Optimal Control of Oscillation Timing and Entrainment Using Large Magnitude Inputs: An Adaptive Phase-Amplitude-Coordinate-Based Approach

The candidate reproduces the paper’s adaptive phase–isostable reduction under rank-1 perturbations and linear-in-parameter structure, including: (i) effective input Ue and reduction (Eqs. 7, 11–13), (ii) the choice ṗ = −(i/Q)(u+p0−p) that yields ψ̇ = κ(p)ψ and the 2D system for (θ,p) (Eq. 14), and (iii) the Pontryagin setup with Hamiltonian, adjoint ODEs, and the projected pointwise minimizer for Δu (Eqs. 16, 19–20). The algebraic forms of λ̇1, λ̇2 and the saturated control law match the paper exactly. Any differences are presentational only.