This paper presents two numerical methods for solving the controlled Rayleigh nonlinear oscillator problem. The first method is based on construction of interpolation polynomials to approximate the states and subsequent control using the roots of Legendre polynomials as collocation nodal points. In the second method, we look for a piecewise continuous approximation polynomial for each state and a piecewise constant function for the control function. We show that this method leads to better results and enables us to accurately compute switching times. These methods are easy to implement, and yield very accurate results.
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