The objective of this article is to present geometric and numerical techniques developed to study the orbit transfer between Keplerian elliptic orbits in the two-body problem or between quasi-Keplerian orbits in the Earth-Moon transfer when low propulsion is used. We concentrate our study on the energy minimization problem. From Pontryagin's maximum principle, the optimal solution can be found solving the shooting equation for smooth Hamiltonian dynamics. A first step in the analysis is to find in the Kepler case an analytical solution for the averaged Hamiltonian, which corresponds to a Riemannian metric. This will allow to compute the solution for the original Kepler problem, using a numerical continuation method where the smoothness of the path is related to the conjugate point condition. Similarly, the solution of the Earth-Moon transfer is computed using geometric and numerical continuation techniques.

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Regular Perturbations in Optimal Control

Geometric and Numerical Techniques in Optimal Control of Two and Three-Body Problems

https://link.springer.com/content/pdf/10.1007/s10559-021-00414-1.pdf

Approximate Optimal Controller for Weakly Nonlinear Evolutionary Equation of Parabolic Type

Feedback systems

On perturbation methods in stochastic control

Radon-Nikodym derivatives in case of rational spectral densities.- Differentiation of measures related to stochastic processes.- Dynkin games.- An introduction to the stochastic calculus of variations.- On one-dimensional Markov SDEs.- Some problems in sequential analysis.- A stochastic differential equation for Feller's one-dimensional diffusions.- A result of the iterated logarithm type for a certain class of stochastic processes.- Approximation of large deviations estimates and escape times and applications to systems with small noise effects.- On strong solutions of stohastic equations with respect to semimartingales.- Inverse problems in stochastic Riemannian geometry.- Some results on likelihood ratios for two-parameter processes.- Controllability of stochastic systems.- Solving the Zakai equation by ito's Method.- Simple and efficient linear and nonlinear filters by regular perturbation methods.- The non linear filtering equations.- On robust approximations in nonlinear filtering.- Smoothing of a diffusion process conditionned at final time.- First passage times in stochastic models of physical systems and in filtering theory.- Adaptive stochastic filtering problems - The continuous time case.- Between the chapters: An editor's note.- On perturbation methods in stochastic control.- A control problem in a manifold with nonsmooth boundary.- Some recent results on the control of partially observable stochastic systems.- Optimal controls for partially observed stochastic systems using nonstandard analysis.- Stochastic control with tracking of exogenous parameters.- Nisio semi-group associated to the control of Markov processes.- Optimal control of partially observed diffusions via the separation principle.- A class of singular stochastic control problems.- Sur l'arret optimal de processus a deux indices reels.- Duality theory for some stochastic control models.- On the control of jump processes.- A partially observed inventory problem.- On impulsive control with long run average cost criterion.- Separation theorem for optimal impulse control with discontinuous observations.- Optimal control based on observations on the boundary.

Stochastic differential systems : proceedings of the 2nd Bad Honnef Conference of the SFB 72 of the DFG at the University of Bonn, June 28-July 2, 1982

Regular Perturbations in Optimal Control

Citations

Geometric and Numerical Techniques in Optimal Control of Two and Three-Body Problems

Approximate Optimal Controller for Weakly Nonlinear Evolutionary Equation of Parabolic Type

References

Feedback systems

On perturbation methods in stochastic control

Stochastic differential systems : proceedings of the 2nd Bad Honnef Conference of the SFB 72 of the DFG at the University of Bonn, June 28-July 2, 1982

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