Mixed H_2/H_∞ Output-feedback Simple Adaptive Control

摘要

A mixed H_2 and H_∞ output-feedback Simple Adaptive Control (SAC)rnproblem for continuous-time systems is considered. The stability ofrnclosed-loop SAC is related to the Almost Strictly Positive Real (ASPR)rnproperty of the controlled plant: if a plant is ASPR, there exists a staticrnoutput-feedback gain K* (parameter-dependent, possibly) which stabi-rnlizes the plant and makes it Strictly Positive Real (SPR). The SPR prop-rnerty also provides an infnite gain margin: the system remains asymp-rntotically stable with any gain that is larger than K*. This paper sug-rngests a new SAC scheme for Single-Input Single-Output (SISO) systems,rnwhich further specifies the adaptive gain in order to guarantee not onlyrnpassivity and stability of the closed-loop but also prescribed H_2/H_∞ -rnnorm bounds. Sufficient conditions to mixed H_2=H_∞ SAC synthesis arernpresented; they are expressed in terms of Bilinear Matrix Inequalitiesrn(BMIs), which can be solved using local iterations. Numerical examplesrnare given that illustrate the method and its validity.