This chapter introduces key elements of dynamical systems theory with special emphasis on those concepts leveraged in the next chapters for the design of control systems and machine learning methods based on reproducing kernel Hilbert spaces. Special emphasis is given to the notions of stability, boundedness, attractivity, and control of Lyapunov functions. A dedicated section discusses distributed parameter systems.

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Elements of Dynamical Systems Theory

  • Andrew J. Kurdila,
  • Andrea L’Afflitto,
  • John A. Burns

摘要

This chapter introduces key elements of dynamical systems theory with special emphasis on those concepts leveraged in the next chapters for the design of control systems and machine learning methods based on reproducing kernel Hilbert spaces. Special emphasis is given to the notions of stability, boundedness, attractivity, and control of Lyapunov functions. A dedicated section discusses distributed parameter systems.