Robust optimal pole-clustering in a vertical strip and disturbance rejection for uncertain Lagrange's systems

Abstract

Abstract. This paper presents an approach to design a state-feedback robust control law for uncertain Lagrange's systems such that the designed closed-loop systems have the properties of robust pole-clustering within a vertical strip and disturbance rejection with an Ha-norm constraint. This approach is based on solving an algebraic Riccati equation with the adjustable scalars and prespecified parameters. The uncertainties considered include both unstructured and structured uncertainties in the system and the input matrices. Also, a constraint is established to verify that the proposed robust LQRs preserve//2 optimality with respect to a specific quadratic cost function.

Robust Control Design for Two-link Nonlinear Robotic System

“…Proof: Please refer to the approach developed in [6,8] and utilizing the new model in Section 2. It is also noticed that:…”

<title>Robust control for structural systems with uncertainties</title>

“…By extension of Lemma 2 in [10], it is known that the closed-loop system (10) is of the a-degree relatively stable as (12) and &degree disturbance attenuation as (11)if (Ac÷)TP+P(Ac+aI)4P(F÷F)(F÷iF)TP+._CTC<O. By extension of Lemma 2 in [10], it is known that the closed-loop system (10) is of the a-degree relatively stable as (12) and &degree disturbance attenuation as (11)if (Ac÷)TP+P(Ac+aI)4P(F÷F)(F÷iF)TP+._CTC<O.…”

“…Many physical problems, such as aeronautical systems, mechanical systems, structural systems, and flexible structures can be described via Lagrange's equation using the state-space model [10]. Many physical problems, such as aeronautical systems, mechanical systems, structural systems, and flexible structures can be described via Lagrange's equation using the state-space model [10].…”

“…Many physical problems, such as aeronautical systems, mechanical systems, structural systems, and flexible structures can be described via Lagrange's equation using the state-space model [10]. In [10] the considered uncertainties are in both the system matrix and the control input matrix, but not in the disturbance input matrix. In such cases robustness of a control system for the structural system stability and its performance toward attenuation of external hazard disturbance is important.…”

A ModifiedD-KIteration Approach for the Decentralizedℋ∞Control of Civil Structures with Parametric Uncertainties

“…There are also some efforts on the robust controller design preconsidering the uncertainties. Wang et al [22] studied the robust controller design for the uncertain structure, whose uncertainties located in the system matrices and control input matrices. Wang et al [23] also developed a state feedback controller for the uncertainties in the disturbance input matrix.…”