Resource Management in Wireless Control Systems
This project is motivated by modern cyber-physical systems (CPSs) appearing in applications such as smart buildings or industrial automation. These systems are characterized by multiple sensor, actuator, and controller devices at different physical locations, communicating wirelessly with each other. The closed loop performance of such control systems is tightly coupled with the wireless communication. The latter not only introduces uncertainties such as packet drops and delays in the closed loop, but also depends on how the available communication resources are utilized. In particular a key resource for wireless sensors is the power used for communication. The work in this project is focused on the development of efficient resource management methods that are aware of the control performance requirements of the physical plant. Two important thrusts in this project are power management for single loop systems, as well scheduling and power management for control systems over shared wireless channels.
Power management for single-loop control systems
We consider a fundamental wireless control architecture shown in Fig. 1. A sensor sends plant state measurement packets with adjusted transmit power to a controller over a wireless channel. The wireless channel is modelled as random fading, so that the probability of successful packet decoding at the controller depends on the sensor transmit power and the channel fading state. Higher transmit power means efficient delivery of the information at the controller and more accurate control operation, hence a trade-off between power consumption and control performance emerges. To explore this trade-off we consider a joint linear quadratic and average power cost. We are interested in designing a power allocation policy adapted to channel and plant states at the sensor, as well as a control input policy adapted to received information at the controller.
Finding jointly optimal communication and control policies is well-known to be hard, hence we develop a methodology to separate the two designs. The resulting control policy is a linear quadratic regulator, and the communication policy balances estimation cost at the controller and transmit power cost. Qualitatively the optimal communication policy has an opportunistic nature shown in Fig. 2, and similar suboptimal policies are derived in this work. No transmission (zero power) is selected under small observed plant state innovations or under unfavorable channels. That is because the measurement is not very informative, or the transmission is very costly respectively. Otherwise transmit power increases with plant innovation, i.e., larger estimation error requires higher transmit power. Moreover power decreases with channel quality, i.e., it is cheaper to transmit over a more favorable channel. It is worth noting that such a power policy generalizes the recently popular notions of event-triggered control where a communication (or actuation) occurs when plant state exceeds some threshold. The policies in this work explicitly capture the amount of transmit power that needs to be allocated, leading to a more quantified version of the event-triggered transmit-or-not decision. Furthermore, our model explicitly captures and exploits channel quality variability.
Control over shared wireless channels
We consider multiple control loops closing over a shared wireless medium, as shown in Fig. 3. Contention is resolved by a centralized scheduler who decides which control system attempts to communicate and close the loop at each time step. The multiple access channel is modelled as random fading, varying over time and among systems. The scheduled system at each time step decides on its transmit power, which along with its corresponding channel state determines the probability of getting the message across. We are interested in scheduling and power allocation policies that guarantee level of control performance for each of the systems, while also trying to minimize the total average power consumption. These policies are allowed to opportunistically adapt and exploit the varying channel conditions, which at certain times become more favorable for some control systems than others.
The stochasticity of the shared wireless medium considered here makes the analysis of control performance significantly complex. Typical approaches for scheduling in networked control systems based on time-domain control performance abstractions and offline/periodic scheduling sequences are hard to employ. In this work we propose a stochastic Lyapunov control performance abstraction for each system over the shared wireless medium. The communication design then needs to guarantee that all Lyapunov functions are decreasing in expectation at the same time step, with predefined decrease rates. Suitable channel-aware scheduling and power allocation policies then are posed as a stochastic optimization. Offline and online algorithms to discover the optimal communication design are developed. Interestingly, the optimal scheduling has an opportunistic nature, as shown in Fig. 4. Most of the times the control system experiencing the most favorable channel conditions is granted access. Otherwise the scheduler gives channel access more frequently to systems with more demanding control performance requirements.
Future research directions
To accommodate more flexible sensor-actuator systems with multiple devices it is important to analyze and examine decentralized channel access mechanisms, such as random access. Due to the lack of centralized scheduling, collisions can occur in this case if many devices try to communicate concurrently and this makes maintaining plant stability and performance challenging tasks. Furthermore since information is decentralized, e.g., sensors have information only about their respective plant and channel conditions, developing efficient ways to coordinate the overall system becomes a key question.