Dear Dr. Liming Yuan
I think the papers
https://en.wikipedia.org/wiki/Model_predictive_control
&
https://web.stanford.edu/class/archive/ee/ee392m/ee392m.1056/Lecture14_MPC.pdf
&
http://control.asu.edu/Classes/MMAE543/543Lecture24.pdf
are very important for answer.
Best Regards
Hi All,
Despite the introduction of the closed loop in an optimal control, it remains that the MPC retains advantages, in particular the processing of the sensitivity concerning the predicted initial value as well as an automatic adaptation of the calculation of the set points.
Best regards
Hi All,
Despite the introduction of the closed loop in an optimal control, it remains that the MPC retains advantages, in particular the processing of the sensitivity concerning the predicted initial value as well as an automatic adaptation of the calculation of the set points.
Best regards
Certainty equivalence property (CEP) is another name for model-predictive control (MPC). Based on CEP, it does not differ whether you include additive noise into calculation or not. It means it does not matter whether you consider the system as xdot=ax+bu+ w, or without additive disturbance variable as: xdot=ax+bu, anyway the optimal control-law is indifferent for the two linear systems, regardless of including disturbance variable (w), or neglecting it. The property has been proven in the following paper for the linear case (LQG):Article The Certainty Equivalence Property in Stochastic Control Theory
Moreover, as I've tried it myself, even for nonlinear case, the CEP strongly holds, as long as noise is additive (xdot=f(x,u)+w), not multiplicative as (xdot=(f(x,u)+w*x), and in addition, while cost is quadratic.
Both optimal output-feedback control, and MPC, give similar control-law (or gains) for the stochastic system (xdot=f(x,u)+w), with or without disturbance variable w, but not for the stochastic system (xdot=f(x,u)+w*x). In the case of (xdot=f(x,u)+w*x), ignoring the multiplicative disturbance is not allowed, and if multiplicative term (w*x) is neglected, the optimal control-law found, would be dissimilar for the two-type of systems, and might not be robust with respect to multiplicative disturbance. This property is simply the certainty equivalence property (CEP), or through another terminology, the model-predictive control (MPC). Notice that, it seems MPC is based on discrete optimization for minimum cost, hence MPC has some other variant setup and independent format from optimal-control, but they are analogous as optimal output-feedback control is usually analytic and continuous, while MPC seems as discrete version of that, based on optimization.
MPC is resourceful when analyzing disturbance is not simple, hence CEP is used to authorize ignorance of disturbance variable.
The optimal output feedback controller is essentially just a matrix multiplication, while the model predictive control has some fundamental advantages when there are constraints, which are explicitly taken into consideration in the computation of the optimal control trajectory. Optimal output-feedback control cannot consider constraints, they have to be added in a separate step. Also note that standard MPC requires to solve an optimization problem at each sample.
For more detail, we have : https://en.wikipedia.org/wiki/Model_predictive_control
best regards
- Badges
- Science topic
- Similar topics
- Engineering
- Control Theory
- Control Systems
- Control Systems Engineering