Raffaele Romagnoli

Raffaele Romagnoli, Bruce H. Krogh, Bruno Sinopoli

Software rejuvenation has been proposed as a strategy to protect cyber-physical systems (CSPs) against unanticipated and undetectable cyber attacks. The basic idea is to refresh the system periodically with a secure and trusted copy of the online software so as to eliminate all effects of malicious modifications to the run-time code and data. Following each software refresh a safety controller assures the CPS is driven to a safe state before returning to the mission control mode when the CPS is again vulnerable attacks. This paper considers software rejuvenation design from a control-theoretic perspective. Invariant sets for the Lyapunov function for the safety controller are used to derive bounds on the time that the CPS can operate in mission control mode before the software must be refreshed and the maximum time the safety controller will require to bring the CPS to a safe operating state. With these results it can be guaranteed that the CPS will remain safe under cyber attacks against the run-time system and will be able to execute missions successfully if the attacks are not persistent. The general approach is illustrated using simulation of the nonlinear dynamics of a quadrotor system. The concluding section discusses directions for further research.

Raffaele Romagnoli, Bruce H. Krogh, Dionisio de Niz et al.

Software rejuvenation protects cyber-physical systems (CSPs) against cyber attacks on the run-time code by periodically refreshing the system with an uncorrupted software image. The system is vulnerable to attacks when it is communicating with other agents. Security is guaranteed during the software refresh and re-initialization by turning off all communication. Although the effectiveness of software rejuvenation has been demonstrated for some simple systems, many problems need to be addressed to make it viable for real applications. This paper expands the scope of CPS applications for which software rejuvenation can be implemented by introducing architectural and algorithmic features to support trajectory tracking. Following each software refresh, while communication is still off, a safety controller is executed to assure the system state is within a sufficiently small neighborhood of the current point on the reference trajectory. Communication is then re-established and the reference trajectory tracking control is resumed. A protected, verified hypervisor manages the software rejuvenation sequence and delivers trusted reference trajectory points, which may be received from untrusted communication, but are verified using an authentication process. We present the approach to designing the tracking and safety controllers and timing parameters and demonstrate the secure tracking control for a 6 DOF quadrotor using the PX4 jMAVSim quadrotor simulator. The concluding section discusses directions for further research.

Zhuoyuan Wang, Raffaele Romagnoli, Saviz Mowlavi et al. · cmu

Physics-informed machine learning offers a promising framework for solving complex partial differential equations (PDEs) by integrating observational data with governing physical laws. However, learning PDEs with varying parameters and changing initial conditions and boundary conditions (ICBCs) with theoretical guarantees remains an open challenge. In this paper, we propose physics-informed deep B-spline networks, a novel technique that approximates a family of PDEs with different parameters and ICBCs by learning B-spline control points through neural networks. The proposed B-spline representation reduces the learning task from predicting solution values over the entire domain to learning a compact set of control points, enforces strict compliance to initial and Dirichlet boundary conditions by construction, and enables analytical computation of derivatives for incorporating PDE residual losses. While existing approximation and generalization theories are not applicable in this setting - where solutions of parametrized PDE families are represented via B-spline bases - we fill this gap by showing that B-spline networks are universal approximators for such families under mild conditions. We also derive generalization error bounds for physics-informed learning in both elliptic and parabolic PDE settings, establishing new theoretical guarantees. Finally, we demonstrate in experiments that the proposed technique has improved efficiency-accuracy tradeoffs compared to existing techniques in a dynamical system problem with discontinuous ICBCs and can handle nonhomogeneous ICBCs and non-rectangular domains.

Zhuoyuan Wang, Raffaele Romagnoli, Kamyar Azizzadenesheli et al. · cmu

Accurately quantifying long-term risk probabilities in diverse stochastic systems is essential for safety-critical control. However, existing sampling-based and partial differential equation (PDE)-based methods often struggle to handle complex varying dynamics. Physics-informed neural networks learn surrogate mappings for risk probabilities from varying system parameters of fixed and finite dimensions, yet can not account for functional variations in system dynamics. To address these challenges, we introduce physics-informed neural operator (PINO) methods to risk quantification problems, to learn mappings from varying \textit{functional} system dynamics to corresponding risk probabilities. Specifically, we propose Neural Spline Operators (NeSO), a PINO framework that leverages B-spline representations to improve training efficiency and achieve better initial and boundary condition enforcements, which are crucial for accurate risk quantification. We provide theoretical analysis demonstrating the universal approximation capability of NeSO. We also present two case studies, one with varying functional dynamics and another with high-dimensional multi-agent dynamics, to demonstrate the efficacy of NeSO and its significant online speed-up over existing methods. The proposed framework and the accompanying universal approximation theorem are expected to be beneficial for other control or PDE-related problems beyond risk quantification.

Raffaele Romagnoli, Jasmine Ratchford, Mark H. Klein

Control systems are indispensable for ensuring the safety of cyber-physical systems (CPS), spanning various domains such as automobiles, airplanes, and missiles. Safeguarding CPS necessitates runtime methodologies that continuously monitor safety-critical conditions and respond in a verifiably safe manner. A fundamental aspect of many safety approaches involves predicting the future behavior of systems. However, achieving this requires accurate models that can operate in real time. Motivated by DeepONets, we propose a novel strategy that combines the inductive bias of B-splines with data-driven neural networks to facilitate real-time predictions of CPS behavior. We introduce our hybrid B-spline neural operator, establishing its capability as a universal approximator and providing rigorous bounds on the approximation error. These findings are applicable to a broad class of nonlinear autonomous systems and are validated through experimentation on a controlled 6-degree-of-freedom (DOF) quadrotor with a 12 dimensional state space. Furthermore, we conduct a comparative analysis of different network architectures, specifically fully connected networks (FCNN) and recurrent neural networks (RNN), to elucidate the practical utility and trade-offs associated with each architecture in real-world scenarios.

Raffaele Galliera, Konstantinos Mitsopoulos, Niranjan Suri et al.

Addressing complex cooperative tasks in safety-critical environments poses significant challenges for multi-agent systems, especially under conditions of partial observability. We focus on a dynamic network bridging task, where agents must learn to maintain a communication path between two moving targets. To ensure safety during training and deployment, we integrate a control-theoretic safety filter that enforces collision avoidance through local setpoint updates. We develop and evaluate multi-agent reinforcement learning safety-informed message passing, showing that encoding safety filter activations as edge-level features improves coordination. The results suggest that local safety enforcement and decentralized learning can be effectively combined in distributed multi-agent tasks.