EDRS

The effectiveness of control algorithms in large-scale cyber-physical systems relies not only on advancements in sensing, computation, and communication but also on the availability of methods to design controllers capable of stabilizing nonlinear systems under nominal operating conditions. However, stabilization alone is insufficient; achieving satisfactory performance is equally critical. In Optimal Control (OC), performance is typically encoded in the cost function that the control policy aims to minimize. This highlights the need for OC algorithms that leverage Neural Network (NN) models to enable sophisticated closed-loop behaviors, such as collision avoidance or waypoint tracking in robot swarms. The challenge lies in constraining the search for high-performance controllers to those that ensure closed-loop guarantees, such as stability and robustness.

This course will equip PhD students with contemporary theoretical and computational tools for designing and deploying NN-based controllers with embedded theoretical guarantees for closed-loop systems. The course begins with a focus on recent optimal control methods for linear systems, emphasizing the direct design of closed-loop maps rather than control policies (e.g., Youla parametrizations, Internal Model Control, System-Level Synthesis). We then review stability tools for nonlinear systems, including L2 gains, dissipativity, and the small-gain theorem. Building on the first part, we teach a recent approach to nonlinear OC, termed "performance boosting," which utilizes NNs and automatic differentiation to enhance closed-loop system performance without compromising existing properties. The final section extends performance boosting to large-scale systems, where multiple nonlinear local systems interact dynamically, relying solely on local measurements for control deployment.