Dissertation

2018

#### Degree Name

Doctor of Philosophy

#### Department

Electrical and Computer Engineering

#### Major

Electrical Engineering

Nicola Elia

#### Abstract

In this thesis, we study the problem of network implementable controllers for network distributed systems. Network distributed control problem gains importance by the increase in networked system applications in many areas which require network distributed control and estimation. By network implementable controller, we mean controller can be implemented over the given network with the predefined/given delay and sparsity constraints.

We define all stabilizing controllers by re-interpreting plant and controller. We define a congruent stable plant of the original plant which is not necessarily stable, such that the controller of the congruent plant is linearly function of the original plant's controller. When we put structural constraints on all stabilizing controllers of the stable congruent plant, these controllers embody controllers of the main plant. Therefore, all stabilizing controllers of the original plant are defined as all stabilizing controllers of the congruent plant with structural constraints. In the view of this problem, we obtain all stabilizing controller parametrization of the original plant wherein equality constraints are introduced on the Youla parameter. Moreover, we define a necessary and sufficient problem to attain a controller in the form of norm minimization problem benefiting formulated all stabilizing controller parametrization and provide a solution method for it.

Moreover, we introduce a doubly-coprime factorization of blkdiag(I_{n_x}, K) which allows us to have a network implementable state-space realization of a structured controller, K, which inherits sparsity and delay constraints introduced by the given network in z-domain, of a network distributed system with order n_x. By network implementable state-space realization, we mean state-space realization can be expressed as a strictly causal interaction of some sub-systems over the given network. We call such structured controllers as network realizable controller, i.e. controllers whose network implementable state-space realization can be obtained. Moreover, using the formulated controller problem, we provide a network realizable controller problem by introducing sparsity and delay constraints on the Youla parameter. Introduced network realizable controller problem is in the form of norm minimization problem with structural constraints introduced on Youla parameter. Afterwards, we obtain its equivalent unconstrained network realizable controller problem which allows us to attain a solution in infinite dimensional space benefiting existing solution methods of H_2 problem.

Moreover, we define a model matching problem and present an optimal network realizable controller problem. The formulated optimal network realizable controller problem is a constrained problem. To obtain an unconstrained problem formulation, we define a relaxation by a Lagrange multiplier and benefit from the vectorization method introduced in the literature. Formulated unconstrained problem allows us to obtain a solution using existing solution methods wherein solution lies in infinite dimensional space. Once the optimal network realizable controller is obtained, we obtain a network implementable state-space realization of it using the method we have introduced.

Furthermore, we provide an alternative all stabilizing network realizable controller \linebreak parametrization benefiting existing Youla parametrization which requires to have an initial controller. We show that when the given initial controller is network realizable, one can parametrize all stabilizing network realizable controllers with a network realizable Youla parameter. Moreover, we introduce network realizable controllers in the form of delayed controllers for strongly connected networked plants which allow us to parametrize all stabilizing network realizable controllers with the Youla parametrization aforementioned. We derive a model matching problem and define a necessary and sufficient optimal network realizable controller problem as a function of initial network realizable controller with sparsity and delay constraints introduced on Youla parameter. Moreover, we provide its equivalent unconstrained problem benefiting vectorization method wherein a solution in infinite dimensional space can be obtained benefiting existing solution methods.

Gulnihal Kucuksayacigil

en

application/pdf

134 pages

COinS