cvx_paramReachSet

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

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)

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

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)

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)