H2 Optimal Coordination of Homogeneous Agents Subject to Limited Information Exchange

Controllers with a diagonal-plus-low-rank structure constitute a scalable class of controllers for multi-agent systems. Previous research has shown that diagonal-plus-low-rank control laws appear as the optimal solution to a class of multi-agent H2 coordination problems, which arise in the control of wind farms. In this paper we show that this result extends to the case where the information exchange between agents is subject to limitations. We also show that the computational effort required to obtain the optimal controller is independent of the number of agents and provide analytical expressions that quantify the usefulness of information exchange

Conservatism and Scalability for Distributed Controller Synthesis of Interconnected Systems

Due to computational limitations, scalability constitutes one of the major concerns of the controller synthesis of large-scale systems. The aim of this project is to analyze the conservatism introduced by imposing specific structures on the constraints involved in the controller synthesis and then to reduce the conservatism imposing less structure, however still achieving some degree of decomposition

Optimal network implementable controllers for networked systems

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\u27s 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

Análisis y síntesis de estrategias de control para sistemas de larga escala: aplicación al espejo primario de GTC

El espejo primario del Gran Telescopio de Canarias es un sistema de gran escala fuertemente acoplado. Este acoplamiento, junto con la alta dimensionalidad de la planta hacen que sea complicado diseñar un controlador multivarible para el espejo del telescopio. Pese a ello se han diseñado diversos controladores atendiendo a una estrategia local-global consistente en la aplicación al sistema de dos acciones de control a distinto nivel. Los objetivos que se plantean son cancelar las oscilaciones del sistema consiguiendo, al mismo tiempo, que éste alcance el estado de consigna en el menor tiempo posible. De entre los controladores multivariables diseñados destaca uno por asignación de polos. Para llevar a cabo el estudio de la estabilidad del sistema en lazo cerrado con el control local-global se introducen los operadores de lifting y lifting inverso, que permiten expresar el sistema en lazo cerrado en función de una única frecuencia de muestreo y, por tanto, aplicar los métodos clásicos para el análisis de la estabilidad de los sistemas lineales. Se desarrolla un método para el desacoplo de la dinámica del espejo primario del gran telescopio de Canarias, que consiste en un cambio en la base de vectores propios del sistema. Los resultados obtenidos se formalizan y generalizan con objeto de poder aplicar este procedimiento a todos aquellos sistemas cuyas matrices de estado cumplan las mismas propiedades que las primario del gran telescopio. Una vez que se ha introducido el procedimiento para el desacoplo de la dinámica del espejo se realiza un estudio de cómo afecta a éste el hecho de incluir en el modelo del sistema las incertidumbres en la dinámica del espejo y el ruido producido por la acción del viento sobre los segmentos. Por último trata el problema del control de un modelo a escala del espejo primario del gran telescopio de Canarias. La maqueta consiste en dos únicos segmentos cuadrados cuya dinámica se ha modelado empleando un modelo ARMAX clásico. Los controladores diseñados para la maqueta corresponden a una estrategia integral, un compensador y un controlador H-infinito. A pesar de que con éste último se consigue mejorar ligeramente los resultados alcanzados con los dos primeros controladores, la estabilidad de la planta con incertidumbres en lazo cerrado supone una restrinción importante de cara, sobre todo, a conseguir rechazo al ruido en la frecuencia propia de los segmentos