# cvx_paramReachSet

computes the parameterized approximation of the time-point reachable set.

## Contents

- Syntax
- Description
- Input Arguments
- Output Argument
- See Also
- References

## Syntax

[c_Rparam,G_Rparam] = cvx_paramReachSet(obj,var_s,var_Gctrl,var_RabsEerr,Rfexp,AB_d,RlinW,termRegSet)

## Description

This function computes the center and generator matrix of the zonotope representing the parameterized time-point reachable set as described in [1, Eq. 19a and Eq. 20].

## Input Arguments

obj | instance of class computeTermRegNonlinSysLinApproach
var_s | generator scaling factors (positive double vector of dimension; [obj.termRegOrder*obj.nx,1])
var_Gctrl | generator matrix of zonotopic representation of the invariance-preserving control law (double matrix of dimension; [obj.nu,obj.termRegOrder*obj.nx])
var_RabsEerr | reachable set due to set of abstraction errors (struct with the fields:; .c: center of var_Rerr; (double vector of length nx); .G: generator matrix of var_Rerr; (double matrix); )
Rfexp | reachable set of the linearized system due to the constant input "dynamics evaluted at expansion point" (class: zonotope)
AB_d | horizontal concatenation of system matrix and input matrix of the linearized system dynamics (class: matZonotope)
RlinW | reachable set of the linearized dynamics due to the disturbances (class: zonotope)
termRegSet | current candidate for the the terminal region (class: zonotope)

## Output Argument

c_Rparam | center of the parameterized reachable set at the next time step (double array of dimension [nx,1])
G_Rparam | generator matrix of the parameterized reachable set at the next time step (double array)

## 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

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