Numerical solution of a fuzzy time-optimal control problem

In this paper, we consider a time-optimal control problem with uncertainties. Dynamics of controlled object is expressed by crisp linear system of differential equations with fuzzy initial and final states. We introduce a notion of fuzzy optimal time and reduce its calculation to two crisp optimal control problems. We examine the proposed approach on an example.

💡 Research Summary

The paper tackles a classic time‑optimal control problem under uncertainty by allowing the initial and terminal states to be fuzzy sets rather than precise points. The plant dynamics remain a crisp linear differential equation, preserving the well‑studied structure of linear time‑optimal control. The authors first formalize the notion of a “fuzzy optimal time” as the fuzzy set of all possible minimal travel times that satisfy every admissible pair of initial and final states drawn from the respective fuzzy sets. To compute this object, they employ the α‑cut representation of fuzzy sets: for each confidence level α∈