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Research

My primary research focuses on safety and performance-guaranteed autonomy, and efficient computation. 

  • optimal control and game theories to guarantee safety and performance

  • efficient computational methods using Hopf-Lax theory and reinforcement learning

  • applications

** [Ux], [Jx], [Cx] can be found in Publications.

1. Theoretical guarantees for safety and performance: Hamilton-Jacobi analysis

  • What is this? Hamilton-Jacobi analysis solves optimal control problems or differential games by formulating partial differential equations.

  • related publications: [C9], [U3] 

  • Advantages:

    • theoretical guarantees of safety and optimal performance for several classes of practical problems

    • fundamental methods that can potentially create techniques in combination with other methods

  • Challenges: Its computation is intractable for high-dimensional systems.​

2. Hopf-Lax theory

  • What is this? Hopf-Lax theory is a field that finds an analytic solution to Hamilton-Jacobi partial differential equations.

  • related publications: [J9], [J8], [J7], [J5], [C8], [C7]

  • Advantages:

    • efficient computation for high-dimensional systems

    • stronger theoretical guarantees via convexification than other methods

  • Challenges: The mathematical foundation is not been established.​

3. Safe reinforcement learning 

  • What is this? Safe reinforcement learning trains safe policies for dynamic systems and finds safety discrimination.

  • related publications: [U4]

  • Advantages:

    • good at data-based systems​

    • better data efficiency and training accuracy than other approaches by reducing learning processes via the analytic design of the neural network architecture

4. Applications

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aerial vehicle's navigation [J7], [C8]

ground vehicle's navigation [U4]

5. Past research topics

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teleoperation [J1], [C2]

maintenance robot for wind turbines [J2], [C4]

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