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# mpt_reachXU

## PURPOSE

MPT_REACHXU One-step reachability computation for an affine system

## SYNOPSIS

function [Xn, V] = mpt_reachXU(X0, U0, A, B, f, Options)

## DESCRIPTION

MPT_REACHXU One-step reachability computation for an affine system

Xn = mpt_reachXU(X0, U0, A, B);
Xn = mpt_reachXU(X0, U0, A, B, f);
[Xn, V] = mpt_reachXU(X0, U0, A, B);

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DESCRIPTION
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Computes set Xn such that

Xn = { xn | xn = A*x + B*u + f, x \in X0, u \in U0}

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INPUT
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X0       - set of initial conditions on states
U0       - set of initial conditions on inputs
A, B, f  - state update matrices

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OUTPUT
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Xn       - polytope Xn (may be not full dimensional)
V        - vertices of Xn

see also POLYTOPE/RANGE, MPT_REACHSETS

## CROSS-REFERENCE INFORMATION

This function calls:
• chebyball CHEBYBALL Computes center and radius of the largest ball inscribed in a polytope
• dimension DIMENSION Returns dimension of the given polytope
• end END Returns the last element in a given polytope array
• extreme EXTREME Calculates extreme points of a given polytope
• isfulldim ISFULLDIM Checks if a polytope is full dimensional
• polytope POLYTOPE Default constructor for the POLYTOPE object
• projection PROJECTION Projection of a polytope or a polytope array
• range RANGE Affine transformation of a polytope
• size SIZE Returns size of the given polytope object
• mpt_reachXU MPT_REACHXU One-step reachability computation for an affine system
This function is called by:
• mpt_reachXU MPT_REACHXU One-step reachability computation for an affine system

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