Qualitative Analysis of Dynamical Systems.

Date of Submission

December 1997

Date of Award

Winter 12-12-1998

Institute Name (Publisher)

Indian Statistical Institute

Document Type

Master's Dissertation

Degree Name

Master of Technology

Subject Name

Computer Science


Electronics and Communication Sciences Unit (ECSU-Kolkata)


Ray, Kumar Sankar (ECSU-Kolkata; ISI)

Abstract (Summary of the Work)

Modelling of dynamical systems is broadly classified into two catagories,i.e quantita- tive modelling and qualitative modelling.Currently,the most research works are based on the qualitative analysis rather than quantitative analysis because of its dependace on many factors such as nature of the plant(e.g.size ,complexity,nonlinerity,time-varying parameters,dynamic interactions),control objective and specifications, and cost consid- erations.Graph theoritic analysis of dynamical systems,uncertain system modelling and robust control or the qualitative analysis of interconnected systems have been fields where qualitative, rather than quantitative, results are the main motivation of researhese investigations try to follow the method of a control expert. Experienced control e..teers are able to solve their control task even if many details of the system dynamics are not known or deliberately neglected, because their knowledge about the principal bel + iral patterns, such as the existence of oscillations, saturation effects or limit cycles, or about the current output of the process in terms of subsets of the state space, rat accurate qualitative values, is sufficient for many control purposesOne of the main problems in qualitative modelling is the con ervatism of the results. Even for simple examples,such as mass-spring system,qualitative models yield a large et of trajectories.Although it can be proved that this set includes the qualitative description of the real system trajectory,this set also includes many beliavioural forms th:t no physically real dynamical system can perform(spurious solutions).The main reason for this is that the qualitative model is based on inadequate information about the real system, because the quality spaces used are too coarse.To circumvent this situation is the motivation for incorporating a new transition matrix concept which is capable of including more information about the system. This new kind of qualitative model has the form of nondeterministic or stochastic automata.Here it is assumed that the qualitative value r(k)} is received by means of a direction-wise quan- tiser. It can be shown that for a qualitatively given initial state (z(0)), the qualitative system trajectory is ambiguous. As a cosequence of the ambiguities of system perfor- mance, nondeterministic and stochastic automata are proposed as a resonable forms of qualitative models.These kinds of models can be used to analyse the qualitative behaviour of the system and, moreover, to design a qualitative controller. Here the work is based on the design of a qualitative controller for a pole balancing problem(inverted pendu- lum).The design procedure as well as the simulation results are discussed step by step by considering new transition matrix.


ProQuest Collection ID: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:28843063

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Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.



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