Assume that each node assigns equal weights to each incoming edge. Then, for instance, the update equation for x1 is x1 (t+1) = (x2+x3+x4)/3. Assume that each node can measure the state of the incoming neighbors. Then, for instance, node x1 can measure independently the state of x2, x3, and x4 at each time step (and itself, x1). Using the measured values, each node aims to compute the state of all other nodes.1. Which node can reconstruct the state of the other nodes?2. You are an attacker that aims to prevent x1 from calculating the correct state of theother nodes, while remaining undetected from x1. As an attacker, you can target asubset of the other nodes (inject an input signal into some nodes). What is a smallest set of nodes that you need to target? How would you choose the attack inputs?3. Repeat the analysis for x3.4. Assume that an attacker can only compromise 1 node. Using the measurementscollected by x1, which are contained in the attached matrix, determine which node has been compromised.
Microsoft Word - HW3.docx Consider the following consensus network: Assume that each node assigns equal weights to each incoming edge. Then, for instance, the update equation for x1 is x1 (t+1) = (x2+x3+x4)/3. Assume that each node can measure the state of the incoming neighbors. Then, for instance, node x1 can measure independently the state of x2, x3, and x4 at each time step (and itself, x1). Using the measured values, each node aims to compute the state of all other nodes. 1. Which node can reconstruct the state of the other nodes? 2. You are an attacker that aims to prevent x1 from calculating the correct state of the other nodes, while remaining undetected from x1. As an attacker, you can target a subset of the other nodes (inject an input signal into some nodes). What is a smallest set of nodes that you need to target? How would you choose the attack inputs? 3. Repeat the analysis for x3. 4. Assume that an attacker can only compromise 1 node. Using the measurements collected by x1, which are contained in the attached matrix, determine which node has been compromised. Microsoft Word - HW3.docx Consider the following consensus network: Assume that each node assigns equal weights to each incoming edge. Then, for instance, the update equation for x1 is x1 (t+1) = (x2+x3+x4)/3. Assume that each node can measure the state of the incoming neighbors. Then, for instance, node x1 can measure independently the state of x2, x3, and x4 at each time step (and itself, x1). Using the measured values, each node aims to compute the state of all other nodes. 1. Which node can reconstruct the state of the other nodes? 2. You are an attacker that aims to prevent x1 from calculating the correct state of the other nodes, while remaining undetected from x1. As an attacker, you can target a subset of the other nodes (inject an input signal into some nodes). What is a smallest set of nodes that you need to target? How would you choose the attack inputs? 3. Repeat the analysis for x3. 4. Assume that an attacker can only compromise 1 node. Using the measurements collected by x1, which are contained in the attached matrix, determine which node has been compromised.