# Differences between RHC and control horizon in MPC

I have used model predictive control strategy in order to optimize a linear discrete SISo model.

For example:

$$x(t+1)=-2x(t)+4u(t)$$

Where I want to regulate my state $$x(t)$$ at the desired point (a simple regulating problem).

In every step, I predict $$20$$ future samples such that MPC optimizes next $$20$$ time instances (prediction horizon$$=20$$) and obtains $$20$$ responses for control variable(control horizon $$=20$$) then based on RHC technique, I just apply $$10$$ samples to model. I know both control horizon and prediction horizon are $$20$$ samples. but what about applied samples ($$10$$ samples) what can I name my applied samples?

• It's not called anything particular, and I would not try to invent some special name to this. It's just MPC but with the small change that you don't update already after one sample as often as one normally does. – Johan Löfberg Apr 25 '19 at 20:01
• Just a remark: Using acronyms without writing them out at the first usage is a very bad communication style. – MachineLearner Apr 25 '19 at 20:45

• control time steps = control sampling time $T_s$, manipulated variable = control variable $\boldsymbol{u}(t)$, more formulation at here. – Arash Jul 7 '19 at 8:52