Liapunov theory applied to control, games, and boundedness of generalized dynamical systems

Stonier, Russel James (1978). Liapunov theory applied to control, games, and boundedness of generalized dynamical systems PhD Thesis, School, Centre or Institute, The University of Queensland. doi:10.14264/uql.2014.448

       
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Author Stonier, Russel James
Thesis Title Liapunov theory applied to control, games, and boundedness of generalized dynamical systems
School, Centre or Institute School, Centre or Institute
Institution The University of Queensland
DOI 10.14264/uql.2014.448
Publication date 1978
Thesis type PhD Thesis
Supervisor J. M. Skowronski
Language eng
Subjects 0101 Pure Mathematics
Formatted abstract
Since its introduction, Liapunov's qualitative direct or "second" method has been applied in a variety of problems, particularly in non-linear mechanics and control systems.

In Chapter 1, we apply the Liapunov method in a study of various boundedness and ultimate boundedness properties of generalized dynamical systems. Strong and weak reachability of compact sets by such systems is also discussed.

We proceed in Chapters 2, 3 and 4 to examine the application of Liapunov theory in the discussion of qualitative objectives of two person games whose dynamics are firstly modelled by contingent equations, and then more abstractly by generalized dynamical systems. Particular attention is given to the modelling of two person games by generalized dynamical systems (Chapters 3 and 4), and the qualitative objectives are so chosen to make use of some results established in Chapter 1.

In Chapter 5, we again employ the Liapunov method in finding sufficient conditions in a control problem. Sufficient conditions are found for the qualitative objective - reachability of the target set Ccontrollability); and for the quantitative objective - minimization of an integral performance index. For problems with particular performance index, combined sufficiency theorems are given for both open loop and closed loop control functions. Our results are extended to the saddle point problem in a two person differential game.
Keyword Lyapunov functions

Document type: Thesis
Collection: UQ Theses (RHD) - UQ staff and students only
 
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