computeTermRegNonlinSysOpt

abstract superclass for optimization-based approaches for computing terminal regions of nonlinear systems.

Syntax
Description
Input Arguments
Output Arguments
See Also
References

Syntax

obj = computeTermRegNonlinSysOpt(X,U,W,xEq,uEq,termRegOrder)
obj = computeTermRegNonlinSysOpt(X,U,W,xEq,uEq,termRegOrder,solverSettings)

Description

This class and its childclasses provide all methods required for formulating and solving the convex [1] or polynomial [2] approximations of the terminal region optimization problem in [2, Eq. (6)] as well as the methods for verifying correctness of the candidate solutions.

Input Arguments

X

set of admissible states (class: interval / polytope / zonotope)

U

set of admissible control inputs (class: interval / polytope / zonotope)

W

set of uncertain disturbances (class: zonotope)

xEq

equilibrium state (array of dimension [X.dim,1])

uEq

equilibrium control input (array of dimension [U.dim,1])

termRegOrder

order of the zonotope representing the terminal region (positive integer)

verbose

if set to true, the algorithm prints information about each iteration to the command window. If set to false, no iterative output is shown.

solverSettings

(optional) struct with the following optional fields

.penaltyWeight

penalty weight for soft constraints, see [1, Remark 4] (positive scalar)

.convergenceTolerance

convergence tolerance, see [1, Eq. 18] (positive scalar)

.constraintTolerance

constraint tolerance (positive scalar)

.maxIter

max. number of iterations (positive integer)

.maxCostTerms

maximum admissible number of addends in the cost function, see [1, Remark 2] (positive interger)

.tr_maxRelErr

max. relative approximation error (see [1, App. II]) (0 < tr_malRelErr < 1)

.tr_shrink

scaling factor for shrinking the trust region (see; [1, App. II]) (0 < tr_shrink < 1)

.tr_grow

scaling factor for enlarging the trust region (see; [1, App. II]) (1 < tr_grow)

Output Arguments

obj

generated instance of the class computeTermRegNonlinSysOpt

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.