Hamilton-Jacobi Reachability (HJR) is a central framework in safe control theory. While HJR has traditionally focused on a few fundamental tasks, there is increasing interest in scaling to more complex objectives. Recent works have studied the exact decomposition of the value functions for two fundamental dual-objective tasks in the adversary-free setting. However, not all value function decompositions in HJR remain valid with an adversary. In this work, we develop theoretical approaches to certify that for these two composite value functions, the proposed decompositions still hold with an adversary. Finally, we show how these results can solve issues that arise when applying HJR to optimal drug regimen design.
Networked SEIR models describe epidemic spread within and between interacting subpopulations through contact-supported nonlinear transmission. Standard polynomial liftings based on complete ordered Kronecker tensors yield linear higher-dimensional representations, but their dimen…
Finite Reliability Representations (FRR) certify when a cell-constant policy is sufficient for reliable decision-making in a partially observed system with a known physical noise floor. In practice, however, sensing and execution noise can be latent and context-dependent. This pa…
This article presents a novel, numerically viable algorithm for solving sparse robust optimal control problems in continuous time. We consider a constrained linear noisy system governed by an ordinary differential equation (ODE), with an $L^1$-type objective function in line with…
This paper investigates the optimal safety control problem of nonlinear control systems by proposing novel high-order control barrier functions (HOCBFs). Different from zeroing HOCBFs, two novel HOCBFs are derived and the safety controllers are designed in an explicit way. Next,…
The growing supply of retired electric vehicle batteries presents an opportunity for second-life stationary energy storage, but assembling heterogeneous retired cells into reliable packs is challenging due to substantial variation in capacity, DC internal resistance (DCIR), and s…
This article establishes a new numerically viable technique for solving a class of constrained, nonconvex, continuous-time optimal control problems (OCPs) for linear systems that commonly arise in aerial and aerospace applications. The lossless convexification technique is employ…