A method to control the motion of flexible systems is developed. In the proposed approach, the control inputs are defined as a linear combination of piecewise continuous (basis) functions and adjustable parameters (control vector) which are obtained by solving an optimal control problem. The continuous-time optimal control problems are formulated and converted into the discrete-time optimal control problems. Algorithms of determining the control vectors are developed for a variety of control problems: point-to-point control and trajectory following control of linear time varying system, point-to-point control of linear periodic system and nonlinear system. The control problems with and without constraints are formulated.; Conditions for the existence of optimal solution and the requirements for the number of basis functions are derived for two different optimal control formulations, i.e. the fixed terminal state and penalised state formulation. It is shown that the proposed algorithm applied to linear system with input constraints generates a sequence converging to the optimal solution.; A simulation study has been conducted to illustrate the applicability and evaluate the performance of the proposed method. The approach was demonstrated to a number of (flexible) mechanical systems: reorientation of a flexible spacecraft using a linear and nonlinear dynamic models, control of flapping motion of rotorcraft blade whose dynamics is described by equations with periodically varying coefficients, control of two disk system, design example for multi-input system.
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