Constraint Enforcement

Modify control actions to satisfy constraints and action bounds

Since R2021a

Libraries:
Simulink Control Design / Constraint Control

Description

The Constraint Enforcement block computes the 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.

$\begin{array}{l} f_{x} + g_{x} u \leq c \\ u_{\min} \leq u \leq u_{\max} \end{array}$

Here:

f_x and g_x are coefficients of the constraint function.
c is a bound for the constraint function.
u_min is a lower bound for the control action.
u_max 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.

Examples

Train Reinforcement Learning Agent with Constraint Enforcement

Train a reinforcement learning agent with actions constrained using the Constraint Enforcement block.

Open Live Script

Enforce Constraints for PID Controllers

Apply a known constraint function to a PID control application using the Constraint Enforcement block.

Open Live Script

Learn and Apply Constraints for PID Controllers

Learn and apply an unknown constraint function for a PID control application using the Constraint Enforcement block.

Open Live Script

Train RL Agent for Adaptive Cruise Control with Constraint Enforcement

Train a reinforcement learning agent for adaptive cruise control with enforced constraints on velocity and following distance.

Open Live Script

Ports

Input

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u0 — Control actions
scalar | vector

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.

fx — Constraint function offset coefficient
scalar | vector

Offset coefficient f_x in the following constraint equation.

$f_{x} + g_{x} u \leq c$

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.

gx — Constraint function linear coefficient
scalar | vector | matrix

Linear coefficient g_x in the following constraint equation.

$f_{x} + g_{x} u \leq c$

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

c — Constraint bounds
scalar | vector

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

$f_{x} + g_{x} u \leq c$

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.

umax — Action signal upper bounds
scalar | vector

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.

umin — Action signal lower bounds
scalar | vector

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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u* — Modified control action
scalar | vector

Modified control action returned by the QP solver.

If the solver finds a 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.

exitflag — Optimization status
`1` | `2` | `3` | `4` | `0` | negative integer

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

Exit Flag	Description
`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

Number of constraints — Number of constraints
`1` (default) | positive integer

Specify the number of constraints to enforce.

Programmatic Use

Block Parameter: nc

Type: character vector

Default: '1'

Number of actions — Number of actions
`1` (default) | positive integer

Specify the number of actions to apply bounds to and optimize.

Programmatic Use

Block Parameter: nu

Type: character vector

Default: '1'

Constraint bound — Constraint bounds
`0` (default) | finite scalar | vector

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'

Use external source — Add external constraint bound input port
`off` (default) | `on`

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'

Use external source for upper bound — Add upper action bound input port
`off` (default) | `on`

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'

Use external source for lower bound — Add lower action bound input port
off (default) | on

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

Sample time — Optimization sample time
`0.1` (default) | positive scalar

Specify the sample time for running the optimization.

Programmatic Use

Block Parameter: Ts

Type: character vector

Default: '0.1'

Maximum iterations — Maximum optimization iterations
`200` (default) | positive integer

Specify the maximum number of optimization iterations.

Programmatic Use

Block Parameter: maxiter

Type: character vector

Default: '200'

Constraint tolerance — Tolerance for constraint violations
`1e-6` (default) | nonnegative scalar

Specify a tolerance value for constraint violations.

Programmatic Use

Block Parameter: tol

Type: character vector

Default: '1e-6'

Optimization status — Add exit flag output port
`off` (default) | `on`

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'

Ignore constraints when QP is infeasible — Disable constraints when optimization is infeasible
`off` (default) | `on`

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'

Ignore action bounds when QP is infeasible — Disable action bounds when optimization is infeasible
`off` (default) | `on`

When you select this parameter, if the initial QP problem is infeasible, the block reruns the optimization with the action bounds disabled. The block ignores this parameter if both the umax and umin input ports are 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

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

The Constraint Enforcement block supports code generation for double-precision signals only.

Version History

Introduced in R2021a

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R2023b: Library location changed

The Constraint Enforcement block is now in the Simulink Control Design/Constraint Control sublibrary.

In R2023b, when you open a model saved in a previous release, the library links for Constraint Enforcement blocks update automatically.

Constraint Enforcement

Description

Examples

Train Reinforcement Learning Agent with Constraint Enforcement

Enforce Constraints for PID Controllers

Learn and Apply Constraints for PID Controllers

Train RL Agent for Adaptive Cruise Control with Constraint Enforcement

Ports

Input

u0 — Control actions scalar | vector

fx — Constraint function offset coefficient scalar | vector

gx — Constraint function linear coefficient scalar | vector | matrix

c — Constraint bounds scalar | vector

Dependencies

umax — Action signal upper bounds scalar | vector

Dependencies

umin — Action signal lower bounds scalar | vector

Dependencies

Output

u* — Modified control action scalar | vector

exitflag — Optimization status 1 | 2 | 3 | 4 | 0 | negative integer

Dependencies

Parameters

Number of constraints — Number of constraints 1 (default) | positive integer

Programmatic Use

Number of actions — Number of actions 1 (default) | positive integer

Programmatic Use

Constraint bound — Constraint bounds 0 (default) | finite scalar | vector

Dependencies

Programmatic Use

Use external source — Add external constraint bound input port off (default) | on

Programmatic Use

Use external source for upper bound — Add upper action bound input port off (default) | on

Programmatic Use

Use external source for lower bound — Add lower action bound input port off (default) | on

Programmatic Use

Sample time — Optimization sample time 0.1 (default) | positive scalar

Programmatic Use

Maximum iterations — Maximum optimization iterations 200 (default) | positive integer

Programmatic Use

Constraint tolerance — Tolerance for constraint violations 1e-6 (default) | nonnegative scalar

Programmatic Use

Optimization status — Add exit flag output port off (default) | on

Programmatic Use

Ignore constraints when QP is infeasible — Disable constraints when optimization is infeasible off (default) | on

Programmatic Use

Ignore action bounds when QP is infeasible — Disable action bounds when optimization is infeasible off (default) | on

Programmatic Use

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

Version History

R2023b: Library location changed

See Also

Topics

u0 — Control actions
scalar | vector

fx — Constraint function offset coefficient
scalar | vector

gx — Constraint function linear coefficient
scalar | vector | matrix

c — Constraint bounds
scalar | vector

umax — Action signal upper bounds
scalar | vector

umin — Action signal lower bounds
scalar | vector

u* — Modified control action
scalar | vector

exitflag — Optimization status
`1` | `2` | `3` | `4` | `0` | negative integer

Number of constraints — Number of constraints
`1` (default) | positive integer

Number of actions — Number of actions
`1` (default) | positive integer

Constraint bound — Constraint bounds
`0` (default) | finite scalar | vector

Use external source — Add external constraint bound input port
`off` (default) | `on`

Use external source for upper bound — Add upper action bound input port
`off` (default) | `on`

Use external source for lower bound — Add lower action bound input port
off (default) | on

Sample time — Optimization sample time
`0.1` (default) | positive scalar

Maximum iterations — Maximum optimization iterations
`200` (default) | positive integer

Constraint tolerance — Tolerance for constraint violations
`1e-6` (default) | nonnegative scalar

Optimization status — Add exit flag output port
`off` (default) | `on`

Ignore constraints when QP is infeasible — Disable constraints when optimization is infeasible
`off` (default) | `on`

Ignore action bounds when QP is infeasible — Disable action bounds when optimization is infeasible
`off` (default) | `on`

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.