Building upon my vision of gaining a comprehensive understanding of dynamical systems, automatic control, and applications of AI, my research broadly covers the following themes. For further details and potential future efforts, please click the title of each research topic.

As a crucial step before implementing controls for systems with uncertainties, it is necessary to gain a better understanding of the solution's behaviors, such as the continuity/differentiability, stability, reachability, and safety-related properties. We develop fundamental mathematical analysis and novel analytical tools addressing safety-critical control. 

For systems with limited knowledge, identifying system properties from observable data is vital to decision-making. We develop data-driven tools to estimate the winning set (w.r.t. the control objectives) and safety operation ranges. 

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Formal abstractions enable autonomous decision-making of dynamical systems to achieve complex tasks and compute a holistic reference on controllable regions of initial conditions (winning sets) with quantifiable errors. We develop abstraction analysis and computation tools for stochastic formal verification and control synthesis. 

In continuous environments, optimality-related quantities for finite-dimensional dynamical systems usually exist in the lifted function/functional spaces, which are solutions to optimality-induced partial differential equations (PDEs). We develop analysis and computation tools in this regard.