The problem of the synthesis of adaptive nonlinear dynamical systems providing unknown parametrical drift was solved. The problem of the optimal stabilization of nonlinear holonomic and nonholonomic systems into adaptive statement was formulated and solved. The solution of the problem of optimal synthesis of adaptive nonlinear dynamical systems with the general form connections was obtained. The synthesis of adaptive controlled systems on the basis of the Hamilton-Jacobi canonical transformations was realized. The solution was achieved for the optimization problem of adaptive controlled systems with distributive parameters. The problem of optimal stabilization of nonlinear stochastic systems was solved. Some problems of the solid body stochastic motion were formulated and solved. The investigation was conducted for the question about motion of nonlinear dynamical systems with stochastic connections and concerning of stochastic nonstability presence. Optimal parametrical synthesis of nonlinear stochastic systems with the random stoppage moment was realized. The solution of the problem for the optimal nonlinear adaptive filtering about Kalman-Bucy method was obtained. The differential principle of motion completness for the variable-mass point into space was proposed. Using this principle as the base the equations describing the hyperreactive motion was derived and properties of this motion was studied.
Main publications:
Tertychny-Dauri V. Yu. Adaptive Mechanics. Dordrecht, Boston, London: Kluwer Academic Publishers, 2002. 507 p.
