Hamilton-Jacobi Reachability for Viability Analysis of Constrained Waste-to-Energy Systems under Adversarial Uncertainty

Abstract: This paper investigates the problem of maintaining the safe operation of Waste-to-Energy (WtE) systems under operational constraints and uncertain waste inflows. We model this as a robust viability problem, formulated as a zero-sum differential game between a control policy and an adversarial disturbance. Within a Hamilton-Jacobi framework, the viability kernel is characterized as the zero sublevel set of a value function satisfying a constrained Hamilton-Jacobi-Bellman (HJB) equation in the viscosity sense. This formulation provides formal guarantees for ensuring that system trajectories remain within prescribed operational limits under worst-case scenarios. Compared to existing viability studies, this work introduces a rigorous HJB-based characterization explicitly incorporating uncertainty, tailored to nonlinear WtE dynamics. A numerical scheme based on the Local Lax-Friedrichs method is employed to approximate the viability kernel. Numerical experiments illustrate how increasing inflow uncertainty significantly reduces the viability domain, shrinking the safe operating envelope. The proposed method is computationally tractable for systems of moderate dimension and offers a basis for synthesizing robust control policies, contributing to the design of resilient and sustainable WtE infrastructures.