Multi-Objective Trajectory Optimization by a Hierarchical Gradient Algorithm with Fuzzy Decision Logic

The rest-to-rest maneuver problem of the flexible space structure is the two point boundary value problem (TPBVP) and is solved by some gradient methods. If TPBVP is strongly restricted by the constraints, TBVP becomes ill-defined problem, and the solution meeting all constraints cannot be obtained. However, reasonable suboptimal solutions are often needed since real plants are necessary to be controlled. In order to obtain such suboptimal solutions, we have developed a modified version of the hierarchy gradient method by installing fuzzy decision logic. Constraints are classified into non-fuzzy constraints and fuzzy constraints according to their priorities. Fuzzy constraints having trade-off relationship with each other are compromised reasonably by fuzzy decision logic. The usefulness of the proposed method is numerically and experimentally demonstrated by applying to the rest-to-rest slew maneuver problem of a flexible space structure, where fuzzy constraints are final time, sensitivity of residual vibration energy with respect to the structure frequency uncertainty, and maximum bending moment at the root of flexible appendage.

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