In the Model Predictive Control Toolbox, the default implementation of MPC uses slack variables to handle constraints. Setting these slack variables to zero converts the constraints into hard constraints. The constraint violation penalty weight indicates the weightage given to the slack variable in a minimization problem, as detailed here:
Raising this weight to a high value makes the constraints stricter.
Here's how it can be done:
- If using the standard cost function and the propertynlmpc.Optimization.ReplaceStandardCostis set tofalse, increasing thenlmpc.Weights.ECRvalue raises the weight on the slack variables. More details are available here:
- When specifying a custom cost function for a nonlinear MPC controller, it's possible to replace or augment the standard quadratic MPC cost function. By default, anlmpccontroller replaces the standard cost function with the custom one, treating all constraints as hard constraints.
- To combine standard and custom costs, setnlmpc.Optimization.ReplaceStandardCostto false, similar to the first scenario, allowing adjustments to thenlmpc.Weights.ECR property.
The attached file example_R2024b.m contains a simple example with a custom cost function andnlmpc.Optimization.ReplaceStandardCostset totrue, treating the constraint 
as a hard constraint.
as a hard constraint. The plot of the states shows that state x remains within 5, even when the reference/desired state is 10.
For more detailed information, check out these pages:
- Specify Constraints for Nonlinear MPC:https://www.mathworks.com/help/releases/R2024b/mpc/ug/specify-constraints-for-nonlinear-mpc.html
- Specify Cost Function for Nonlinear MPC:https://www.mathworks.com/help/releases/R2024b/mpc/ug/specify-cost-function-for-nonlinear-mpc.html
I believe this will assist you!
