Distributed control of large-scale systems : a Takagi-Sugeno fuzzy model-based approach

• Autor(a) principal: Rodrigo Farias Araújo
• Data de Publicação: 2019
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Repositório Institucional da UFMG
• Texto Completo: http://hdl.handle.net/1843/31445; https://orcid.org/0000-0002-9234-3507
• topic: Distributed control; Large-scale systems; Nonlinear systems; Takagi-Sugeno fuzzy models; Interconnected systems; Engenharia elétrica; Sistemas não- lineares

Large-scale systems have become increasingly common in modern society where many real systems are widely distributed in space and consist of a large number of interconnected subsystems with strong coupling among them. In this context, this thesis addresses the problem of distributed control of large-scale nonlinear systems which are described by TS fuzzy models interconnected by sector nonlinearities. An approach based on Lyapunov theory is used as a starting point for the distributed controller synthesis. A quadratic block-diagonal Lyapunov function is used to check the asymptotic stability of large-scale systems via sufficient conditions described in terms of LMI. In the first moment, this thesis deals with networked systems such no decomposition technique is applied to large-scale systems. Creating a large number of LMI usually generated when dealing with large-scale systems is prevented by defining an augmented vector created with state vectors and association functions of subsystems. In this case, state constraints and saturation in the control input are also considered, which are often found in practice and are generated by limitations in the physical system or in the description of models that represent them. Besides that, the proposed approach also allows to maximize the estimate of the domain of attraction where initial conditions belonging to the region converge asymptotically to the equilibrium point. In the sequel, the synthesis problem of distributed controllers for large-scale nonlinear systems is solved utilizing the so-called chordal decomposition. This decomposition takes advantage of the sparsity pattern of the graph associated with the large-scale system to decrease the computational complexity of the problem. Thus, the analysis of the computational complexity and the running time of the method show that solutions can be provided with reasonable computational efforts, even though the number of subsystems is very large. Finally, aiming to illustrate the effectiveness of the proposed methods for distributed control design, the stabilization of multiple inverted pendulums connected by nonlinear springs and the control of electrical power systems are considered.