Purdue University Graduate School

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posted on 2022-08-09, 19:17 authored by Jia ZhangJia Zhang


This thesis studies networked Gaussian linear control systems with random delays. Networked control systems is a popular topic these years because of their versatile applications in daily life, such as smart grid and unmanned vehicles. With the development of these systems, researchers have explored this area in two directions. The first one is to derive the inherent rate-cost relationship in the systems, that is the minimal transmission rate needed to achieve an arbitrarily given stability requirement. The other one is to design achievability schemes, which aim at using as less as transmission rate to achieve an arbitrarily given stability requirement. In this thesis, we explore both directions. We assume the sensor-to-controller channels experience independently and identically distributed random delays of bounded support. Our work separates into two parts. In the first part, we consider networked systems with only one sensor. We focus on deriving a lower bound, R_{LB}(D), of the rate-cost tradeoff with the cost function to be E{| x^Tx |} ≤ D, where x refers to the state to be controlled. We also propose an achievability scheme as an upper bound, R_{UB}(D), of the optimal rate-cost tradeoff. The scheme uses lattice quantization, entropy encoder, and certainty-equivalence controller. It achieves a good performance that roughly requires 2 bits per time slot more than R_{LB}(D) to achieve the same stability level. We also generalize the cost function to be of both the state and the control actions. For the joint state-and-control cost, we propose the minimal cost a system can achieve. The second part focuses on to the covariance-based fusion scheme design for systems with multiple > 1 sensors. We notice that in the multi-sensor scenario, the outdated arrivals at the controller, which many existing fusion schemes often discard, carry additional information. Therefore, we design an implementable fusion scheme (CQE) which is the MMSE estimator using both the freshest and outdated information at the controller. Our experiment demonstrates that CQE out-performances the MMSE estimator using the freshest information (LQE) exclusively by achieving a 15% smaller average L2 norm using the same transmission rate. As a benchmark, we also derive the minimal achievable L2 norm, Dmin, for the multi-sensor systems. The simulation shows that CQE approaches Dmin significantly better than LQE. 


Degree Type

  • Doctor of Philosophy


  • Electrical and Computer Engineering

Campus location

  • West Lafayette

Advisor/Supervisor/Committee Chair

Chih-Chun Wang

Additional Committee Member 2

Stanley Chan

Additional Committee Member 3

David J. Love

Additional Committee Member 4

Xiaojun Lin