Optimal Design of Wireless Control Systems

This research thrust deals with wireless sensor and actuator networks installed to monitor and control physical dynamical processes, for example in state estimation, building automation, or the Internet-of-Things. The focus is on wireless communication design principles for reliable autonomous connectivity in the face of limited, uncertain, and shared resources. The highlight of the approach is a co-design perspective; the transmitted information carries crucial value for the dynamic monitoring and control application that should be taken into account when designing the communication.

Low-power Wireless Control Systems

Figure 1. Wireless control system architecture. The sensor measures current plant state x(k) and transmits with power p(k) over fading channel h(k). Messages are decoded at the controller with a certain success probability. The controller selects plant inputs given current information.

The figure represents a fundamental wireless control architecture revealing the fundamental co-design of communication resources and control resources. By increasing the transmit power at the sensor side we can improve instantaneously the channel reliability at the receiver/controller, rendering valuable current plant information at the latter to use in feedback control and improve the state dynamically at the next time step. On the other hand, this power increase depletes faster the communication resources at the sensor. It becomes apparent that a balance between power allocation and the dynamic control performance is desirable.

I analyzed this co-design problem and obtained a theoretical characterization of the optimal dynamic power allocation policy at the sensor. The novelty of this characterization is its opportunistic nature; when the plant deviates from the desired operating equilibrium point, or when the channel conditions become less favorable, the sensor needs to increase its transmit power to communicate more reliably to the controller. This is a paradigm shift from the current approaches which would separate the two design aspects, control and communication. Technically my result was achieved in a stochastic control framework using the Bellman equation for minimizing an average linear quadratic regulation cost joint with the average power expenditures.

More information can be found at the IEEE Trans. on Aut. Control paper, and the ACC 2013 paper. To overcome the computational burden of obtaining the optimal policy, tractable suboptimal power allocation policies with performance guarantees were devised in the CDC 2016 paper.

Spectrum Management for Connected Control Systems

Figure 3. Control over a shared wireless medium.

In practice wireless control systems are not in isolation, but operate concurrently in industrial or home automation environments creating the need to share available channel spectrum among devices. Intuitively, this complicates the problem because independent control systems as in this figure become now coupled over the shared wireless medium. Conventional approaches overcome this challenge by fixing periodic time-division rules, for example round-robin scheduling. On the one hand this manages to decouple the control systems and enhance determinism, but is not a true co-design as it disregards the random nature of the wireless medium.

My contribution is a novel opportunistic scheduling perspective, exploiting channel state information to provide both desirable control performance guarantees and also low resource utilization. Intuitively, as the wireless channel conditions vary randomly over time and among links, they create different transmission opportunities across systems and across time. I proved that the structure of the optimal scheduler ranks all systems according to a measure of their control needs and channel opportunities, and dynamically grants channel access to the best one. In contrast to the traditional periodic rules, control systems are not decoupled across time, but decoupled across channel states. The latter is technically facilitated by an abstraction of control performance using Lyapunov functions, whose decrease rate provides a single-time step performance specification, in contrast to the periodic scheduling paradigm which is often combinatorial over a time horizon. To find the optimal mechanism, both offline as well as online learning algorithms using only channel sequences observed during system execution are developed.

More information can be found at the IEEE Trans. on Aut. Control paper, and the ICCPS 2014 paper.

Decentralized Spectrum Management

Beyond centralized approaches, allowing each sensor in \figref{random_access} to decide independently whether to access the channel would eliminate implementation and scheduling overheads of a central authority. However the lack of coordination among the transmitting sensors creates wireless interferences and packet collisions that may result in control performance degradation, or worse, loss of stability. My contribution is a framework for designing wireless random access mechanisms with control performance guarantees despite interferences as a constrained optimization problem. I proved an intuitive decoupled characterization of the optimal random access design. Each sensor should access the channel at a rate proportional to the desired control performance of its loop, and inverse proportional to the aggregate interference it causes on all other control loops. Moreover I developed algorithms to compute the optimal access rates without coordination among the sensors by either Lagrange dual arguments (see the Arxiv report and the CDC 2015 paper) or game-theoretic tools (see the NECSYS 2015 paper). I also proved that it is possible to allow sensors to opportunistically adapt to their local plant observations to improve performance in ICCPS 2016 paper).

Privacy and Security For Estimation and Control

While connectivity enhances operation and lowers costs, it also opens security vulnerabilities. Wireless communication is particularly susceptible due to the broadcast nature of the medium, where everyone can have access to transmit or receive messages. In my postdoctoral work I have been involved in the following privacy and security topics.

Secrecy in Estimation and Control

A most fundamental vulnerability in wireless cyber-physical systems is eavesdropping. Due to the broadcast nature of the wireless medium, eavesdroppers may intercept packets gaining access to critical system-state information online. Using this information the attacker breaches privacy and confidentiality, e.g., may identify a private system model or track a private state of the system online. This is a passive attack that cannot be easily detected, hence requires proactive measures for secrecy. In recent works we have developed novel countermeasures exploiting the model of the system dynamics as well as inherent wireless channel uncertainty. Using these two elements, we have developed communication schemes which guarantee that the eavesdropper is unable to track the system state for a long time horizon. These are control-theoretic resource-efficient countermeasures that can be used alongside or in place of more computationally intense encryption mechanisms. For more information see the IFAC 2017 paper and the Arxiv report.

Resilient sensor management

Attackers may exploit vulnerabilities to compromise devices, alter sensor measurements, or deny services and availability. These challenges call for a new system design perspective which is often termed resiliency, i.e., the ability to withstand attacks. In this context we have developed algorithms for resilient sensor management subject to, e.g., denial-of-service or wireless jamming attacks. Our algorithm is particularly suitable for large-scale applications due to its low-computational complexity while it also exploits the problem structure to provide strong performance guarantees. For more information see the CDC 2017 paper.

Cryptography for Optimization and Control Algorithms

Cryptographic tools are a classic solution to protect data from unauthorized users and its advantage is that it can be applied in a wide range of applications. Tailoring this tool to be employed in specific cyber-physical applications, such as state estimation or control from encrypted sensor measurements, opens up new opportunities to strengthen systems security. We have illustrated this by using cryptography in optimization algorithms over encrypted data, specifically quadratic optimization solvers using partially homomorphic encryption. Our algorithm enjoys strong cryptographic security guarantees, permitting privacy-preserving optimization, i.e., a server is able to solve a requested optimization problem over encrypted data without the ability to decrypt them. For more information see the CDC 2016 paper.