Research

For systems with limited knowledge, identifying system properties from observable data is vital to decision-making. We develop data-driven tools to estimate the system transition, winning set (with respect to the control objectives) and safe operation ranges, as well as to synthesize feasible controllers.

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.

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.

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.