An analytical solution to dynamic quantization problem of nonlinear control systems

This paper addresses a problem of finding an optimal dynamic quantizer for nonlinear control subject to discrete-valued signal constraints. The quantizers to be studied are in the form of a nonlinear difference equation and are evaluated by the performance index expressing the difference between the resulting quantized system and the usual (unquantized) system. To solve the problem, we first derive lower and upper bounds of the optimal performance, which presents an optimal dynamic quantizer in a closed form. The performance of the proposed quantizer is demonstrated by numerical simulations.