The Effect of Software (and Communication) Reliability and Security on Control Systems

Transcription

1 The Effect of Software (and Communication) Reliability and Security on Control Systems Bruno Sinopoli Assistant professor Department of ECE Carnegie Mellon University

2 Convergence of domains Control Cyber Communication Physical Computing

3 Control Applications

4 u Classical control theory vs networked control systems Plant Controller Classical control design Sensor State estimator Availability of data when needed Instantaneous communication Fixed delays Networked control in Sensor Networks? communication Communication Network Plant Aggregate Sensor computation State Controller estimator communication Communication Network?

5 Questions How do we enrich system theory with software and communication models? What are the key properties of such models for control? how can they be described quantitatively? Data Consistency, Timing properties, energy consumption etc. How does software and communication affect closed loop performance? How do we design/analyze CPS? What type of analysis tools? What algorithms (control)? what software infrastructure (who computes, where does computation take place)? What communication infrastructure? What is the effect of compromised software in the closed loop? Is CPS security any different from cyber security?

6 Timing properties Density of arrived packets Control interval Max-delay Packets are time-stamped T Delay Density of arrived packets T delay 80% 20% Delay

7 How does control design and analysis change? Consider the estimation problem Plant Aggregate Sensor Comm. Network State Estimator Erasure Channel: packets are either lost or received Single Packet: All the observations made at time k are sent in one packet Memoryless: γ i s are i.i.d.

8 Modified Kalman Filter Equations The arrival of the observation at time t can be modeled as a binary random variable Kalman Filter Equations Note: K t+1 and are random variables, since they depend on We need to give a statistical description of

9 What we know Estimation Error Estimator is unstable (for unstable system) if no observation is timely received and processed?what happens in between? is the tradeoff? Estimator is stable if all observations are timely received and processed 0 1 Network Reliability

10 Stability can be lost due to the unreliability of the cyber portion of systems E[P ]

11 The control problem Communication Network Plant Aggregate Sensor Communication Network Controller State estimator What is the minimum arrival probability that guarantees acceptable performance of estimator and controller? How is the arrival rate related to the system dynamics? Can we design estimator and controller independently? Are the optimal estimator and controller still linear? Can we provide design guidelines?

12 The information set is defined by the communication protocol used. Actuators Plant Sensors u a t = ν t u c t ν t θ t Communication Network γ t State Feedback Kalman Filter TCP-like UDP-like TCP-like with probabilistic Acknowledgement

13 Stability conditions depend upon the protocol used

14 More information yields a larger stability region

15 Networked Control System: multi-channel case? Communication Network Plant Sensor Network Communication Network Controller State estimator? Questions: Given a statistical description of the communication channels: -How do you send sensory information so as to maximize estimation performance? -How do you design and send control inputs to the actuators?

16 Example: Stable plant with two identical actuators Consider the following: Optimal controller prefers the actuator along the most reliable channel

17 Unstable plant with two identical actuators Both channels need to be meet minimum requirements for stability

18 Example: Unstable Batch Reactor Two Input - Two Output system: linearized and discretized equations

19 Stability depends upon reliability of both sensor and control channels

20 Conclusions Software properties are intimately tied to the application Interactions are complex, analytical tools are limited Need to create the right abstractions Need tools to quantify performance parameters Stochastic models provide more flexibility for tradeoff analysis