Using the LSS adjoint for simultaneous plant and control optimization of chaotic dynamical systems

Cagliari, Luiz Victor R. Repolho; Hicken, Jason E.; Mishra, Sandipan

doi:10.1007/s00158-021-02987-z

Cited by 5 publications

(1 citation statement)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The morale is that, when u M, we should notice that we can perhaps already get something useful with a simple extension of the numerical tools we already have. When the unstable contribution is large, or when better accuracy is desired, for example near design optimal, we need to further compute the unstable contribution [7,12,37].…”

Section: A Nimentioning

confidence: 99%

Backpropagation in hyperbolic chaos via adjoint shadowing

2024

Nonlinearity

View full text Add to dashboard Cite

To generalise the backpropagation method to both discrete-time and continuous-time hyperbolic chaos, we introduce the adjoint shadowing operator S acting on covector fields. We show that S can be equivalently defined as: S is the adjoint of the linear shadowing operator S; S is given by a ‘split then propagate’ expansion formula; S ( ω ) is the only bounded inhomogeneous adjoint solution of ω. By (a), S adjointly expresses the shadowing contribution, a significant part of the linear response, where the linear response is the derivative of the long-time statistics with respect to system parameters. By (b), S also expresses the other part of the linear response, the unstable contribution. By (c), S can be efficiently computed by the nonintrusive shadowing algorithm in Ni and Talnikar (2019 J. Comput. Phys. 395 690–709), which is similar to the conventional backpropagation algorithm. For continuous-time cases, we additionally show that the linear response admits a well-defined decomposition into shadowing and unstable contributions.

show abstract

Section: A Nimentioning

confidence: 99%