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This paper considers the optimal tracking control (OTC) problem for bilinear systems affected by sinusoidal disturbances, and gives a successive approximation approach to solve analogous problems for general bilinear systems. For a given bilinear OTC problem, a sequence of linear problems is constructed, and their solutions are shown to converge to the desired solution. By iteratively solving the...
In this paper, we show discretized Lyapunov functions for various nonlinear dynamical systems by using the method that the authors have proposed. We use Kushner's scheme of difference approximation with directions and Alcaraz et al.'s quantization of Markov processes to approximate Lyapunov equations by linear Schroumldinger-like equations. We construct time-invariant functions concerned with the...
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