Molecular Modelling 

Many natural and engineered systems are composed of a set of coupled layers or a network of subsystems, characterized by different time scales and structural patterns. New notions, from multiplex networks to networks of networks, have been proposed to explore the properties of these systems, focusing mainly on their structural integrity and robustness. Consider a multiplex network, i.e., a set of coupled layered networks, where different layers have different characteristics. Such a system can be modeled as a layered network whose interconnections between layeres capture the interactions between a node in one layer and its counterpart in another layer. Similarly, in a network of networks each node itself is a network or a multi-input and multi-output (MIMO) subsystem. Different nodes (subsystems) could have total different dimensions and dynamics. This is rather different from the view of controlled framework where it is assumed that all the nodes share the same type of dynamics or even just scalar dynamics.

Developping a framework to control networks of networks is  a necessary step to understand the control principles of complex systems. Some controllability conditions on the overall network topology, the node dynamics, the external control inputs, and the inner interactions have been derived for a networked MIMO system. The controllability of the networked MIMO system is an integrated result of multiple factors, which cannot be decoupled into the controllability of the individual subsystem or the properties solely determined by the network topology.A general framework to systematically explore the control of networks of networks lacks.

Biological systems, being complex systems, are 'noisy'. Two kinds of noise affect them: first the intrinsic randomness of individual events and second the extrinsic influence of changing environments. On cellular level the intrinsic noise is rooted in the low copy number of biomolecules or diffusive cellular dynamics.

In quantum control it is difficult, if not impossible , to acquire information about quantum states without destroying them. Second, some classes of quantum control tasks, such as controlling quantum entanglement and protecting quantum coherence, are unique for quantum systems. There are no corresponding tasks in classical control theory.