Projection Scheme and Adaptive Control for Symmetric Matrices With Eigenvalue Bounds

• 成果类型: Article
• 署名作者: Moghe, Rahul; Akella, Maruthi R.
• 署名单位: University of Texas System; University of Texas Austin
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3153458
• 发表日期: 2023
• 页码: 1738-1745
• 关键词: Symmetric matrices; Eigenvalues and eigenfunctions; Adaptive control; Matrix decomposition; stability analysis; Numerical stability; Trajectory tracking; eigenvalue bounds; inertia identification; Lyapunov stability; projection method

摘要

A projection scheme to handle eigenvalue bounds for adaptive control with uncertain symmetric matrix parameters is introduced. Conventional parameter projection techniques are generally unable to handle explicit eigenvalue bounds. The continuous projection scheme presented here maintains the closed-loop stability properties for adaptive controllers while simultaneously satisfying a priori available eigenvalue bounds of the uncertain symmetric matrix valued parameters. The projection scheme uses the eigen decomposition of the symmetric matrix parameter to project its eigenvalues to lie within the prescribed bounds. The eigenvalues of the symmetric matrix may be lower bounded or upper bounded or both. A direct adaptation over the eigenvalues and the eigen projections of the symmetric matrix parameter is also derived to help circumvent expensive eigen decomposition calculations. The new projection here shows improved performance in numerical simulations of rigid body attitude tracking control and trajectory tracking of robotic manipulators with unknown inertia parameters.