# Barrier Certificate Enforcement

Modify control actions to satisfy barrier certificate constraints and action bounds

*Since R2022a*

**Libraries:**

Simulink Control Design /
Constraint Control

## Description

The Barrier Certificate Enforcement block computes the modified control actions that are closest to specified control actions subject to barrier certificate constraints and action bounds.

The block uses a quadratic programming (QP) solver to find the control action
*u* that minimizes the function $${\left|u-{u}_{0}\right|}^{2}$$. Here, *u*_{0} is the unmodified
control action.

The solver applies the following constraints to the optimization problem.

$$\begin{array}{l}{q}_{x}{f}_{x}+{q}_{x}{g}_{x}u+\gamma {h}_{x}^{\beta}\ge 0\\ {u}_{\mathrm{min}}\le u\le {u}_{\mathrm{max}}\end{array}$$

Here:

*f*and_{x}*g*are functions defined by the plant dynamics $$\dot{x}=f(x)+g(x)u$$._{x}*h*is the control barrier function._{x}*q*is the partial derivative of the control barrier function over states_{x}*x*.*γ*is the constraint factor.*β*is the constraint power.*u*_{min}is a lower bound for the control action.*u*_{max}is an upper bound for the control action.

The Barrier Certificate Enforcement block requires Optimization Toolbox™ software.

For more information on barrier certificate enforcement, see Barrier Certificate Enforcement for Control Design.

## Examples

## Ports

### Input

### Output

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2022a**