Dual control theory
Encyclopedia
Dual control theory is a branch of control theory
that deals with the control of systems whose characteristics are initially unknown. It is called dual because in controlling such a system the controller's objectives are twofold:
These two objectives may be partly in conflict.
Dual control theory was developed by Alexander Aronovich Fel'dbaum in 1960. He showed that in principle the optimal
solution can be found by dynamic programming
, but this is often impractical; as a result a number of methods for designing sub-optimal dual controllers have been devised.
: if you are driving a new car you want to get to your destination cheaply and smoothly, but you also want to see how well the car accelerates, brakes and steers so as to get a better feel for how to drive it, so you will do some test manoeuvers for this purpose. Similarly a dual controller will inject a so-called probing (or exploration) signal into the system that may detract from short term performance but will improve control in the future.
Control theory
Control theory is an interdisciplinary branch of engineering and mathematics that deals with the behavior of dynamical systems. The desired output of a system is called the reference...
that deals with the control of systems whose characteristics are initially unknown. It is called dual because in controlling such a system the controller's objectives are twofold:
- (1) Action: To control the system as well as possible based on current system knowledge
- (2) Investigation: To experiment with the system so as to learn about its behavior and control it better in the future.
These two objectives may be partly in conflict.
Dual control theory was developed by Alexander Aronovich Fel'dbaum in 1960. He showed that in principle the optimal
Optimal control
Optimal control theory, an extension of the calculus of variations, is a mathematical optimization method for deriving control policies. The method is largely due to the work of Lev Pontryagin and his collaborators in the Soviet Union and Richard Bellman in the United States.-General method:Optimal...
solution can be found by dynamic programming
Dynamic programming
In mathematics and computer science, dynamic programming is a method for solving complex problems by breaking them down into simpler subproblems. It is applicable to problems exhibiting the properties of overlapping subproblems which are only slightly smaller and optimal substructure...
, but this is often impractical; as a result a number of methods for designing sub-optimal dual controllers have been devised.
Example
To use an analogyCar analogy
The car analogy is a common resort exploited by engineering textbooks to ease the understanding of some abstract concepts found within it.-Uses of car analogies:...
: if you are driving a new car you want to get to your destination cheaply and smoothly, but you also want to see how well the car accelerates, brakes and steers so as to get a better feel for how to drive it, so you will do some test manoeuvers for this purpose. Similarly a dual controller will inject a so-called probing (or exploration) signal into the system that may detract from short term performance but will improve control in the future.