A convex optimization approach to adaptive stabilization of discrete-time LTI systems with polytopic uncertainties

作者：Lee Dong Hwan; Joo Young Hoon^*; Tak Myung Hwan

来源：International Journal of Adaptive Control and Signal Processing, 2015, 29(9): 1116-1134.

DOI：10.1002/acs.2525

• LTI systems
• convex optimization
• quadratic programming
• adaptive control
• polytopic uncertainty
• LMI

This paper suggests a simple convex optimization approach to state-feedback adaptive stabilization problem for a class of discrete-time LTI systems subject to polytopic uncertainties. The proposed method relies on estimating the uncertain parameters by solving an online optimization at each time step, such as a linear or quadratic programming, and then, on tuning the control law with that information, which can be conceptually viewed as a kind of gain-scheduling or indirect adaptive control. Specifically, an admissible domain of stabilizing state-feedback gain matrices is designed offline by means of linear matrix inequality problems, and based on the online estimation of the uncertain parameters, the state-feedback gain matrix is calculated over the set of stabilizing feedback gains. The proposed stabilization algorithm guarantees the asymptotic stability of the overall closed-loop control system. An example is given to show the effectiveness of the proposed approach.

• 出版日期2015-9