A Zero-Sum Game Framework for Optimal Sensor Placement in Uncertain Networked Control Systems under Cyber-Attacks

This paper proposes a game-theoretic approach to address the problem of optimal sensor placement against an adversary in uncertain networked control systems. The problem is formulated as a zero-sum game with two players, namely a malicious adversary and a detector. Given a protected performance vertex, we consider a detector, with uncertain system knowledge, that selects another vertex on which to place a sensor and monitors its output with the aim of detecting the presence of the adversary. On the other hand, the adversary, also with uncertain system knowledge, chooses a single vertex and conducts a cyber-attack on its input. The purpose of the adversary is to drive the attack vertex as to maximally disrupt the protected performance vertex while remaining undetected by the detector. As our first contribution, the game payoff of the above-defined zero-sum game is formulated in terms of the Value-at-Risk of the adversary's impact. However, this game payoff corresponds to an intractable optimization problem. To tackle the problem, we adopt the scenario approach to approximately compute the game payoff. Then, the optimal monitor selection is determined by analyzing the equilibrium of the zero-sum game. The proposed approach is illustrated via a numerical example of a 10-vertex networked control system.Comment: 8 pages, 3 figues, Accepted to the 61st Conference on Decision and Control, Cancun, December 202

ISAACS: Iterative Soft Adversarial Actor-Critic for Safety

The deployment of robots in uncontrolled environments requires them to operate robustly under previously unseen scenarios, like irregular terrain and wind conditions. Unfortunately, while rigorous safety frameworks from robust optimal control theory scale poorly to high-dimensional nonlinear dynamics, control policies computed by more tractable "deep" methods lack guarantees and tend to exhibit little robustness to uncertain operating conditions. This work introduces a novel approach enabling scalable synthesis of robust safety-preserving controllers for robotic systems with general nonlinear dynamics subject to bounded modeling error by combining game-theoretic safety analysis with adversarial reinforcement learning in simulation. Following a soft actor-critic scheme, a safety-seeking fallback policy is co-trained with an adversarial "disturbance" agent that aims to invoke the worst-case realization of model error and training-to-deployment discrepancy allowed by the designer's uncertainty. While the learned control policy does not intrinsically guarantee safety, it is used to construct a real-time safety filter (or shield) with robust safety guarantees based on forward reachability rollouts. This shield can be used in conjunction with a safety-agnostic control policy, precluding any task-driven actions that could result in loss of safety. We evaluate our learning-based safety approach in a 5D race car simulator, compare the learned safety policy to the numerically obtained optimal solution, and empirically validate the robust safety guarantee of our proposed safety shield against worst-case model discrepancy.Comment: Accepted in 5th Annual Learning for Dynamics & Control Conference (L4DC), University of Pennsylvani

Multi-Layer Cyber-Physical Security and Resilience for Smart Grid

The smart grid is a large-scale complex system that integrates communication technologies with the physical layer operation of the energy systems. Security and resilience mechanisms by design are important to provide guarantee operations for the system. This chapter provides a layered perspective of the smart grid security and discusses game and decision theory as a tool to model the interactions among system components and the interaction between attackers and the system. We discuss game-theoretic applications and challenges in the design of cross-layer robust and resilient controller, secure network routing protocol at the data communication and networking layers, and the challenges of the information security at the management layer of the grid. The chapter will discuss the future directions of using game-theoretic tools in addressing multi-layer security issues in the smart grid.Comment: 16 page