Seminars

Advances in machine learning and control theory have significantly expanded the capabilities of autonomous systems, yet key challenges persist in ensuring safety, stability, interpretability, and computational efficiency—particularly for unknown systems, and high-dimensional or multi-agent scenarios. This talk is divided into three modules. First, we talk about developing interpretable and expressive models for safe and stabilizing control subject to input constraints. Control Barrier Functions (CBFs) have been instrumental in ensuring safety; however, methods based on CBF often exhibit limitations in handling complex state/input safety specifications and providing stability for general input-constrained nonlinear systems in the presence of external disturbances. We propose Universal Barrier Functions (UBFs) to address these issues. UBFs combine stability, safety, and input constraints into a single differentiable function, thus enabling the use of UBF-based Quadratic Programs (UBF-QP) to synthesize safe and stabilizing controllers for nonlinear systems (including non-control affine systems). Building upon the foundation of UBFs, we explore the application of Koopman Operator Theory (KOT) to transform nonlinear systems into higher-dimensional linear representations, facilitating easier linear controller design and analysis. We derive KOT-based lifted space global linear models from the first principles for quadrotors and 6-DOF rigid body systems and show pointwise convergence of the approximation error of the states to zero for both these systems. Furthermore, we propose a learning-based KOT approach for unknown systems to synthesize safe and stabilizing controllers. Second, we will talk about theoretical guarantees for planning under uncertainty where we propose an information-theoretic belief-space planner termed as IG-PRM*, that balances travel distance with sensing cost. This planner is shown to be asymptotically optimal, making it well-suited for environments where sensing and actuation resources are limited. Finally, we discuss leveraging learned black-box ML models to improve the computational efficiency of optimization-based controllers without losing interpretability or theoretical guarantees. We first present TransformerMPC, which utilizes transformer neural networks to predict which constraints would be active and which will essentially be redundant along the system trajectories and provide better warm-starts for MPC solvers, thereby accelerating the MPC process. In addition, TransformerMPC can be augmented with any off-the-shelf MPC solvers. Lastly, we propose a Multi-Agent Integral Control Barrier Function (MA-ICBF) for safe and scalable multi-agent control under limited actuation. We show that MA-ICBF ensures safety and scalability for more than 1000 agents and minimizes deadlocks while not compromising computational efficiency and constraint satisfaction.