Volume 17, Number 3
S-AI-IoT : Formal Agent Specification, Mathematical Modeling, and Stability Analysis of the Hormonal Orchestration Framework
Authors
Said Slaoui, Mohammed V University, Morocco
Abstract
Constrained Internet of Things (IoT) environmentsrequire adaptive orchestration mechanisms capable of jointlymanagingsensingquality, connectivity, energyconstraints, resilience, and securitywhileremainingcomputationally frugal and intrinsicallyexplainable. This article develops the formalmathematicalframework of S-AI-IoT, a bio-inspiredsparse AI architecture based on hormonal orchestration and specialized agent activation for distributedIoTsystems.The article introduces the completeformalspecification of 24 specializedIoT agents organizedinto six functionalfamilies, eachdefinedthrough explicit activation conditions, input-output contracts, resource profiles, and operationalconstraints. It furtherdevelops the mathematicalfoundations of the hormonal orchestration layer, includinglogistic-saturatedemissionfunctions, stochasticreaction-diffusion dynamics over dynamicIoT graphs, Lyapunov-based global stabilityanalysis, Euler-Maruyamadiscretizationwithbounded projection, duty-cycle energy modulation, primal-dual constrained orchestration, and distributedsymbolicengram memory withintrinsicexplainabilityguarantees. The proposedframeworkestablishes, to the best of the author’sknowledge, one of the first formallyspecified and stability-analyzed hormonal regulation architectures that unifies reaction-diffusion dynamics, constrainedoptimization, symbolic memory, and explainablesparse orchestration within a single operationalframework for distributedIoTsystems. The resulting architecture supports adaptive decisionmakingundersevereresourceconstraintswhilepreservingenergyfrugality, distributedrobustness, and causal traceability of behavioraldecisions.
Keywords
IoT, formal agent specification, reaction-diffusion, Lyapunov stability, primal-dual optimization, hormonal orchestration, symbolic engram memory, intrinsic explainability