Robust observer structures and control design for linear and nonlinear dynamical systems with applications
Anahita Moradmand · 2023
This thesis focuses on designing different class of observers and controllers for linear and nonlinear systems. We categorize the topics into two primary parts: the first focusing on observer design, and the second on controller design and stability analysis. In the initial step, a robust fault detection approach using observers for linear systems is proposed where we combine the unknown input observer UIO and an extended proportional integral observer PIO, which has a fading term for robust fault detection (PIFUIO). We extend our result to nonlinear systems with special structures as the design of nonlinear observers had limitations for general types of nonlinear systems. In the second step, the analysis and design of positive systems are considered whereby positive stabilization and the design of positive unknown input observer (PUIO) are introduced. Then, the robust stability analysis of this class of systems is studied in which the robust stability is formulated in terms of LMI. The class of separable positive nonlinear systems is also analyzed and the design of the observer and controller are provided. Moreover, we extend our design from Lipschitz type nonlinearity to state-dependent type by focusing on interconnected systems where we propose a distributed control architecture to take advantage of the global performance similar to centralized control and leverage the benefits of decentralized control. Finally, the problem of optimal control of nonlinear interconnected systems is addressed. --Author's abstract