Second Look at Approximating Differential Inclusions

Fahroo, Fariba; Ross, I. Michael

doi:10.2514/2.4686

Cited by 31 publications

(16 citation statements)

References 12 publications

(23 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If a given problem meets all the conditions for both theorems to hold, then the Legendre pseudospectral method provides superior convergence properties with respect to any RK method. Numerical experiments confirm this point [42][43][44][45]; consequently, the Legendre pseudospectral method has become an attractive choice for an upgrade of the OTIS software package [12]. Of course, the software package DIDO uses pseudospectral methods exclusively, and independent tests [30,46,47] of DIDO with other tools have consistently shown its superior performance.…”

Section: Theoretical Foundationsmentioning

confidence: 91%

Low-Thrust, High-Accuracy Trajectory Optimization

Ross

Gong

Sekhavat

2007

Journal of Guidance, Control, and Dynamics

Self Cite

View full text Add to dashboard Cite

Section: Theoretical Foundationsmentioning

confidence: 91%

Low-Thrust, High-Accuracy Trajectory Optimization

Ross

Gong

Sekhavat

2007

Journal of Guidance, Control, and Dynamics

Self Cite

View full text Add to dashboard Cite

“…Ross and F. Fahroo of the Naval Postgraduate School. DIDO employs a direct Legendre psuedospectral [7][8][9][10][11][12] technique that uses the NLP solver SNOPT. Since the formulation of a problem using a direct Legendre psuedospectral method does not determine the adjoint equations, another tool must be employed to link the solutions generated by indirect methods and direct methods.…”

Section: A Solution Methodologymentioning

confidence: 99%

Optimal Trajectory Reconfiguration and Retargeting for a Reusable Launch Vehicle

Shaffer

Ross

Oppenheimer

et al. 2005

AIAA Guidance, Navigation, and Control Conference and Exhibit

View full text Add to dashboard Cite

Autonomous reusable launch vehicles (RLV) are being pursued as low-cost alternatives to expendable launch vehicles and the Shuttle. The employment of autonomous, reusable launch vehicles requires additional guidance and control robustness to fulfill the role of an adaptive human pilot, in the event of failures or unanticipated conditions. The guidance and control of these vehicles mandate new guidance strategies that are able to identify and adapt to vehicle failures during the flight and still return to earth safely. This work utilizes an online trim algorithm that provides the outer loop with the feasible range of Mach number and angle of attack, for which the vehicle can be rotationally trimmed. The algorithm allows one to include 6-degree-of-freedom (DOF) trim effects and constraints in a reduced order dynamical model which is used in the solution of an optimal control problem. A direct pseudospectral method is used to solve a two-point-boundary-value problem which determines the optimal entry trajectory subject to appropriate constraints such as normal load, dynamic pressure limits, heat load limits, and state dependent constraints.

show abstract

“…This method which has been extensively described in Refs. 13,[15][16][17][18][19][20][21]27, is based on approximating the state and control variables by Lagrange interpolating polynomials. The unknown coefficients are the values of the variables at the interpolating nodes which in this method are the quadrature points, the Legendre-Gauss-Lobotto (LGL) points.…”

Section: The Legendre Pseudospectral Methodsmentioning

confidence: 99%

Towards Real-Time Computation of Optimal Controls for Nonlinear Systems

Ross

Fahroo

Strizzi

2002

AIAA Guidance, Navigation, and Control Conference and Exhibit

Self Cite

View full text Add to dashboard Cite

Computing optimal controls for nonlinear nonsmooth dynamical systems is an extremely challenging task. In recent years, we introduced a family of pseudospectral methods for the accurate computation of optimal controls for highly nonlinear systems. While these methods are applicable for generic nonlinear systems, they can also be exploited for systems that exhibit certain differential-geometric properties. These techniques are encoded in the reusable software package, DIDO. In this paper, we harness the structured sparsity of pseudospectral methods and show that a significant increase in computation speed can be achieved. This facilitates a rapid design of the outer-loop of a two-degree-of-freedom control system. We demonstrate the viability of our approach for several example problems involving smooth nonlinearities, path constraints and control saturation limits.

show abstract

Second Look at Approximating Differential Inclusions

Cited by 31 publications

References 12 publications

Low-Thrust, High-Accuracy Trajectory Optimization

Low-Thrust, High-Accuracy Trajectory Optimization

Optimal Trajectory Reconfiguration and Retargeting for a Reusable Launch Vehicle

Towards Real-Time Computation of Optimal Controls for Nonlinear Systems

Contact Info

Product

Resources

About