In linear systems theory it's a well known fact that a regulator given by the cascade of an oscillatory dynamics, driven by some regulated variables, and of a stabiliser stabilising the cascade of the plant and of the oscillators has the ability of blocking on the steady state of the regulated variables any harmonics matched with the ones of the oscillators. This is the well-celebrated internal model principle. In this paper we are interested to follow the same design route for a controlled plant that is a nonlinear and periodic system with period T : we add a bunch of linear oscillators, embedding n o harmonics that are multiple of 2$π$/T , driven by a "regulated variable" of the nonlinear system, we look for a stabiliser for the nonlinear cascade of the plant and the oscillators, and we study the asymptotic properties of the resulting closedloop regulated variable. In this framework the contributions of the paper are multiple: for specific class of minimum-phase systems we present a systematic way of designing a stabiliser, which is uniform with respect to n o , by using a mix of high-gain and forwarding techniques; we prove that the resulting closed-loop system has a periodic steady state with period T with a domain of attraction not shrinking with n o ; similarly to the linear case, we also show that the spectrum of the steady state closed-loop regulated variable does not contain the n harmonics embedded in the bunch of oscillators and that the L 2 norm of the regulated variable is a monotonically decreasing function of n o. The results are robust, namely the asymptotic properties on the regulated variable hold also in presence of any uncertainties in the controlled plant not destroying closed-loop stability.
Cooperative Control of Parallel Actuators for Linear Robust Output Regulation of Uncertain Linear Minimum-phase Plants
School of Mathematics and Statistics, Fuzhou University（福州大学数学与统计学院）；Guangdong Provincial Key Laboratory of Fully Actuated System Control Theory and Technology, School of Automation and Intelligent Manufacturing, Southern University of Science and Technology（南方科技大学自动化与智能制造学院）
Shared Linear Quadratic Regulation Control: A Reinforcement Learning Approach
MIT Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology（麻省理工学院计算机科学与人工智能实验室）；Laboratory of Information and Decision Systems, Massachusetts Institute of Technology（麻省理工学院信息与决策系统实验室）
