Scenario Approach-based Parametric Optimal Control for Uncertain Dynamical Systems via the Variational Iteration Method

Idiri, Ghania

doi:10.30473/coam.2026.76729.1376

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	Scenario Approach-based Parametric Optimal Control for Uncertain Dynamical Systems via the Variational Iteration Method
Control and Optimization in Applied Mathematics
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 06 خرداد 1405 اصل مقاله (398.06 K)
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.30473/coam.2026.76729.1376
نویسنده
Ghania Idiri^*
Laboratoire de Conception et Conduite des Systèmes de Production, Université Mouloud Mammeri, 15 000 Tizi-Ouzou, Algérie
چکیده
In this paper, a systematic design approach for the parametric optimization of uncertain dynamical systems with bounded parameter uncertainties is proposed. The methodology proceeds in two stages. In the first stage, the control input is expressed as a finite linear combination of polynomial basis functions, and an approximate analytical solution of the state equation is derived using the Variational Iteration Method, which is a semi-analytical iterative technique that avoids discretization and linearization. Substituting this approximate trajectory into the performance index yields a robust min–max optimization problem parameterized by the control coefficients. In the second stage, the robust optimization problem is converted into a tractable scenario optimization problem by drawing a finite number of independent and identically distributed samples from the uncertainty set. The resulting problem is solved using a genetic algorithm. The effectiveness of the proposed approach is demonstrated through two application examples. The first example concerns an uncertain linear-quadratic regulator, and the second addresses an uncertain nonlinear optimal control problem. Optimal control and state trajectories are provided for a set of samples. In addition, the optimal value of the performance index is reported, showing that this value does not exceed the threshold imposed by the proposed approach. The paper concludes by discussing limitations, including dependence on the accuracy of the Variational Iteration Method approximation and the assumption of a known probability distribution over the uncertainty set, and identifies directions for future research.
تازه های تحقیق
A two-stage parametric optimization framework is proposed for the optimal control of uncertain dynamical systems with bounded parameter uncertainties. The control input is represented as a finite linear combination of polynomial basis functions to enable a tractable parametric formulation. The Variational Iteration Method is employed to derive an approximate analytical solution of the state equation, avoiding discretization and linearization. Substituting the approximate trajectory into the performance index yields a robust min–max optimization problem parameterized by the control coefficients. The robust problem is converted into a scenario optimization problem via finite i.i.d. sampling from the uncertainty set, ensuring probabilistic feasibility guarantees. The resulting scenario optimization problem is solved using a genetic algorithm. The approach is validated on two application examples: an uncertain linear-quadratic regulator and an uncertain nonlinear optimal control problem. The framework is extensible to fractional-order systems, multi-state multi-input systems, and constrained optimal control problems.
کلیدواژه‌ها
Optimal control؛ Parametric optimization؛ Uncertain system؛ Variational iteration method؛ Scenario approach

مراجع
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Scenario Approach-based Parametric Optimal Control for Uncertain Dynamical Systems via the Variational Iteration Method