initialGuessSet_mRPI
computes an (invariant) outer approximation of the minimal robust positively invariant set of the linearized dynamics.
Contents
Syntax
minRPIset = initialGuessSet_mRPI(obj,dynamics,Q,R,flag_invariant)
Description
To obtain an initial guess for the optimization-based approaches for computing terminal regions of nonlinear systems, we compute an outer approximation of the minimal robust positvely invariant (mRPI) set of the linearized dynamics (based on [1, Alg. 2]). By default, the loop in [1, Alg. 2, line 10-16] is omitted and the output order of initGuess is set to a user-defined value (see description of input arguments). If the additional input argument flag_invariant is set to true, this loop is executed.
Input Arguments
|
obj |
instance of class computeTermRegNonlinSysOpt |
|
dynamics |
instance of class termRegNonlinSysDynamics |
|
Q |
state weighting matrix (positive-definite matrix of dimension; [obj.nx,obj.nx]) |
|
R |
control input weighting matrix (positive-definite matrix of dimension; [obj.nu,obj.nu]) |
|
flag_invariant |
(optional), see description - if omitted or false, the user-defined order is chosen as opts.termRegOrder (logical) |
Output Arguments
|
minRPIset |
outer approximation of the mRPI set (class: termRegNonlinSysLinApproach) |
See also
References
[1] Gruber et al., "Computing safe sets of linear sampled-data systems", 2021, IEEE Control Systems Letter, vol. 5, no. 2, pp. 385-390.
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