State-feedback representation of continuous-time MPC minimizers

Determine whether a minimizer of the continuous-time model predictive control cost functional for the nonlinear interacting particle system can be represented as a state feedback of the form u(t)=α(X_t,V_t).

Background

The paper contrasts continuous-time model predictive control with instantaneous rolling horizon control. For the nonlinear interacting particle system, the continuous-time MPC problem minimizes a cost functional whose dependence on the control is mediated through the state trajectory. The authors identify two difficulties with using this general MPC formulation: the optimization problem lacks an apparent coercive or convex structure, and it is unresolved whether an optimal control can be expressed as a state-feedback law. This representation is important because a state feedback is required to interpret the resulting closed-loop dynamics within the IDA-PBC framework. The paper therefore proceeds with the instantaneous rolling horizon method instead of resolving this question for general continuous-time MPC.

References

Second, even if a minimizer $u$ exists, it is not clear whether it can be represented by a state feedback $u(t) = \alpha (X_t, V_t)$.

— Feedback approaches for set-point stabilization of interacting particle systems  (2608.17222 - Happ et al., 18 Aug 2026) in Section 3, Instantaneous rolling horizon control, paragraph preceding the introduction of the instantaneous rolling horizon control method