Dual control theory is a branch of control theory that deals with the control of systems whose characteristics are initially unknown. Control theory is an interdisciplinary branch of Engineering and Mathematics, that deals with the behavior of Dynamical systems The desired output 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 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. Optimal control theory, a modern extension of the Calculus of variations, is a mathematical optimization method for deriving control policies. In Mathematics and Computer science, dynamic programming is a method of solving problems exhibiting the properties of Overlapping subproblems and
Example
To use an analogy: 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. The car analogy is a common resort exploited by Engineering textbooks to ease the understanding of some abstract concepts found within it 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.
References
- Fel'dbaum, A. A. , "Dual control theory, Parts I and II", Automation and Remote Control, Vol. 21, No. 9, April 1961, pp. 874-880 and Vol. 21, No. 11, May 1961, pp. 1033-1039. (Russian originals dated September 1960, 1240-1249 and November 1960, pp. 1453-1464)
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