Adaptive robust periodic output regulation

by Zhen Zhang

Institution: The Ohio State University
Department: Electrical Engineering
Degree: PhD
Year: 2007
Keywords: Output regulation
Record ID: 1795015
Full text PDF: http://rave.ohiolink.edu/etdc/view?acc_num=osu1187118803


In this work, we investigate the output regulation problem for minimum-phase systems driven by periodic exosystems. Our ultimate goal is to achieve robust regulation with a semiglobal domain of convergence for specific classes of nonlinear minimum-phase systems. The class of exosystems under consideration is that of parameter-dependent periodically-varying linear systems for which periodic non-harmonic solutions exist. We start with considering the problem of periodic output regulation for linear systems. Necessary and sufficient conditions for the solvability of the problem based on the existence of periodic solutions of Sylvester differential equations are derived. These conditions constitute a generalization to the periodic case of the celebrated algebraic regulator equations of Francis. In order to extend the solution of robust regulators to more general classes of time-varying exosystems, we proposed a classification of the immersion mappings based on the underlying observability property, and describe the connections between different canonical realizations of internal models. Then the robust regulation for parameter-dependent periodic exosystems is considered. Here we show that a non-minimal realization of the resulting periodic internal model is instrumental in achieving the possibility of performing adaptive redesign to deal with parameterized families of exosystem models. A key feature of the proposed solution lies in the fact that a persistence of excitation condition is not required for asymptotic regulation. In addition, we show how the difficulty of obtaining classical immersions in the time-invariant nonlinear regulation problem can be overcome to some degree by combining a generalized immersion condition and our proposed adaptive periodic internal-model. The results for linear minimum-phase plant models can be extended to the nonlinear settings with assumption of partial state feedback. The outcome of this research is expected to contribute significantly to the existing theory by extending the classes of exosystem models that can be dealt with using internal model-based design. Applications of the proposed methodology include control of oscillatory phenomena that can be modeled by time-varying exosystems, such as oscillations with a periodically modulated frequency, parametric resonance, and attitude/orbital regulation for control of satellite formations on highly elliptic orbits.