Modeling and optimization of elastic system motions by the method of integro-differential relations

An algorithm is developed for the construction of an optimal control system, satisfying prescribed performance criteria and the possibility of optimizing the motions of elastic systems with distributed perameters. The integro-differential relation (IDR) approach for the construction of solutions for a wide class of boundary value problems is developed, and a performance criterion for the resulting solutions is used. The problem is to find an optimal control u(t) that drives the chart from initial to terminal states in the given time T, and minimizes a performance index J[u] in the class U of admissible controls. The dynamic properties of controlled elastic systems with distributed parameters were examined by finite dimensional approximation methods, such as separation of variable, and decomposition method. In the case of IDR method, some strict local relations in a boundary value problem are replaced by integral relations.