BUILD & RUN · V(Ψ)

Read the equation

This relation contains a squared-state or squared-error term. Squaring makes that contribution nonnegative and increases the penalty for larger magnitudes; the surrounding definition specifies whether it is a cost, normalization or summary statistic.

Terms & definitions

The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.

How it works

1. Read V(Ψ) as the quantity being defined or updated by this relation.

2. Substitute the source-defined variables or recorded values and follow the displayed arithmetic and indexing exactly.

3. Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.

Assumptions & limits

Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.

Original context

LYAPUNOV FUNCTION (stability proof)

V(Ψ) = ½‖Ψ - Ψ*‖² + λΣ_f(φ_f - φ*)²

Stability condition: dV/dt ≤ -α‖Ψ - Ψ*‖² for some α > 0
Satisfied when: γ_i > η_max × ‖J‖_∞ for all i

LEARNING MONOTONICITY THEOREM

V(Ψ) = ½‖Ψ - Ψ*‖² + λΣ_f(φ_f - φ*)²

Related builds