Difference between revisions of "Fuller's problem"
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=== C Code === | === C Code === |
Revision as of 10:03, 7 August 2009
Fuller's problem | |
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State dimension: | 1 |
Differential states: | 2 |
Discrete control functions: | 1 |
Interior point equalities: | 4 |
The first control problem with an optimal chattering solution was given by <bibref>Fuller1963</bibref>. An optimal trajectory does exist for all initial and terminal values in a vicinity of the origin. As Fuller showed, this optimal trajectory contains a bang-bang control function that switches infinitely often.
The mathematical equations form a small-scale ODE model. The interior point equality conditions fix initial and terminal values of the differential states.
Contents
Mathematical formulation
For almost everywhere the mixed-integer optimal control problem is given by
Parameters
We use .
Reference Solutions
Source Code
C Code
The differential equations in C code:
Miscellaneous and further reading
An extensive analytical investigation of this problem and a discussion of the ubiquity of Fuller's problem can be found in <bibref>Zelikin1994</bibref>, a recent investigation of chattering controls in relay feedback systems in <bibref>Johansson2002</bibref>.
References
<bibreferences/>