Abstract
The first part of the paper deals with the general problem of forcing a non-linear process to follow a specified (discrete-time) trajectory. The performance is measured by a functional of the vector error and input sequences and the inputs are assumed to be constrained. By the use of standard methods of calculus the optimum controller is shown to require the solution of a system of difference equations of twice the order of the process to be controlled with boundary conditions at the terminal instant dependent on the performance measure. A simple geometric interpretation of the problem is given. The second part of the paper is concerned with a more specific class of problem in which the process is linear, and the performance objective is one of the following: (1) To force the process from an arbitrary initial state as close as possible to a specified terminal state in a fixed number of steps. (2) To force the process from the initial state to a specified terminal state in a fixed number of steps with minimum ‘effort’. (3) To force the process from the initial state to a specified terminal state in a minimum number of steps. A special-purpose computer which performs the required computation in real time is proposed as the on-line optimum controller.
Published Version
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