Legendre-Tau Approximations for LQR Feedback Control of Acouustic Pressure Fields

Active noise control techniques have become increasingly important in problems where noise reduction is required without addition of signiicant amount of mass. In this work, a one dimensional example of an active noise control problem is presented. The problem is formulated as a periodic linear quadratic tracking problem. Then an approximation framework based on the Legendre-Tau method for approximating the control system is developed and stability and convergence results are given for approximation. Numerical examples are presented to illustrate convergence of the computational method and the dependence of the solutions on the various parameters which deene the control problem.

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