Optimization based controller synthesis for interconnected dynamical systems
Description: While the analysis of stand-alone control systems has reached some maturity, the dynamical systems and control communities face severe challenges due to the emergence of important new application fields, mainly in the area of large-scale interconnected systems and networks (control of communication networks, control of multi-agent systems, distributed sensing, decision making and control, tele-operation, controlled interaction with neural networks in biology,¡K). A typical modern control system is no longer a stand-alone system, but rather a heterogeneous collection of physical, information and communication systems. These new applications are described by highly complex models, exhibiting nonlinearities, different time-scales, as well as latency and saturation in the coupling. They require new types of controller or a hierarchy of controllers which are suitable for a distributed implementation, and which are not only expected to meet the nominal specifications, but also to scale well with respect to the system and network size. A common property of such controllers is that i) they need to be highly structured and ii) their dimension is much smaller than the dimension of the coupled system. This precludes the use of standard control design methods which typically results in optimal controllers with order larger or equal to the dimension of the plant. However, the recently developed direct optimization approaches for reduced order controller design (work by Noll, Apkarian, Burke, Lewis and Overton), are promising in this context, as our first results with delayed-coupled systems indicate.
The aim of this PhD project is to develop generic numerical methods for synthesizing controllers for large-scale interconnected dynamical systems, within an eigenvalue optimization framework. In order to master the overall complexity, an important challenge consists of exploiting structure and sparsity, both in the control design and it the development of numerical algorithms. The objectives are
1) Performing a qualitative analysis of the coupling effects in interconnected dynamical control systems, in order to reveal the underlying mechanisms. Attention will be paid to the influence of the network structure and topology, in relation with the local dynamics, on the overall behavior of the system, and to the generality and scalability of the results. This study will lead to the definition of appropriate controller structures, suitable for a distributed implementation and able to decouple the dynamics at different hierarchical levels;
2) Developing and implementing optimization based synthesis methods to compute the parameters of these controllers. The design specifications concern stability, robustness and performance measures in a ƒ¸2-ƒ¸„V setting, possibly combined with direct time-domain specifications;
3) Applying the results to the stability problem of relative equilibria, with particular emphasis to the control of ¡§swarms¡¨ of robots and to the analysis of networks of Hindmarch Rose models for neurons (the latter fits within an existing collaboration with the Eindhoven University of Technology) .
The research will be carried out at the Numerical Analyis and Applied Mathematics Section of the K.U.Leuven
Key words: control, optimization, numerical methods
Latest application date: 2010-08-01
Financing: dbof-scholarship
Type of Position: scholarship
Duration of the Project : 4 years
Research group: Department of Computer Science
Phd,Optimization based controller synthesis ,KUL,Belgium
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