A method for approximating dynamical processes by finite-state systems†

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Abstract
In many complex control processes, the problem of determining optimal control policies can be considerably simplified from the stand-points of computation and implementation, if the mathematical model can be adequately described by a finite-state sequential system, i.e. a discrete-time system whose input (control) and state spaces are finite-state. However, in physical situations, one usually formulates the mathematical models in the form of a set of ordinary differential equations resulting from certain physical laws. Therefore, it is desirable to have systematic methods far approximating such mathematical models by finite-state systems. This paper describes a simple method for approximating a finite set of first-order ordinary differential equations by the finite-state system. The validity and application of the method are discussed and illustrated by examples. Also, the main problem associated with the implementation of control systems using finite-state models will be discussed briefly.

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