The problem of power-consumption-optimal reorientation with simultaneous retardation of a spherically symmetric body with an unspecified time
✍ Scribed by A.N. Sirotin
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 627 KB
- Volume
- 68
- Category
- Article
- ISSN
- 0021-8928
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✦ Synopsis
Some special features of the solutions of the problem of the optimal control of the spatial reorientation and simultaneous total retardation of the initial rotation of an absolutely solid spherically symmetric body in the case of an unspecified time are studied. The principal moment of the external applied forces serves as the control. The quality of the control process is estimated by an integral functional which characterizes the overall power consumption required to accomplish the manoeuvre. In a special case, this functional has the form of the well-known integral-quadratic functional. It is established that the problem of controlling the reorientation and simultaneous retardation of a rigid body with an unspecified time in the class of measurable controls, which is optimal with respect to power consumption, has no solutions for almost any initial conditions. One of the possible minimizing sequences is explicitly constructed. It is shown that the smallest values of the objective functionals in the problem of reorientation with retardation and in the problem of the total retardation of the initial rotation are identical. In particular, zero minimum power consumptions corresponds to the reorientation of a spherically symmetric body from a position of rest into a position of rest if the time at which the process terminates is not fixed. The uniqueness of the solution of the problem of optimal retardation is proved when an additional assumption is made concerning rigorous normalization.