Adaptive Resistance Principle (ARP) — Overview

What is ARP? A simple adaptive law for conductance that increases with the magnitude of the driving signal and decays with a time constant. It behaves like a causal exponential tracker/low‑pass of |I| with closed‑form solutions.

Core Equation

dG/dt = α·|I(t)| − μ·G(t),   α > 0, μ > 0, G ≥ 0

Key Properties

• Closed‑form with exponential kernel; piecewise constant inputs converge toward G∞ = (α/μ)·|I|.
• Discrete‑time Euler update: G[k+1] = (1 − μΔt)·G[k] + αΔt·|I[k]|.
• Global exponential stability to G∞ under constant input.

For the full reference with derivations, see the ARP Reference post.

Back to ARP blog index