Geometric Aspects of Interconnection and Damping Assignment - Passivity-Based Control
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This dissertation deals with smooth feedback stabilization of control-affine systems via Interconnection and Damping Assignment - Passivity-Based Control (IDA-PBC). The IDA-PBC methodology is a feedback control design technique that aims to establish or manipulate a port-Hamiltonian structure of the closed-loop system. For a mechanical control system, a port-Hamiltonian system is a natural description of the dynamics, and several effective controller designs have been presented for this class of systems. In other fields of engineering, the development of such controller design is an active area of research. In particular, applications of IDA-PBC techniques prove to be difficult in practice for process control applications where the concept of energy is usually ill-defined. This thesis seeks to extend the application of the IDA-PBC methodology beyond mechanical control systems. This is achieved by following three directions of research. First, we establish conditions under which a port-Hamiltonian system can be written as a feedback interconnection of two port-Hamiltonian system. We identify such an interconnection structure for linear control systems based on their intrinsic properties. Second, as observed in application of IDA-PBC to non-mechanical systems, several additional assumptions on the structure of the desired port-Hamiltonian system can effectively reduce the complexity of the matching problem. We establish a unified approach that considers these additional assumptions. Third, we connect the matching problem to the classical feedback equivalence approach. We show that feedback equivalence between control-affine systems can be employed to construct some feasible interconnection and damping structures.