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Infinite-horizon optimal control for fractional-order systems

Establish comprehensive results for infinite-horizon optimal control of fractional-order dynamical systems, such as fractional-order linear time-invariant models, by characterizing the existence and structure of optimal policies and costs beyond specialized finite-horizon settings.

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Background

In contrast to classical integer-order LTI systems where LQR has well-developed infinite-horizon solutions, fractional-order systems' non-local memory effects complicate analysis and control.

The paper notes that while finite-horizon optimal control has been tackled under specific assumptions, comprehensive results for the infinite-horizon case are lacking, underscoring a gap in the theoretical foundations for fractional-order optimal control.

References

For finite horizons, optimal control problems have been addressed under specific assumptions (Li & Chen, 2008), but no comprehensive results exist for infinite horizons.

— End-to-End Learning Framework for Solving Non-Markovian Optimal Control (2502.04649 - Zhang et al., 7 Feb 2025) in Section 1 (Introduction)