Minimum-amplitude control of linear discrete systems

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Abstract
This paper treats the problem of generating a minimum-amplitude control sequence which will drive a linear discrete system from some arbitrary initial state to a desired final state in a fixed number of control iterations. It is well known that this problem is equivalent to that of finding a minimum l ∞ normed solution to a set of under-determined linear equations (Cadzow 1071). With this in mind, an algorithmic procedure for finding such a solution is presented. This algorithm is developed by incorporating some elegant theorems from functional analysis. The resultant algorithm is computationally efficient and can be used in many real-time control applications, as is demonstrated by a specific example. Its computation efficiency is shown to easily exceed that of the linear programming algorithm used to find a minimum l ∞, norm solution.

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