arXiv subjects

Ali Bouland

Publications and source records attributed to Ali Bouland.

4 recordsLinked to original sources

arXiv2026

Control of the Fluidic Pinball using the Quadratic-Quadratic Regulator

The fluidic pinball presents a significant benchmark for nonlinear flow control, managing the complex interactions of three cylinder wakes. This study addresses the stabilization of the fluidic pinball to its unstable steady-state solution using a model-based nonlinear feedback strategy. We propose a framework that combines interpolatory model order reduction (IMOR) with the quadratic-quadratic regulator (QQR), a feedback control methodology that is specifically suited to the quadratic nonlinearity of the Navier-Stokes equations. A finite element model (FEM) of the problem coupled with IMOR is used to produce a reduced-order model (ROM) that accurately represents the input-output dynamics of the actuated wake. The performance of the QQR control is evaluated against the traditional linear feedback control for two different Reynolds numbers, $Re_D = 30$ and $Re_D = 50$. At $Re_D = 30$, the QQR controller is able to stabilize the wake and reaches the desired performance criteria 40.1\% faster than using a linear feedback controller. More significantly, at $Re_D = 50$, the QQR controller successfully stabilizes the wake, whereas the linear controller fails to overcome the nonlinearity of the flow. The QQR control effectively suppresses vortex shedding, resulting in the elimination of lift oscillations and a reduction in the drag coefficient. These results demonstrate that the IMOR-QQR framework provides an effective model-based control strategy that can manage nonlinear hydrodynamic instabilities in such complex wake flows.

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arXiv2025

Tailoring Reproducing Kernels for Optimal Control via Policy Iteration

This paper presents a novel approach to formulating the actor-critic method for optimal control by casting policy iteration in reproducing kernel Hilbert spaces (RKHSs -- also known as native spaces). By tailoring the reproducing kernel and RKHS to the dynamics of the nonlinear optimal control problem, we leverage recent advancements in characterizing error bounds from statistical and machine learning theory. These approximations define a general strategy to select the bases of the actor-critic networks, and we formally guarantee for the first time that this basis selection procedure leads to closed-form error bounds for the individual steps of policy iteration. These bounds often have a geometric and computable form, making them potentially useful for a priori or a posteriori evaluation of candidate collections of scattered bases. Numerical studies subsequently provide qualitative evidence of the practical performance achieved for the full recursion using the algorithms and theory developed for the single-step error bounds.

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arXiv2024

Convergence Rates of Online Critic Value Function Approximation in Native Spaces

In this paper, the evolution equation that defines the online critic for the approximation of the optimal value function is cast in a general class of reproducing kernel Hilbert spaces (RKHSs). Exploiting some core tools of RKHS theory, this formulation allows deriving explicit bounds on the performance of the critic in terms of the kernel and definition of the RKHS, the number of basis functions, and the location of centers used to define scattered bases. The performance of the critic is precisely measured in terms of the power function of the scattered basis used in approximations, and it can be used either in an a priori evaluation of potential bases or in an a posteriori assessments of value function error for basis enrichment or pruning. The most concise bounds in the paper describe explicitly how the critic performance depends on the placement of centers, as measured by their fill distance in a subset that contains the trajectory of the critic.

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arXiv2023

Rates of Convergence in Certain Native Spaces of Approximations used in Reinforcement Learning

This paper studies convergence rates for some value function approximations that arise in a collection of reproducing kernel Hilbert spaces (RKHS) $H(Ω)$. By casting an optimal control problem in a specific class of native spaces, strong rates of convergence are derived for the operator equation that enables offline approximations that appear in policy iteration. Explicit upper bounds on error in value function and controller approximations are derived in terms of power function $\mathcal{P}_{H,N}$ for the space of finite dimensional approximants $H_N$ in the native space $H(Ω)$. These bounds are geometric in nature and refine some well-known, now classical results concerning convergence of approximations of value functions.

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