics Mission

The Geospace Magnetospheric Dynamics (GMD) mission is designed to provide very closely spaced, multipoint measurements in the thin current sheets of the magnetosphere to determine the relation between small scale processes and the global dynamics of the magnetosphere. Its trajectory is specifically designed to optimize the time spent in the current layers and to minimize radiation damage to the spacecraft. Observations are concentrated in the region 8 to 40 R(sub E) The mission consists of three phases. After a launch into geostationary transfer orbit the orbits are circularized to probe the region between geostationary orbit and the magnetopause; next the orbit is elongated keeping perigee at the magnetopause while keeping the line of apsides down the tail. Finally, once apogee reaches 40 R(sub E) the inclination is changed so that the orbit will match the profile of the noon-midnight meridian of the magnetosphere. This mission consists of 4 solar electrically propelled vehicles, each with a single NSTAR thruster utilizing 100 kg of Xe to tour the magnetosphere in the course of a 4.4 year mission, the same thrusters that have been successfully tested on the Deep Space-1 mission.

Russell, C. T.↗
NASA NTRS2015

Adaptive Shape Control for Aerodynamic Design

We present an approach to aerodynamic optimization in which the shape control is adaptively parameterized. Starting from a coarse set of design variables, a sequence of higher-dimensional nested search spaces is automatically generated. Refinement can be either uniform or adaptive, in which case only the most important shape control is added. The relative importance of candidate design variables is determined by comparing objective and constraint gradients, computed at low cost via adjoint solutions. A search procedure for finding an effective ensemble of shape parameters is also given. We first demonstrate this system on a multipoint drag miminization problem in 2D with many constraints, showing that an adaptive parameterization approach consistently achieves smoother, more robust, and faster design improvement than fixed parameterizations. We also establish a 3D shape- matching benchmark, where we demonstrate that our approach automatically discovers the necessary parameters to match a target shape. By largely automating shape parameterization, this work also aims to remove a time-consuming aspect of shape optimization.

Aerodynamic Design↗
NASA NTRS1993

On-board B-ISDN fast packet switching architectures. Phase 1: Study

The broadband integrate services digital network (B-ISDN) is an emerging telecommunications technology that will meet most of the telecommunications networking needs in the mid-1990's to early next century. The satellite-based system is well positioned for providing B-ISDN service with its inherent capabilities of point-to-multipoint and broadcast transmission, virtually unlimited connectivity between any two points within a beam coverage, short deployment time of communications facility, flexible and dynamic reallocation of space segment capacity, and distance insensitive cost. On-board processing satellites, particularly in a multiple spot beam environment, will provide enhanced connectivity, better performance, optimized access and transmission link design, and lower user service cost. The following are described: the user and network aspects of broadband services; the current development status in broadband services; various satellite network architectures including system design issues; and various fast packet switch architectures and their detail designs.

Faris, Faris↗
NASA NTRS1983

Optimal trajectories for aeroassisted orbital transfer

Consideration is given to classical and minimax problems involved in aeroassisted transfer from high earth orbit (HEO) to low earth orbit (LEO). The transfer is restricted to coplanar operation, with trajectory control effected by means of lift modulation. The performance of the maneuver is indexed to the energy expenditure or, alternatively, the time integral of the heating rate. Firist-order optimality conditions are defined for the classical approach, as are a sequential gradient-restoration algorithm and a combined gradient-restoration algorithm. Minimization techniques are presented for the aeroassisted transfer energy consumption and time-delay integral of the heating rate, as well as minimization of the pressure. It is shown that the eigenvalues of the Jacobian matrix of the differential system is both stiff and unstable, implying that the sequential gradient restoration algorithm in its present version is unsuitable. A new method, involving a multipoint approach to the two-poing boundary value problem, is recommended.

Miele, A.↗
NASA NTRS1999

Prediction and Assessment of Reynolds Number Sensitivities Associated with Wing Leading-Edge Radius Variations

The primary objectives of this study were to expand the data base showing the effects of LE radius distribution and corresponding . sensitivity to Rn at subsonic and transonic conditions, and to assess the predictive capability of CFD for these effects. Several key elements led to the initiation of this project: 1) the necessity of meeting multipoint design requirements to enable a viable HSCT, 2) the demonstration that blunt supersonic leading-edges can be associated with performance gain at supersonic speeds , and 3) limited data. A test of a modified Reference H model with the TCA planform and 2 LE radius distributions was performed in the NTF, in addition to Navier-Stokes analysis for an additional 3 LE radius distributions. Results indicate that there is a tremendous potential to improve high-lift performance through the use of a blunt LE across the span given an integrated, fully optimized design, and that low Rn data alone is probably not sufficient to demonstrate the benefit.

