Applied Mathematics Seminar | Jun Liu, Correct-by-Design Control Synthesis: A Temporal Logic Game Approach

An outstanding challenge in the design of reliable engineered systems is the complex interplay between system dynamics and the dynamic environment the system operates in. Central to many engineered systems are feedback control systems that help improve system safety, reliability, and performance.

In this talk, I will present a hierarchical control design framework for dynamical systems, where the control objective is for the system to satisfy certain high-level specifications while interacting with its environment. I will focus on specifications that are expressible in linear temporal logic and present a temporal logic game-based approach to synthesizing provably correct hybrid controllers that render the system to satisfy such specifications. A key step in this approach is to construct finite approximations for nonlinear dynamical systems. I will present computationally efficient procedures for abstracting nonlinear dynamics into finite-state transitions and discuss how analytical tools from dynamical system theory can provide correctness and robustness guarantees for these abstractions. The results will be illustrated with several applications in robot motion planning, composition of pre-designed feedback controllers, and automotive adaptive cruise control. I will conclude the talk with a summary of recent developments and discussions about future directions.