# cvx_zonoContSoftConstraint

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

## Contents

- 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

## See Also

-

## 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.

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