(Computer Control)8. MPC with Constraints

Model Predictive Control

Model Predictive Control with Constraints

From the last note, we have the augmented state space model

If we denote

We have

Now we will discuss different kinds of constraints.

1. Constraints on the control variable incremental variation

We will have

Equally, we have

2. Constraints on the amplitude of control variable

Equally, we have

We can get the following result

3. Output Constraints

We have the conclusion form the last note

We can derive the same result as the previous procedures

4. Conclusion

Example

We have the state space model

The control horizon is 1 and the predictive horizon is 2.

First we have the augmented state space model

Then we get

According to the question

Also we need to calculate J

For k=0

We can get

For k=1

we can get

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