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Many optimal and robust control problems are nonconvex and potentially nonsmooth in their policy optimization forms. In this paper, we introduce the Extended Convex Lifting (ECL) framework, which reveals hidden convexity in classical optimal and robust control problems from a modern optimization perspective. Our ECL framework offers a bridge between nonconvex policy optimization and convex reformulations. Despite non-convexity and non-smoothness, the existence of an ECL for policy optimization not only reveals that the policy optimization problem is equivalent to a convex problem, but also certifies a class of first-order non-degenerate stationary points to be globally optimal. We further show that this ECL framework encompasses many benchmark control problems, including LQR, state-feedback and output-feedback H-infinity robust control. We believe that ECL will also be of independent interest for analyzing nonconvex problems beyond control. 

This paper focuses on the problem of multi-robot source-seeking, where a group of mobile sensors localizes and moves close to a single source using only local measurements. Drawing inspiration from the optimal sensor placement research, we develop an algorithm that estimates the source location while approaches the source following gradient descent steps on a loss function defined on the Fisher information. We show that exploiting Fisher information gives a higher chance of obtaining an accurate source location estimate and naturally leads the sensors to the source. Our numerical experiments demonstrate the advantages of our algorithm, including faster convergence to the source than other algorithms, flexibility in the choice of the loss function, and robustness to measurement modeling errors. Moreover, the performance improves as the number of sensors increases, showing the advantage of using multi-robots in our source-seeking algorithm. We also implement physical experiments to test the algorithm on small ground vehicles with light sensors, demonstrating success in seeking a moving light source.