cvx_zonoContSoftConstraint

implements the constraint functions encoding the (softened) sufficient conditions for zonotope containment.

Syntax
Description
Input Arguments
Output Arguments
See Also
References

Syntax

[cEq,cIneq] = cvx_zonoContSoftConstraint(cIn,GIn,cOut,GOut,Gamma,gamma,Gamma_abs,gamma_abs,ub,slack)

Description

This function implements the sufficient conditions for zonotope containment from [2, Corollary 4] in the softened version presented in [1, Remark 4], i.e. GIn = Gout*Gamma cOut - cIn = GOut*gamma norm([gamma, Gamma],|'inf'|) <= ub + slack slack >= 0 The input argument ub can either be a vector full of ones (for fixed circumbodies zonotope(cOut,Gout), see [2, Corollary 4]) or a vector of generator scaling factors for variable circumbodies of the form zonotope(cOut,Gout*diag(ub)), see [1, Remark 4]). The output arguments are in the form Ceq = 0, cIneq >= 0.

Input Arguments

cIn

center of the inbody (double array of dimension [nx,1])

GIn

generator matrix of the inbody (double array)

cOut

center of the inbody (double array of dimension [nx,1])

GOut

generator matrix of the inbody (double array)

Gamma

auxiliary variable (double array of dimension [size(GOut,2),size(GIn,2)])

gamma

auxiliary variable (double array of dimension [size(GOut,2),1])

Gamma_abs

absolute value of Gamma

gamma_abs

absolute value of gamma

ub

upper bound in the norm condition (double array of dimension [size(GOut,2),1])

slack

slack variable to soften upper bound in the norm condition (double array of dimension [size(GOut,2),1])

Output Arguments

cEq

constraint functions of the equality constraints

cIneq

constraint functions of the inequality constraints

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] S. Sadraddini and R. Tedrake, "Linear Encodings for Polytope Containment Problems," IEEE Conference on Decision and Control, 2019, pp. 4367-4372.

cIn	center of the inbody (double array of dimension [nx,1])
GIn	generator matrix of the inbody (double array)
cOut	center of the inbody (double array of dimension [nx,1])
GOut	generator matrix of the inbody (double array)
Gamma	auxiliary variable (double array of dimension [size(GOut,2),size(GIn,2)])
gamma	auxiliary variable (double array of dimension [size(GOut,2),1])
Gamma_abs	absolute value of Gamma
gamma_abs	absolute value of gamma
ub	upper bound in the norm condition (double array of dimension [size(GOut,2),1])
slack	slack variable to soften upper bound in the norm condition (double array of dimension [size(GOut,2),1])

cEq	constraint functions of the equality constraints
cIneq	constraint functions of the inequality constraints