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This work aims to analyze the State-Dependent Riccati Equation (SDRE) approach in nonlinear optimal control and evaluate its numerical solutions.

The State-Dependent Riccati Equation in Nonlinear Optimal Control: Analysis and Numerical Approximation

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Analysis of SDRE and approximation methods in nonlinear optimal control, indicating its effectiveness and efficiency.

This work aims to analyze the State-Dependent Riccati Equation (SDRE) approach in nonlinear optimal control and evaluate its numerical solutions.
Examined theoretical foundations of SDRE and its relation to the Hamilton-Jacobi-Bellman equation.
Derive residual-based error estimates to assess suboptimality.
Introduced an optimal semilinear decomposition strategy to minimize residuals.
Analyzed offline-online and Newton-Kleinman iterative methods for numerical solution of SDRE.
The Newton-Kleinman method demonstrated better performance in stability and cost-effectiveness compared to the offline-online approach.
Numerical experiments revealed trade-offs between computational efficiency and accuracy in SDRE solutions.

Luca Saluzzi (2026) studied this question.

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