Stability Analysis of Nonlinear Control Systems Using Genetic Programming

Created by W.Langdon from gp-bibliography.bib Revision:1.3973

@PhdThesis{Grosman:thesis,
  author =       "Benyamin Grosman",
  title =        "Stability Analysis of Nonlinear Control Systems Using
                 Genetic Programming",
  school =       "Department of Chemical Engineering, Technion",
  year =         "2008",
  keywords =     "genetic algorithms, genetic programming",
  URL =          "http://www.graduate.technion.ac.il/Theses/Abstracts.asp?Id=24203",
  abstract =     "This thesis describes the use of genetic programming
                 in stability analysis and control synthesis for
                 nonlinear autonomous dynamic systems. The main ideas
                 are associated with the Lyapunov direct method and
                 optimal control synthesis driven by the solution of the
                 Hamilton-Jacobi-Bellman (HJB) equation.

                 A novel genetic programming code was written for the
                 purpose of disclosing non-trivial Lyapunov functions.
                 These functions were used initially for stability
                 analysis, and subsequently for the synthesis of
                 nonlinear optimal controllers. The work required the
                 transformation of abstract mathematical concepts into a
                 computer language format. This included satisfying the
                 general Lyapunov conditions for stability, the
                 identification of connected sets, the detection of
                 their boundaries and other related topics. In addition
                 it was necessary to address optimal control issues,
                 through the near-solution of the
                 Hamilton-Jacobi-Bellman (HJB) equation.

                 The GP has the capacity to discover non-trivial
                 Lyapunov functions that achieve good approximations to
                 the domains of attraction for a variety of nonlinear
                 dynamic systems. Moreover, the task of finding an
                 approximation to the solution of the HJB equation
                 around a working point was demonstrated on a number of
                 autonomous control systems. In cases where the results
                 included non-polynomial terms that are difficult to
                 solve analytically, this obstacle was overcome by using
                 high-order Taylor series expansions. These expansions
                 were shown to be proper Lyapunov functions, which were
                 analysed using a positivity test for multivariable
                 polynomials.

                 Numerous case-studies were examined, including a
                 comparison of the method with the well-known work of
                 Vennelli and Vidyasagar on detecting domains of
                 attraction. Moreover, the control synthesis was
                 compared with well-established control techniques such
                 as feedback linearisation as well as other related
                 works on optimal control.

                 The methodology demonstrated in this work represents a
                 viable attractive alternative analysis method for the
                 investigation of nonlinear dynamic systems, both in
                 open and closed loop, which can be harnessed in
                 numerous fields of research where a guideline for
                 disclosing unknown Lyapunov functions is lacking.",
  notes =        "Supervisor: Prof. Lewin Daniel",
}

Genetic Programming entries for Benyamin Grosman

Citations