Sparse Regression Codes for Networked Control Systems

Abstract

I denne afhandling undersøges Netværksbaserede Control Systemers (NCS) architecturer for Lineare Tidsinvariante (LTI) systemer, hvor et upålideligt båndbredde begrænset netværk med random IID pakketab, forbinder systemet (plant) og controlleren. For at gøre kontrolsystemet robust m.h.t. IID pakketab, bruges en aftagende horizon controller som minimerer en finite horizon cost funktion. For at kunne håndtere båndbredde begrænsede netværk, designes der i denne specialeafhandling sparse contol pakker ved brug af l0 penaliserede optimerings algoritmer på SPARC baserede ordbøger indeholdende IID Gaussiske vektorer eller latticer. Der sendes expectede fremtidige samt et nutidigt control signal til planten, således at N − 1 fremtidige controlsignaler kan genskabes såfremt pakken modtages af planten. De faktorer der adskiller denne specialeafhandling fra andre bidrag er, at der bruges fixed rate vektor quantizere baseret på SPARC, der har et finitivt support og derved kan overloade quantizeren i tilfælde af at der sker oscillationer i planten. Der designes forskellige SPARC ordbøger, der simuleres i et NCS med forskellige pakketabsrater på netværket. Resultaterne viser en god ydelse for bitrater ned til 2.75 bit/symbol når sandsynligheden for IID pakketab ikke overstiger 0.20. Dette ved brug af Gaussiske IID SPARC ordbøger. Lattice SPARC ordbøger opnår derimod ikke den samme ydelse ved disse bitrater, og kræver generelt bit rater på 3.75 eller 4 bit/symbol for at stabilisere et NCS. Til sidst opstilles der en netværksmodel indeholdende to states med hver deres pakketabsrate. Der designes forskellige SPARC ordbøger for hver state netværket kan antage. Der opstilles ligninger baseret på MJLS teori, således stabilitet for et system med givne transitions- og pakketabs sandsynligheder kan analyseres. Til sidst er systemer baseret på disse netværk blevet simuleret.

We study a Networked Control System (NCS) architecture for Linear Time Invariant (LTI) plants, where an unreliable data rate limited network, with random Independent and Identically Distributed (IID) packet dropouts occurring, connects the plant and the controller. To achieve robustness of the control system with respect to IID dropouts, a receding horizon controller is used which minimizes a finite horizon cost function. To deal with rate limited networks, we, in this thesis, wish to design sparse packets using l0 penalized optimization. This is done on Sparse Regression Code (SPARC) dictionaries containing lattices or IID Gaussian samples. We transmit the current and expected future control signals, such that on reception of the packet, the current signal as well as the next N − 1 future control signals can be reconstructed in the plant. The distinguishing factors of this thesis regarding to other available studies is that we use a fixed rate vector quantizer based on SPARC, featuring a finite support which can be overloaded in case of heavy oscillations in the plant. We design different SPARC dictionaries and simulate these in an NCS with different packet dropout rates on the network. Results show good performance at bit rates down to 2.75 bit/symbol with an IID packet dropout probability up to 0.20 when Gaussian IID SPARC dictionaries are used. The performance of a lattice SPARC dictionary is not able to reach these bit rates, and generally requires bit rates of 3.75 or 4 bit/symbol to stabilize the NCS. Finally we state an alternative network model featuring two network states with different dropout probabilities. A different SPARC dictionary is designed for each network state. We stated equations to analyze whether the system with given transition and dropout probabilities is stable using Markov Jump Linear System (MJLS) theory. This is followed by simulations of NCSs featuring these networks.

A master thesis from Aalborg University

Sparse Regression Codes for Networked Control Systems

[Sparse Regression Koder for Netværkedsbaserede Kontrolsystemer]