This means that𝑓 𝑘 −𝑔 𝑘 is𝜅-Lipschitz

We have ∥∇𝑓 𝑘 (𝑝) − ∇𝑔 𝑘 (𝑝) ∥ =2∥𝑝−𝑝 𝑘 +𝛼 𝑘 𝐽 𝑘 ¯C (𝜃) −𝑝+𝑝 𝑘 −𝛼 𝑘 𝐽 𝑘 ¯C ∥ ≤2𝛼 𝑘 [∥𝐽 𝑘 ¯C (𝜃) −𝐽 𝑘 ¯C ∥] ≤2𝛼 𝑘 𝐿1 diamΘ 𝑘 =:𝜅, where the last step follows from Lemma 5

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Policy Optimization with Differentiable MPC: Convergence Analysis under Uncertainty

eess.SY · 2026-01-05 · unverdicted · novelty 4.0

Combining gradient-based policy optimization with recursive system identification in differentiable MPC ensures convergence to an optimal controller under model uncertainty.

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Policy Optimization with Differentiable MPC: Convergence Analysis under Uncertainty eess.SY · 2026-01-05 · unverdicted · none · ref 47
Combining gradient-based policy optimization with recursive system identification in differentiable MPC ensures convergence to an optimal controller under model uncertainty.

This means that𝑓 𝑘 −𝑔 𝑘 is𝜅-Lipschitz

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