Chebyshev Pseudospectral Trajectory Optimization of Differential Inclusion Models

Chebyshev pseudospectral methods have been proven to deal efficiently with complex differential equation models with point-based boundary conditions. Due to the uncertainties underlying any dynamical model, we propose an extension of such methods to the case of differential inclusions problems with boundary conditions expressed as tolerance domains. This enables to deal with time optimal problems for which the initial and the terminal states are not given precisely but rather known to be specified tolerance domains. A numerical example based on a derivative-free minimization method is provided, which shows the soundness of the proposed approach.