This study presents a nonlinear stabilization framework for industrial robotic systems based on differential topology and geometric control theory. System dynamics are modeled on smooth manifolds, where stabilization is achieved through topological invariants and non-smooth feedback control laws. The approach extends classical nonlinear control by incorporating global geometric structures, enabling stabilization of non-triangular and highly coupled systems. Stability analysis is conducted using global asymptotic and finite-time convergence criteria, supported by Lyapunov-topological equivalence principles. Results demonstrate enhanced robustness, rapid convergence, and strong disturbance rejection capabilities in complex nonlinear robotic systems.
Description This white paper introduces Stability Geometry of Biomimetic Robotics (SG-BR) — a conceptual and computational framework that shifts the focus of biomimetic robotics from anatomical imitation to the principles of adaptive stability. The central hypothesis is that biol…
We develop a federal-level decision-support framework for managing a long-run transition to an economy in which artificial intelligence and inexpensive general-purpose robots can perform a substantial share of cognitive and physical tasks. The framework does not forecast the tech…
This paper presents a preview-enhanced synchronous policy-iteration framework for zero-sum differential games in continuous-time Lipschitz nonlinear systems with differentiable bounded disturbances. By embedding finite-horizon reference preview into an augmented error system, the…
Postscript Reflections on the Mathematical Philosophy of Social Quantum Field Theory P.1 Why Another Mathematical Framework? One may reasonably ask why another mathematical framework is needed when graph theory, dynamical systems, statistical mechanics, network science, informati…