Defence Arijit Sarkar: "System-Theoretic Model Reduction for Nonlinear Systems, Subtitle: Structure-Preserving Approaches"
Promotors: 1st promotor: Prof Jacquelien Scherpen, 2nd promotor: Prof Bayu Jayawardhana
Abstract: Complexity reduction and reduced-order modelling of dynamic systems are among the fundamental and beloved research topics within the systems and control community. It's no secret that the crucial need for model reduction is driven by practical applications, due to the demand for faster simulations, simplified analysis, and cheaper control design. Nevertheless, system-theoretical guarantee is one of the important facets of the model reduction paradigm. In this thesis, we consider various structural properties of nonlinear dynamical systems that must be preserved using a balancing-based model reduction approach. First, we consider a generic nonlinear Port-Hamilton structure to propose a structure-preserving model reduction approach. Second, we propose a computationally feasible tensor-based approach to find a nonlinear balancing transformation for polynomial dynamical systems. We also analyse the computational effectiveness of the proposed approach. Third, by extending the framework of differential balancing, we propose an extended differential balancing theory that not only provides flexibility to preserve certain structural properties but also offers a less conservative a priori error bound. Fourth, we propose a novel balancing theory based on stability, excitability, and transparency. Fifth, in this dissertation, we consider constrained nonlinear systems and propose a balancing-based model reduction approach that takes the system's constraints into account. Finally, we propose a scalable lumped parameter model for flexible structures, which are evident in various mechanical components of engineering systems. We choose the paradigm of port-Hamiltonian systems to propose the model and analyse its applicability to retain certain essential physical properties.