Studies On Adaptive Pole Placement Algorithms Of Multivariable Stochastic Systems

In this dissertation, adaptive pole placement algorithm for multivariable system with a general uncertain structure is analyzed, and two kinds of modification strategies for parameter estimation are synthesized and compared. The further improved orientation so as to cancel the necessary condition of controllability of parameter estimation is pointed out. Based on these results, adaptive pole placement algorithm for multivariable stochastic system is brought forward. In the algorithm, the necessary and sufficient condition for stabling multivariable adaptive pole placement systems and two kinds of modification strategies for parameter estimation is proposed. At last, the analysis for the convergence of the closed loop system is given. The recursive modification algorithm is mainly based on the ideal of stochastic approximation and truncation technique to obtain modification strategy for estimated parameters, it is proved that these modification parameters turn out to be a constant vector. The nonrecursive algorithm is proved to terminate in finite steps and turn out to be a constant vector too. Because two modifications estimated models are asymptotically uniformly nonsingular, thus the possible singularity in the adaptive pole placement systems is completely avoided. However the prior knowledge required is only the observability indices of systems, thus, the required prior knowledge is greatly reduced.