FEEDBACK-CONTROL OF QUANTIZED CONSTRAINED SYSTEMS WITH APPLICATIONS TO NEUROMORPHIC CONTROLLERS DESIGN

During the last few years there has been considerable interest in the use of trainable controllers based upon the use of neuron-like element s, with the expectation being that these controllers can be trained, w ith relatively little effort, to achieve good performance. Good perfor mance, however, hinges on the ability of the neural net to generate a ''good'' control law even when the input does not belong to the traini ng set, and it has been shown that neural nets do not necessarily gene ralize well. It has been proposed that this problem can be solved by e ssentially quantizing the state space and then using a neural net to i mplement a table lookup procedure. There is little information on the effect of this quantization upon the controllability properties of the system. In this paper we address this problem by extending the theory of control of constrained systems to the case where the controls and measured states are restricted to finite or countably infinite sets. T hese results provide the theoretical framework for recently suggested neuromorphic controllers, but they are also valuable for analyzing the controllability properties of computer-based control systems.