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The H∞ optimal Control Problem of CSVIU Systems
  • João B. R. do Val,
  • Daniel Campos
João B. R. do Val
Universidade Estadual de Campinas

Corresponding Author:[email protected]

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Daniel Campos
Universidade Estadual de Campinas
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The paper devises a H ∞ -norm theory for the CSVIU (control and state variations increase uncertainty) class of stochastic systems. This system model appeals to stochastic control problems to express the state evolution of a possibly nonlinear dynamic system restraint to poor modeling. Contrary to other H ∞ stochastic formulations that mimic deterministic models dealing with finite energy disturbances, the focus is on the H ∞ control with infinity energy disturbance signals. Thus, the approach portrays the persistent perturbations due to the environment more naturally. In this regard, it requires a refined connection between a suitable notion of stability and the systems’ energy or power finiteness. It delves into the control solution employing the relations between H ∞ optimization and differential games, connecting the worst-case stability analysis of CSVIU systems with a perturbed Lyapunov type of equation. The norm characterization relies on the optimal cost induced by the Min-Max control strategy. The rise of a pure saddle point is linked to the solvability of a modified Riccati-type equation in a form known as a generalized game-type Riccati equation, which yields the solution of the CSVIU dynamic game. The emerging optimal disturbance compensator produces inaction regions in the sense that, for sufficiently minor deviations from the model, the optimal action is constant or null in the face of the uncertainty involved. A numerical example illustrates the synthesis.
15 Apr 2023Submitted to International Journal of Robust and Nonlinear Control
15 Apr 2023Submission Checks Completed
15 Apr 2023Assigned to Editor
15 Apr 2023Review(s) Completed, Editorial Evaluation Pending
25 Apr 2023Reviewer(s) Assigned
05 Jun 2023Editorial Decision: Revise Minor
14 Jul 20231st Revision Received
17 Jul 2023Submission Checks Completed
17 Jul 2023Assigned to Editor
17 Jul 2023Review(s) Completed, Editorial Evaluation Pending
18 Jul 2023Reviewer(s) Assigned
15 Aug 2023Editorial Decision: Revise Minor
01 Sep 20232nd Revision Received
01 Sep 2023Submission Checks Completed
01 Sep 2023Assigned to Editor
01 Sep 2023Review(s) Completed, Editorial Evaluation Pending
07 Sep 2023Reviewer(s) Assigned
09 Oct 2023Editorial Decision: Accept