Gain Scheduled Control of Linear Systems Subject to Actuator Saturation With Application to Spacecraft Rendezvous

• Published in: IEEE transactions on control systems technology Vol. 22; no. 5; pp. 2031 - 2038
• Main Authors: Zhou, Bin, Wang, Qian, Lin, Zongli, Duan, Guang-Ren
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.09.2014; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Actuator saturation; Actuators; Closed loop systems; Control systems; Convergence; Dynamic scheduling; Dynamical systems; Eigenvalues and eigenfunctions; Gain scheduling; invariant set; Linear systems; Mathematical models; Nonlinear dynamics; Rendezvous; semiglobal stabilization; Space vehicles; spacecraft rendezvous; invariant set; semiglobal stabilization; gain scheduling; spacecraft rendezvous; Actuator saturation
• ISSN: 1063-6536; 1558-0865
• DOI: 10.1109/TCST.2013.2296044

This brief is concerned with gain scheduled approaches to the stabilization of linear systems with actuator saturation. For linear systems that are polynomially unstable, using the parametric Lyapunov equation-based and Riccati equation-based design, we propose gain scheduling approaches to increase the design parameter online so as to increase the convergence rates of the closed-loop systems. To apply the proposed gain scheduling approaches, only a scalar differential equation whose right-hand side is a function of the state vector is required to be integrated online. The closed-loop system is proven to be exponentially stable provided some parameters in the scheduling law are properly chosen. The established gain scheduling approaches are also extended to exponentially unstable linear systems with actuator saturation. As applications of the proposed dynamic gain scheduling approaches, the controller design of spacecraft rendezvous systems is revisited. Numerical simulation with the nonlinear model of a spacecraft rendezvous system shows the effectiveness of the proposed gain scheduling approaches.