Optimal control systems by time-dependent coefficients using CAS wavelets. (English) Zbl 1185.49033

Summary: This paper considers the problem of controlling the solution of an initial boundary-value problem for a wave equation with time-dependent sound speed. The control problem is to determine the optimal sound speed function which damps the vibration of the system by minimizing a given energy performance measure. The minimization of the energy performance measure over sound speed is subjected to the equation of motion of the system with imposed initial and boundary conditions. Using the modal space technique, the optimal control of distributed parameter systems is simplified into the optimal control of bilinear time-invariant lumped-parameter systems. A wavelet-based method for evaluating the modal optimal control and trajectory of the bilinear system is proposed. The method employs finite CAS wavelets to approximate modal control and state variables. Numerical examples are presented to demonstrate the effectiveness of the method in reducing the energy of the system.


49M30 Other numerical methods in calculus of variations (MSC2010)
35L05 Wave equation
35L20 Initial-boundary value problems for second-order hyperbolic equations
70Q05 Control of mechanical systems
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
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