Determining attractors, basins of attraction and trajectory control of nonlinear dynamical systems

This dissertation addresses the problem of determining attractors, basins of attraction and trajectory control of nonlinear systems.;The first part of the dissertation develops the Interpolated Cell Mapping (ICM) method, which allows the determination of nonlinear system characteristics with much less computational cost than required by direct numerical integration. Unlike the earlier Simple Cell Mapping (SCM) and related methods, ICM can be used to compute fine scale characterizations, such as fractal boundary structures and strange attractors. A QC;The second part of the dissertation concerns the problem of controlling a given nonlinear system such that it follows a desired trajectory. The problem of adaptive motion control of robot manipulators with unknown parameters is treated. A method is developed that is free from such unrealistic assumptions as measuring angular accelerations in real time. This algorithm also preserves the symmetry of joint velocities in the quadratic term, and therefore can be implemented through a Newton-Euler fast recursive algorithm, thus significantly decreasing the sampling period and increasing accuracy. This algorithm can also express the global convergence rate of tracking errors explicitly.