Isoperimetric Constraint Inference for Discrete-Time Nonlinear Systems Based on Inverse Optimal Control.

Area of Science:

• Optimal control theory
• Mathematical optimization

Background:

• Optimal control problems often involve constraints that are not explicitly known.
• Inferring these constraints is crucial for understanding and replicating optimal system behaviors.

Purpose of the Study:

• To develop a method for recovering unknown isoperimetric constraints from given optimal state and control trajectories.
• To ensure the exact inference of these constraints under specific mathematical conditions.

Main Methods:

• Utilizing Pontryagin's maximum principle to derive recovery equations.
• Establishing verifiable dimensionality and matrix rank conditions for successful constraint inference.

Main Results:

• Successfully derived equations to recover unknown isoperimetric constraints.
• Demonstrated exact inference under specified conditions.
• Extended the methodology to handle multiple optimal trajectories.

Conclusions:

• The proposed method accurately infers unknown isoperimetric constraints in optimal control.
• The technique is robust and applicable to complex scenarios, including multiple trajectories.