This paper formalizes Hamiltonian-Informed Optimal Neural (Hion) controllers, a novel class of neural network-based controllers for dynamical systems and explicit non-linear model predictive control. Hion controllers estimate future states and compute optimal control inputs using Pontryagin's Maximum Principle. The proposed framework allows for customization of transient behavior, addressing limitations of existing methods. The Taylored Multi-Faceted Approach for Neural ODE and Optimal Control (T-mano) architecture facilitates training and ensures accurate state estimation. Optimal control strategies are demonstrated for both linear and non-linear dynamical systems.

This paper proposes to leverage the emerging~learning techniques and devise a multi-agent online source {seeking} algorithm under unknown environment. Of particular significance in our problem setups are: i) the underlying environment is not only unknown, but dynamically changing and also perturbed by two types of non-stochastic disturbances; and ii) a group of agents is deployed and expected to cooperatively seek as many sources as possible. Correspondingly, a new technique of discounted Kalman filter is developed to tackle with the non-stochastic disturbances, and a notion of confidence bound in polytope nature is utilized~to aid the computation-efficient cooperation among~multiple agents. With standard assumptions on the unknown environment as well as the disturbances, our algorithm is shown to achieve sub-linear regrets under the two~types of non-stochastic disturbances; both results are comparable to the state-of-the-art. Numerical examples on a real-world pollution monitoring application are provided to demonstrate the effectiveness of our algorithm.