MPT_ONESTEPCTRL Computes low complexity controller for LTI systems
ctrlStruct = mpt_oneStepCtrl(sysStruct,probStruct)
ctrlStruct = mpt_oneStepCtrl(sysStruct,probStruct,Options)
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DESCRIPTION
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This function computes a low complexity controller for the system defined in
"sysStruct".
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INPUT
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sysStruct - System structure in the sysStruct format
probStruct - Problem structure in the probStruct format
See the MPT Manual for additional details on the structure format or
consult one of the example systems (e.g. Double_Integator) which were
provided with this package.
Options.maxCtr - Maximum number of iterations (default is 1000)
Options.scaling - Scaling the set at each iteration with a parameter
0 < lambda < 1 guarantees finite time convergence to a
robust invariant subset of the maximal control invariant
set. (Default: Options.scaling = 1)
Options.PWQlyap - if set to 1, compute PWQ Lyapunov function (default)
Options.verbose - Optional: level of verbosity
Options.Kinf - If set to 1, then K_inf will be computed. If set to 0,
C_inf will be computed. (default is 0)
Options.set_limit - If the invariant set has a chebychev redius which is
smaller than this value the iteration is aborted.
(Default is 1e-3)
Options.Vconverge - A non-zero value will force the algorithm to break if
relative increase of volume of atractive set at the next
iteration compared to volume of the set at the previous
iteration decreases below this value. E.g.
Options.Vconverge=1 will terminate the procedure if
(Vnew-Vold)/Vold*100 < 1.
NOTE! Currently works only for LTI systems!
NOTE! Value of this option has percents as units!
NOTE! Should only be used if you are computing Kinf set!!!
Options.useprojection - if true, uses projections to obtain feasible set. if
false, feasible sets are obtained by solving a
multi-parametric program.
(Default is true)
Note: If Options is missing or some of the fields are not defined, the default
values from mptOptions will be used (see help mpt_init)
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OUTPUT
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ctrlStruct - Controller structure with following fields:
Pn,Fi,Gi - for region Pn(i).H*x <= Pn.K(i) computed input is U=Fi{i}*x+Gi{i}
Ai,Bi,Ci - cost associated to each region (x'Aix + Bi*x + Ci)
Pfinal - The maximum control invariant set as a polytope object
dynamics - Dynamics active in region Pn(i)
details - Structure with more details about the solution:
lyapunovQ - Output of the function mpt_getPWQLyapFct
lyapunovL - Output of the function mpt_getPWQLyapFct
lyapunovC - Output of the function mpt_getPWQLyapFct
feasible - Output of the function mpt_getPWQLyapFct
loopCtr - Number of iterations needed to converge
feasibleN Set to 1, if LMI analysis was successfull
loopCtr Total number of iterations in computation
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LITERATURE
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"Complexity Reduction of Receding Horizon Control", P. Grieder and M. Morari;
In the Proceedings of the IEEE Conference on Decision and Control 2003, Maui, Hawaii
see also MPT_ITERATIVEPWA