Wahls, Richard A.↗
NASA NTRS1999

Prediction and Assessment of Reynolds Number Sensitivities Associated with Wing Leading-Edge Radius Variations

The primary objectives of this study were to expand the data base showing the effects of LE radius distribution and corresponding sensitivity to Rn at subsonic and transonic conditions, and to assess the predictive capability of CFD for these effects. Several key elements led to the initiation of this project: 1) the necessity of meeting multipoint design requirements to enable a viable HSCT, 2) the demonstration that blunt supersonic leading-edges can be associated with performance gain at supersonic speeds , and 3) limited data. A test of a modified Reference H model with the TCA planform and 2 LE radius distributions was performed in the NTF, in addition to Navier-Stokes analysis for an additional 3 LE radius distributions. Results indicate that there is a tremendous potential to improve high-lift performance through the use of a blunt LE across the span given an integrated, fully optimized design, and that low Rn data alone is probably not sufficient to demonstrate the benefit.

Wahls, Richard A.↗
NASA NTRS2017

End-to-End Trade-Space Analysis for Designing Constellation

Multipoint measurement missions can provide a significant advancement in science return and this science interest coupled with as many recent technological advances are driving a growing trend in exploring distributed architectures for future NASA missions. Distributed Spacecraft Missions (DSMs) leverage multiple spacecraft to achieve one or more common goals. In particular, a constellation is the most general form of DSM with two or more spacecraft placed into specific orbit(s) for the purpose of serving a common objective (e.g., CYGNSS). Because a DSM architectural trade-space includes both monolithic and distributed design variables, DSM optimization is a large and complex problem with multiple conflicting objectives. Over the last two years, our team has been developing a Trade-space Analysis Tool for Constellations (TAT-C), implemented in common programming languages for pre-Phase A constellation mission analysis. By evaluating alternative mission architectures, TAT-C seeks to minimize cost and maximize performance for pre-defined science goals. This presentation will describe the overall architecture of TAT-C including: a User Interface (UI) at several levels of details and user expertise; Trade-space Search Requests that are created from the Science requirements gathered by the UI and validated by a Knowledge Base; a Knowledge Base to compare the current requests to prior mission concepts to potentially prune the trade-space; a Trade-space Search Iterator which, with inputs from the Knowledge Base, and, in collaboration with the Orbit & Coverage, Reduction & Metrics, and Cost& Risk modules, generates multiple potential architectures and their associated characteristics. TAT-C leverages the use of the Goddard Mission Analysis Tool (GMAT) to compute coverage and ancillary data, modeling orbits to balance accuracy and performance. The current version includes uniform and non-uniform Walker constellations as well as Ad-Hoc and precessing constellations, and its cost model represents an aggregate model consisting of Cost Estimating Relationships (CERs) from widely accepted models. The current GUI automatically generates graphics representing metrics such as average revisit time or coverage as a function of cost. The end-to-end system will be demonstrated as part of the presentation.

Mission Desig↗
NASA NTRS1976

Optimal reusable-tug and expendable-kickstage trajectories for high-energy planetary missions including correction for nodal precession

Equations are derived by using branched trajectory optimization techniques and the maximum principle to maximize the payload capability of a reusable tug/expendable kickstage vehicle configuration for planetary missions. The two stages and the payload are launched into a low earth orbit by a single space shuttle. The analysis includes correction for precession of the orbit. This correction is done by the tug. The tug propels the payload and the kickstage to an energy beyond earth escape and returns within a specified time to the precessed orbit. After separating from the tug, the kickstage accelerates the payload to the required injection conditions. Planetary injection conditions are specified by the mission energy and a fixed declination and right ascension of the outgoing asymptote. The multipoint boundary value problem resulting from the analysis is solved by a Newton-Raphson iteration technique. Partial derivatives of the boundary conditions are obtained by perturbing the initial conditions one at a time, integrating the trajectory and adjoint equations, and observing the changes in boundary conditions. Maximum payload capability is derived for two typical mission energies. In addition, the variations of several mission and stage parameters are also examined.

Borsody, J.↗
NASA NTRS1999

Modeling and Simulation Reliable Spacecraft On-Board Computing

The proposed project will investigate modeling and simulation-driven testing and fault tolerance schemes for Spacecraft On-Board Computing, thereby achieving reliable spacecraft telecommunication. A spacecraft communication system has inherent capabilities of providing multipoint and broadcast transmission, connectivity between any two distant nodes within a wide-area coverage, quick network configuration /reconfiguration, rapid allocation of space segment capacity, and distance-insensitive cost. To realize the capabilities above mentioned, both the size and cost of the ground-station terminals have to be reduced by using reliable, high-throughput, fast and cost-effective on-board computing system which has been known to be a critical contributor to the overall performance of space mission deployment. Controlled vulnerability of mission data (measured in sensitivity), improved performance (measured in throughput and delay) and fault tolerance (measured in reliability) are some of the most important features of these systems. The system should be thoroughly tested and diagnosed before employing a fault tolerance into the system. Testing and fault tolerance strategies should be driven by accurate performance models (i.e. throughput, delay, reliability and sensitivity) to find an optimal solution in terms of reliability and cost. The modeling and simulation tools will be integrated with a system architecture module, a testing module and a module for fault tolerance all of which interacting through a centered graphical user interface.

Park, Nohpill↗