Solving a variety of linear time-varying systems of equations with prescribed performance

Solving a linear time-varying system of equations (LTVSE) is commonly encountered in control theory, whereas previous methods for solving LTVSE suffer from inconvenient parameter fine-tuning, insufficient solution accuracy, and high computational overhead. This paper proposes a generic framework for solving a variety of LTVSE. By reformulating different systems, a generic error function is defined. Then, a prescribed-performance solver is proposed by exploiting prescribed performance theory and zeroing dynamics, and the convergence and robustness of the proposed solver are theoretically analyzed. Numerical studies demonstrate that the proposed method is at least one order of magnitude more accurate or efficient than the previous methods for solving LTVSE. More importantly, one can explicitly prescribe the performance of the solver based on available computing resource or the requirements on accuracy and convergence time. Finally, the proposed method is applied to robot control, observer construction and time-varying parameter identification, which reveals its practical value.