Intensional Maxwellian Formalism in Power Electronics: Causal Octonion Control of Distributed Multi-Phase Converters

Abstract

Contemporary power electronics and distributed control systems predominantly rely on extensional mathematical frameworks, treating physical phenomena as memoryless, state-independent variables. This paper proposes a paradigm shift toward an intensional (causal) mathematical formalism, restoring and expanding upon James Clerk Maxwell’s hypercomplex topology. We introduce a dual-layer control architecture for Maximum Power Point Tracking (MPPT) converters and multi-phase systems. The foundational layer maps the physical hardware—specifically thermal entropy, magnetic hysteresis, and material degradation—into a non-associative octonion space (O), enforcing the intensional axiom where the identity of origin inherently alters the computational value (x * x ≠ x²). The observable control variables are subsequently computed in a tensor framework (T_μν). The causal history is projected into the observable tensor layer via the octonion associator [X, Y, Z], which acts as a deterministic, predictive constraint, eliminating the need for reactive sensor feedback loops and empirical lookup tables. Implemented on a standard Cortex-M4 microcontroller (STM32G431) at 30 kHz, the architecture requires only 42.3% of CPU instruction time. Furthermore, this framework inherently resolves distributed swarm consensus, enabling sensorless phase-locking via the shared DC bus.