Trajectories generation under constraints by linearization method Original Research Article

We present in this article a semi-analytical method for trajectories synthesis of nonlinear dynamical systems involved in the static or dynamic state feedback linearization and decoupling method, under multiple nonlinear dynamical contraints. The aim of this method is to use the well-known analytical nonlinear mappings which relate, in the nonlinear decoupling theory, the set of linear admissible control vectors functions, the set of admissible outputs, the set of admissible nonlinear state vectors and the set of admissible nonlinear control vectors, to overcome the numerical integration problem and to transpose it in an optimal problem of an exact algebraic functional. This method which discards the numerical problem of stability and convergence of the solution is particularly useful for complex and large nonlinear dynamical systems.