Vitology and Modern Control Theory: Viability Kernels, Reachability, Invariance, and Control of Viable Continuations

This article systematically compares Vitology with modern control theory and Viability Theory. It examines controllability, reachability, backward reachability, invariant and controlled invariant sets, viability kernels, state and control constraints, robust control, adaptive control, model predictive control, barrier-based safety methods, and control under uncertainty. The analysis shows that a substantial part of the ideas that might superficially appear to be new Vitological constructions already possess mature mathematical counterparts. Viability Theory directly addresses whether admissible evolutions exist that allow a system to remain inside a specified constraint set. Invariant sets formalize persistence inside a prescribed region. Reachability analysis determines states that can be reached from a given state or states from which a target set can be reached. Model predictive control selects actions by forecasting future trajectories under state and control constraints. Robust control studies preservation of required properties under disturbances and uncertainty. Adaptive control modifies controller parameters as new information becomes available. Control barrier functions and related safety methods formalize the preservation of safe sets. On this basis, H7 applies scientific subtraction to Vitological constructions including C_R, C_V, Future Viable States, the Dynamic Viability Boundary, Regulatory Reserve, Regulatory Viability, Aw–Con–CON, Synchroauthenticity, and the Norm of Harmony. If C_V is defined only as a set of trajectories that satisfy specified constraints, it is not independently new relative to Viability Theory. If Future Viable States are defined only as reachable states inside an admissible region, they belong to established reachability mathematics. If the Dynamic Viability Boundary is only the boundary of a changing admissible set, it likewise does not automatically acquire independent novelty. The possible residual contribution of Vitology is therefore reduced to another question: can a predefined multidimensional metrology of V, incorporating system state, recovery potential, regulatory reserves, temporal trajectory, and subsequent viable continuation space, provide reproducible information beyond the strongest existing control and viability models? Eight H7 hypotheses are formulated. The strongest requires comparison of Model A, incorporating the strongest modern control and viability model, with Model B, which adds predefined Vitological variables. Independent scientific value is supported only if Model B demonstrates reproducible added predictive performance on independent data. Keywords Vitology, viability, control theory, Viability Theory, control, reachability, viability kernel, invariance, safe set, constraints, robust control, adaptive control, model predictive control, viable continuation, Regulatory Reserve, Regulatory Viability, Synchroauthenticity, Aw–Con–CON, Norm of Harmony, viability trajectory, cross-domain metrology.