H2-Conic Controller Synthesis
Input-output stability theory is crucial in robust control. Since it does not necessarily involve investigations about properties of states within the system, but only examines the relationships between inputs and outputs, input-output theory simplifies analysis of stability for systems with complicated models or even no clear state-space expressions. As part of input-output theory, the Conic Sector Theorem can be used as a tool in controller synthesis. Compared to the commonly-used Passivity Theorem, the Conic Sector Theorem is applicable to more general cases. For example, the Passivity Theorem cannot be used to synthesize systems with passivity violations caused by factors such as noise, delays, and discretizations. This research investigates application of the Conic Sector Theorem in time-delay systems and develops a controller synthesis procedure that accounts for the optimal performance, robustness, and stability of the system.
Two key contributions are established in this work. First, a survey of theory and designs related to the Passivity Theorem and the conic sector theorem is given. Second, this research develops a method to synthesize conic, observer-based controllers by minimizing an upper-bound on the closed-loop H2-norm. The proposed method can be seen as the dual of an existing optimal synthesis method, but with an alternative initialization to expand the set of plants for which it is feasible. Moreover, the proposed method only involves solving convex optimization problems, thus making them readily solvable with existing software. Numerical simulations show that the new method leads to better performance in some examples and therefore provides a useful alternative tool for robust and optimal control.
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