Geometric, topological, and stochastic approaches in nonlinear control theory

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Nonlinear control theory is an important branch of control theory, with applications in areas and industries as diverse as power grids, aerospace systems, biomedical systems, nano-engineering, process control, chemical engineering, and many others. It stands out by the richness of its problems and the diversity of mathematical areas that it connects to. Worthy of note among the latter is sub-Riemannian geometry, which continues to play a key role in our understanding of nonlinear control systems. By virtue of restricting itself to a narrow and well-behaved class of control systems, linear control theory enjoys a rich and well-established body of theoretical tools and techniques, drawn principally from linear functional analysis. By contrast, nonlinear control theory is far from enjoying this level of maturity, and intensive efforts have been deployed in devising new tools and approaches.