Finite precision optimal controllers design using genetic algorithms

Abstract

In this paper, a linear quadratic gaussian (LQG) control scheme with genetic algorithm (GA) is proposed for analyzing the performances of the realization of a state regulator system on a digital machine. This scheme permits that the optimal controllers with finite precision can stabilize the controlled systems with the desired performances when it is implemented on a digital machine with finite-word-length limitations and finite bit conversions of analog to digital and digital to analog converters. The rounding errors occurred by the coefficientsquantization and the computational errors by additions and multiplications are considered. The conversion parameters of the analog to digital converters are tuned by GA so that the numerical errors can be considerably reduced. Since the separation principle is not valid for systems with the multiplicative noises, a necessary but not sufficient condition” is derived after converting the stochastic problem to a deterministic game theoretic one so that the stability of the closed-loop system is guaranteed. Finally, a simulation example is given to validate the design procedures of the proposed control scheme.

Keywords:

• LQG control
• separation principle
• GA
• finite precision
• rounding errors
• stability