TY - GEN

T1 - Geometric interpretation of adjoint equations in optimal low thrust space flight

AU - Pifko, Steven L.

AU - Zorn, Alan H.

AU - West, Matthew

PY - 2008

Y1 - 2008

N2 - Time-optimal control of two seemingly unrelated problems are solved using Pontryagin's Maximum Principle. The first is a simple double integrator in R2 in which the state is driven to a desired terminal state in minimum time. The second is an orbiting spacecraft in R2 which transitions from its current orbit into a desired terminal orbit in minimum time. In both cases, thrust is continuously available but limited in magnitude. The two problems are related by the gravitational parameter of the major body orbited. As the gravitational parameter is mathematically varied to zero, the orbiting spacecraft takes on the dynamics of a double integrator. A two-point boundary value problem is created when Pontryagin'sMaximum Principle is applied to solve the two problems. Shooting methods are typically used in the solution, but they require reasonably close a priori estimates of the initial or final values of the costate for the shooting method to converge. The adjoint equations of the double integrator have a simple solution. The derived optimal control is shown to be related to the adjoint solution in a simple geometric manner. A method is presented to estimate the initial costate and terminal time for the double integrator problem. The possibility that the initial estimate for the double integrator may provide an initial estimate for the related orbital transfer problem is explored. Numerical examples of the two problems illustrate the method. American Institu

AB - Time-optimal control of two seemingly unrelated problems are solved using Pontryagin's Maximum Principle. The first is a simple double integrator in R2 in which the state is driven to a desired terminal state in minimum time. The second is an orbiting spacecraft in R2 which transitions from its current orbit into a desired terminal orbit in minimum time. In both cases, thrust is continuously available but limited in magnitude. The two problems are related by the gravitational parameter of the major body orbited. As the gravitational parameter is mathematically varied to zero, the orbiting spacecraft takes on the dynamics of a double integrator. A two-point boundary value problem is created when Pontryagin'sMaximum Principle is applied to solve the two problems. Shooting methods are typically used in the solution, but they require reasonably close a priori estimates of the initial or final values of the costate for the shooting method to converge. The adjoint equations of the double integrator have a simple solution. The derived optimal control is shown to be related to the adjoint solution in a simple geometric manner. A method is presented to estimate the initial costate and terminal time for the double integrator problem. The possibility that the initial estimate for the double integrator may provide an initial estimate for the related orbital transfer problem is explored. Numerical examples of the two problems illustrate the method. American Institu

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M3 - Conference contribution

AN - SCOPUS:78651234548

SN - 9781563479458

T3 - AIAA/AAS Astrodynamics Specialist Conference and Exhibit

BT - AIAA/AAS Astrodynamics Specialist Conference and Exhibit

T2 - AIAA/AAS Astrodynamics Specialist Conference and Exhibit

Y2 - 18 August 2008 through 21 August 2008

ER -