Belousova N. Development of adaptive algorithm of identification and control based on Lyapunov's function

The thesis is devoted to development and investigation of adaptive identification and control problems. The algorithms of adaptive identification and control based on direct Lyapunov's method are proposed. Differential equations for tuning a matrix of model parameters have modified structure as compared with classical ones. To solve well-known problems, in which right-hand sides of differential equations for tuning a matrix of model parameters depend on unknown object's parameters, the iterative and recurring algorithms based on gradient methods of minimization of some criteria are proposed. The differential properties of iterative and recurring gradient type algorithms are investigated, the existence and uniqueness of solution of considered problems are established, the theorems on convergence of projection gradient methods for minimization problems are proved. The joint problem of indirect control using recurring identification algorithm is posed, the stability and convergence of solution of joint control problem are investigated.