# cvxSetOpt

computes an updated candidate terminal region and the corresponding safety-preserving controller.

## Contents

- Syntax
- Description
- Input Arguments
- Output Arguments
- See also
- References

## Syntax

[res, opts] = cvxSetOpt(res, opts, enlarge)

## Description

This function computes the ingredients for, solves, and post-processes the solution of the convex programming approximation for the computation of a robust control invariant (RCI) set for a nonlinear sampled-data system.

## Input Arguments

candTermReg | current candidate for the terminal region (class: zonotope)
opts | structure containing the algorithm settings
.X | set of admissible states (class: interval)
.U | set of admissible control inputs (class: interval)
.W | set of disturbances (class: interval)
.nx | dimension of state space
.nu | dimension of input space
.nw | dimension of disturbance space
.Ninter | number of intermediate time steps [{1} / positive integer]
.timeStep | sampling time [{0.1} / positive scalar]
.timeStepCtrl | sampling time for the control inputs [-.timeStep/-.Ninter]
.xEq | equilibrium point for the terminal region
.uEq | control input for the equilirium point
.trustRegionAlg | structure containing the trust region and parameters for updating the trust region
.scvx | parameters for successive convexification
.sys | structure containing the nonlinearSys object modeling the dynmical system
.linDyn | strucutre containing the matrices of the linearized dynamical system
enlarge | enlargement factor for abstraction error - optional argument (class: double)

## Output Arguments

res | structure containing the results of the last iteration
.termReg | updated candidate terminal Region (class: zonotope)
.inputFF | sets representing the safety-preserving controller associated with -.termReg (cell array of zonotopes)
.assignInput | maps generators of -.inputFF to generators of -.termReg (cell array of double arrays)
.flag | indicates feasibility of the solution of convex program (class: boolean)
.time.cvx | (approx. of) solver time
.time.cvxSetup | elasped time for setting up the convex program in standard form
.cost.set | set whose volume is was maximized (-.termReg or inscribed set) (class: zonotope)
.linReach.Rtp | approximation of the time-point reachable set, see [1] (class: zonotope)
.linReach.Rti | approximation of the time-interval reachable set, see [1] (class: zonotope)
opts | updated opts structure - updated fields:
.trustRegionAlg.trustRegion | updated trust region (class: zonotope)

## See also

`terminalRegion`, `termRegNonlinSysLinApproach`

## References

[1] L. Schäfer et al. "Scalable Computation of Robust Control Invariant Sets of Nonlinear Systems", 2023, IEEE Transactions on Automatic Control [2] M. Althoff et al. "Reachability Analysis of Nonlinear Systems with Uncertain Parameters using Conservative Linearization", 2008 47th IEEE Conference on Decision and Control, 2008, pp. 4042-4048

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