Contributions to analysis and control of takagi-sugeno systems via piecewise, parameter-dependent, and integral lyapunov functions

• Autores: Iván Temoatzin González Germán
• Directores de la Tesis: Antonio Sala (dir. tes.), Miguel Ángel Bernal Reza (dir. tes.)
• Lectura: En la Universitat Politècnica de València ( España ) en 2018
• Idioma: español
• Tribunal Calificador de la Tesis: Fernando Tadeo (presid.), J. V. Salcedo (secret.), Kevin Guelton (voc.)
• Programa de doctorado: Programa de Doctorado en Automática, Robótica e Informática Industrial por la Universitat Politècnica de València
• Materias:
  • Matemáticas
    • Investigación operativa
      • Sistemas de control
      • Formulación de sistemas
• Enlaces
  • Tesis en acceso abierto en: RiuNet
• Resumen

  • This thesis considers a Lyapunov-based approach for analysis and control of nonlinear systems whose dynamical equations are rewritten as a Takagi-Sugeno model or a convex polynomial one. These structures allow solving control problems via convex optimisation techniques, more specifically linear matrix inequalities and sum-of-squares, which are efficient tools from the computational point of view. After providing a basic overview of the state of the art in the field of Takagi-Sugeno models, this thesis address issues on piecewise, parameter-dependent and line-integral Lyapunov functions, with the following contributions:

    An improved algorithm to estimate the domain of attraction of nonlinear systems for continuous-time systems. The results are based on piecewise Lyapunov functions, linear matrix inequalities, and geometrical argumentations; level-set approaches in prior literature are significantly improved.

    A generalised parameter-dependent Lyapunov function for synthesis of controllers for Takagi-Sugeno systems. The approach proposed a multi-index control law that feeds back the time derivative of the membership function of the Takagi-Sugeno model to cancel out the terms that cause a priori locality in the Lyapunov analysis.

    A new integral Lyapunov function for stability analysis of nonlinear systems. These results generalise those based on line-integral Lyapunov functions to the polynomial framework; it turns out path-independency requirements can be overridden by an adequate definition of a Lyapunov function with integral terms.