Abstract
A singular optimal control problem with a performance index given by the total energy of the system is formulated, and functional analysis ideas are used to reduce the control problem to consider certain integral equations. In particular, the optimal control profile for minimum-energy control is obtained in an analytic manner. It is not necessary for the approach to take the second variation into consideration in spite of singular problems. The number of integral equations to be solved is equal to the number of control variables, which is usually much smaller than that of the state variables in the case of large space structures. The time-optimized control can be obtained numerically for the minimum-energy maneuver as the least-time maneuver that does not violate the constraints on the control inputs. The results of the present formulation are compared with that of multiple bang-bang time-optimal control using a simple model. The advantages of the present formulation are discussed on such control performance issues as the reduction of the control effort and the appropriate implementation of continuous controlled jets.
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