PhD ceremony Mr. N. Monshizadeh Naini: Model reduction and control of complex systems

PhD ceremony: Mr. N. Monshizadeh Naini

Dissertation: Model reduction and control of complex systems

Promotor(s): prof. H.L. Trentelman, prof. M.K. Camlibel

Faculty: Mathematics and Natural Sciences

This thesis addresses several problems related to model reduction and control of complex systems. First, an extended balanced truncation method is established for model reduction of switched linear systems (SLS). Second, we propose a method to reduce the dynamic order of agents in a network, while stability or synchronization is preserved in the reduced order model. In addition, we establish a priori model reduction error bounds to compare the behavior of the original network to that of the reduced order model. Third, in contrast to the previous order reduction approach, we aim at reducing the size of the underlying interconnection structure. For this purpose, a model reduction technique is proposed which is based on clustering the vertices (agents) of the underlying communication graph by means of suitable graph partitions. As a forth problem, we carry out stability and synchronization analysis for networks where agents have general, yet identical, linear dynamics and the underlying communication topology may switch arbitrarily within a finite set of admissible topologies. Fifth, we investigate the property of strong structural controllability for systems defined on a graph. In particular, we will show that there is a one-to-one correspondence between the set of leaders rendering the network controllable and the so-called zero forcing sets. Finally, the disturbance decoupling problem for networks of dynamical agents is studied from a graph topological perspective. Conditions in terms of graph partitions are proposed that guarantee the solvability of the disturbance decoupling problem.