Abstract
The methods of optimal control are applied to the problems of the theory of smart structures. Two optimization problems in the theory of smart structures are formulated and solved. These problems are concerned with the damping of mechanical oscillations by controlling the rigidity of the structure and applied force. The optimal controls are obtained in the form of optimal syntheses. In the first problem, the optimization criterion is to minimize the time required to transfer the system to a required state. The recurrent formula for the segments constituting the switching curve is derived. The second optimization problem is concerned with reduction of energy of oscillations by controlling the coefficient of rigidity of the structure. The objective of optimal control is to transfer the system to a given lower energy level in a minimal time. An explicit expression for all the segments of the switching curve is obtained.
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