Traditional optimal control schemes, such as LQR, MPC, relies on an accurate model of the underlying system. Modeling accuracy, therefore, directly impacts controller success and performance. However, often it is hard to capture the global dynamics with a high accuracy. To overcome this problem, we develop an active learning framework based on Bayesian optimization that can automate the process of controller design for a specific task even in the absence of dynamics model based on the performance observed in experiments on the physical system.
Reachability analysis provides optimal control and guarantees for safety-critical dynamic systems. However, the computational complexity of reachability analysis grows exponentially with system dimension, making this method intractable for high-dimensional or multi-agent systems. We are working on finding approximate and exact solutions to high-dimensional reachability problems by decomposing systems into multiple subsystems. These subsystems can be solved separately, then recombined to provide full system information.