References of "SIAM Journal on Control & Optimization"
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See detailSubmersions, Hamiltonian systems and optimal solutions to the rolling manifolds problem
Grong, Erlend UL

in SIAM Journal on Control & Optimization (2016), 54(2), 536-566

Given a submersion $\pi:Q \to M$ with an Ehresmann connection~$\calH$, we describe how to solve Hamiltonian systems on $M$ by lifting our problem to $Q$. Furthermore, we show that all solutions of these ... [more ▼]

Given a submersion $\pi:Q \to M$ with an Ehresmann connection~$\calH$, we describe how to solve Hamiltonian systems on $M$ by lifting our problem to $Q$. Furthermore, we show that all solutions of these lifted Hamiltonian systems can be described using the original Hamiltonian vector field on $M$ along with a generalization of the magnetic force. This generalized force is described using the curvature of $\calH$ along with a new form of parallel transport of covectors vanishing on $\calH$. Using the Pontryagin Maximum Principle, we apply this theory to optimal control problems $M$ and $Q$ to get results on normal and abnormal extremals. We give a demonstration of our theory by considering the optimal control problem of one Riemannian manifold rolling on another without twisting or slipping along curves of minimal length. [less ▲]

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See detailMetric regularity of Newton's iteration
Aragón Artacho, Francisco Javier UL; Dontchev, A. L.; Gaydu, M. et al

in SIAM Journal on Control & Optimization (2011), 49(2), 339-362

For a version of Newton's method applied to a generalized equation with a parameter, we extend the paradigm of the Lyusternik–Graves theorem to the framework of a mapping acting from the pair “parameter ... [more ▼]

For a version of Newton's method applied to a generalized equation with a parameter, we extend the paradigm of the Lyusternik–Graves theorem to the framework of a mapping acting from the pair “parameter-starting point” to the set of corresponding convergent Newton sequences. Under ample parameterization, metric regularity of the mapping associated with convergent Newton sequences becomes equivalent to the metric regularity of the mapping associated with the generalized equation. We also discuss an inexact Newton method and present an application to discretized optimal control. [less ▲]

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