checkInvariance
computes the reachable set of the dynamical system and checks whether the the terminal region is a robust control invariant set.
Contents
Syntax
Description
This function is part of the verification procedure described in [1, Sec. III 2]: first over-approximations of the reachable sets are computed and, second, satisfaction of the constraints in [1, Eq. (6a), (6b)] / [2, Eq. (6b),(6c)] is checked. If the state constraint in [1, Eq. (6b)] / [2, Eq. (6c)] is violated, the difference of the support function of the reachable set in the violating direction A(j,:) and b(j) are computed (the set of admissible states is assumed to be represented as a polytope {x: A*x <= b}). This difference is used to tighten the set of admissible states in the next iteration of the verification procedure ({A*x <= b - b_tight}).
Input Arguments
|
obj |
instance of class computeTermRegNonlinSysOpt |
|
dynamics |
instance of class termRegNonlinSysDynamics |
|
termReg |
converged solution (class: termRegNonlinSysOpt) |
Output Arguments
|
flagInvariance |
indicates satisfaction of the invariance constraint in [1, Eq. 6a] (class: logical) |
|
flagStateConstraints |
indicates satisfaction of the state constraint in [1, Eq. 6b] (class: logical) |
|
b_tight |
tightening vector for the state constraint in [1, Eq. 6b] (non-negative double vector) |
See Also
@computeTermRegNonlinSysOpt/verifyTerminalRegion
References
[1] L. Schäfer et al. "Scalable Computation of Robust Control Invariant Sets of Nonlinear Systems", in IEEE Transactions on Automatic Control, vol. 69, no. 2, pp. 755-770, 2024. [2] L. Schäfer and M. Althoff, "Computing Robust Control Invariant Sets of Nonlinear Systems Using Polynomial Controller Synthesis," American Control Conference, 2024, pp. 4162-4169.
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