Unified Riccati theory for optimal permanent and sampled-data control problems in finite and infinite time horizons
Résumé
We revisit and extend the Riccati theory, unifying continuous-time linear-quadratic optimal permanent and sampled-data control problems, in finite and infinite time horizons. In a nutshell, we prove that:
-- when the time horizon T tends to $+\infty$, one passes from the Sampled-Data Difference Riccati Equation (SD-DRE) to the Sampled-Data Algebraic Riccati Equation (SD-ARE), and from the Permanent Differential Riccati Equation (P-DRE) to the Permanent Algebraic Riccati Equation (P-ARE);
-- when the maximal step of the time partition $\Delta$ tends to $0$, one passes from (SD-DRE) to (P-DRE), and from (SD-ARE) to (P-ARE).
Our notations and analysis provide a unified framework in order to settle all corresponding results.
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