# Constraint Enforcement

Modify control actions to satisfy constraints and action bounds

• Library:

## Description

The Constraint Enforcement block computes modified control actions that are closest to specified control actions subject to constraints and action bounds.

The block uses a quadratic programming (QP) solver to find the control action u that minimizes the function ${|u-{u}_{0}|}^{2}$. Here, u0 is the unmodified control action.

The solver applies the following constraints to the optimization problem.

`$\begin{array}{l}{f}_{x}+{g}_{x}u\le c\\ {u}_{\mathrm{min}}\le u\le {u}_{\mathrm{max}}\end{array}$`

Here:

• fx and gx are coefficients of the constraint function.

• c is a bound for the constraint function.

• umin is a lower bound for the control action.

• umax is an upper bound for the control action.

The Constraint Enforcement block requires Optimization Toolbox™ software.

For more information on constraint enforcement, see Constraint Enforcement for Control Design.

## Ports

### Input

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Unmodified control actions, specified as a scalar or a vector.

If the Number of actions parameter is `1`, connect u0 to a scalar signal. Otherwise, connect u0 to a vector signal with length equal to Number of actions.

Offset coefficient fx in the following constraint equation.

`${f}_{x}+{g}_{x}u\le c$`

If the Number of constraints parameter is `1`, connect fx to a scalar signal. Otherwise, connect fx to a vector signal with length equal to Number of constraints.

Linear coefficient gx in the following constraint equation.

`${f}_{x}+{g}_{x}u\le c$`

Connect gx to an Nc-by-Nu signal, where Nc is equal to the Number of constraints parameter and Nu is equal to the Number of actions parameter.

Run-time constraint bound c in the following constraint function.

`${f}_{x}+{g}_{x}u\le c$`

If the Number of constraints parameter is `1`, connect c to a scalar signal. Otherwise, connect c to a vector signal with length equal to Number of constraints.

If this port is disabled, the block uses the constant constraint bounds specified using the Constraint bound parameter.

#### Dependencies

To enable this input port, select the Use external source parameter.

To specify run-time upper bounds to the action signals, enable this input port. If this port is disabled, the block does not apply any upper bounds to the control actions.

If the Number of actions parameter is `1`, connect umax to a scalar signal. Otherwise, connect umax to a vector signal with length equal to Number of actions.

#### Dependencies

To enable this input port, select the Use external source for upper bound parameter.

To specify run-time lower bounds to the action signals, enable this input port. If this port is disabled, the block does not apply any lower bounds to the control actions.

If the Number of actions parameter is `1`, connect umin to a scalar signal. Otherwise, connect umin to a vector signal with length equal to Number of actions.

#### Dependencies

To enable this input port, select the Use external source for lower bound parameter.

### Output

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Modified control action returned by the QP solver.

If the solver finds solution before reaching the maximum number of iterations, u* outputs this optimal solution.

If the solver reaches the maximum number of iterations, optimization stops and u* outputs a suboptimal solution.

If the initial optimization problem is infeasible, the returned control action depends on the whether the block is configured to ignore constraint or action bounds. For more information, see the exitflag parameter.

If the Number of actions parameter is `1`, u* outputs a scalar signal. Otherwise, u* outputs a vector signal with length equal to Number of actions.

Optimization status of the QP solver. The following table shows the possible status values.

Exit FlagDescription
`1`The solver converged to an optimal solution with all constraints and bounds active. In this case, u* outputs the optimal control actions.
`2`The initial optimization problem was infeasible and the block is configured to ignore all constraints and bounds. In this case, u* outputs the unmodified control action u0.
`3`The initial optimization problem was infeasible. The block reran the optimization ignoring the action bounds and found a feasible solution, which the block outputs in u*.
`4`The initial optimization problem was infeasible. The block reran the optimization ignoring the constraint bounds and found a feasible solution, which the block outputs in u*.
`0`The solver reached the maximum number of iterations. The control actions output in u* might be suboptimal.
negative integer

The initial optimization problem was infeasible and one of the following scenarios applies.

• Rerunning the optimization without action bounds did not produce a feasible solution.

• Rerunning the optimization without constraint bounds did not produce a feasible solution.

• The block is configured to not ignore constraint and action bounds.

In this case, the control actions output in u* are zero.

#### Dependencies

To enable this output port, select the Optimization status parameter.

## Parameters

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Parameters Tab

Specify the number of constraints to enforce.

#### Programmatic Use

 Block Parameter: `nc` Type: character vector Default: `'1'`

Specify the number of actions to bound and optimize.

#### Programmatic Use

 Block Parameter: `nu` Type: character vector Default: `'1'`

Specify constant bounds for constraints. If the Number of constraints parameter is `1`, specify Constraint bound as a finite scalar. Otherwise, specify Constraint bound as a vector of finite value with length equal to Number of constraints.

If your constraints vary at run time, select the Use external source parameter and connect the run-time constraint signal to the c input port.

#### Dependencies

To enable this parameter, clear the Use external source parameter.

#### Programmatic Use

 Block Parameter: `c` Type: character vector Default: `'0'`

Select this parameter to add the c input port for external constraint bounds.

#### Programmatic Use

 Block Parameter: `external_c` Type: character vector Values: `'off'``'on'` Default: `'off'`

Select this parameter to add the umax input port for external upper action bounds.

#### Programmatic Use

 Block Parameter: `external_umax` Type: character vector Values: `'off'``'on'` Default: `'off'`

Select this parameter to add the umin input port for external lower action bounds.

#### Programmatic Use

 Block Parameter: `external_umin` Type: character vector Values: `'off'``'on'` Default: `'off'`
Block Tab

Specify the sample time for running the optimization.

#### Programmatic Use

 Block Parameter: `Ts` Type: character vector Default: `'0.1'`

Specify the maximum number of optimization iterations.

#### Programmatic Use

 Block Parameter: `maxiter` Type: character vector Default: `'200'`

Specify a tolerance value for constraint violations.

#### Programmatic Use

 Block Parameter: `tol` Type: character vector Default: `'1e-6'`

Select this parameter to add the exitflag output port for the optimization status of the QP solver.

#### Programmatic Use

 Block Parameter: `exitflag` Type: character vector Values: `'off'``'on'` Default: `'off'`

When you select this parameter, if the initial QP problem is infeasible, the block reruns the optimization with the constraints disabled.

When you select both this parameter and Ignore action bounds when QP is infeasible, if the initial QP problem is infeasible, the block outputs the unmodified action signal.

#### Programmatic Use

 Block Parameter: `relax_c` Type: character vector Values: `'off'``'on'` Default: `'off'`

When you select this parameter, if the initial QP problem is infeasible, the block reruns the optimization with the action bounds disabled.

When you select both this parameter and Ignore constraints when QP is infeasible, if the initial QP problem is infeasible, the block outputs the unmodified action signal.

#### Programmatic Use

 Block Parameter: `relax_u` Type: character vector Values: `'off'``'on'` Default: `'off'`

## Extended Capabilities

Introduced in R2021a

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