This paper presents an up to date advances in time-domain system identification using fractional models. Both equation-error- and output-error-based models are detailed. In the former models, prior knowledge is generally used to fix differentiation orders; model coefficients are estimated using least squares. The latter models allow simultaneous estimation of model coefficients and differentiation orders using nonlinear programing. As an example, a thermal system is identified using a fractional model and is compared to a rational one.

This article deals with the issue of tracking a reference optimal trajectory for an autonomous nonlinear vehicle model by designing both lateral and longitudinal robust feedback control and a suited feedforward control. In previous works, a strategy based on a human-driver field of view was used to plan an optimal trajectory reference. The optimization has been made using a Genetic Algorithm (GA), and the obtained trajectory has been injected into a Potential Field (PF) so as to be reactive to unforeseen events by using a point mass model. Here, the previously developed GA-PF planification process is integrated in a new complete global planning and tracking method and applied to a validation nonlinear vehicle model. This control tracking method is developed in two strategies: a bicycle model is used as model inversion for feedforward design and a robust control is designed as feedback control in order to take the vehicle (mass and velocity) and road (slope and adherence) parameter variations into account. A lateral nonlinear control and a longitudinal robust control are designed. Realistic autonomous car simulation results are provided on an overtaking scenario and a round-about scenario.

This paper deals with recursive continuous-time system identification using fractional-order models. Long-memory recursive prediction error method is proposed for recursive estimation of all parameters of fractional-order models. When differentiation orders are assumed known, least squares and prediction error methods, being direct extensions to fractional-order models of the classic methods used for integer-order models, are compared to our new method, the long-memory recursive prediction error method. Given the long-memory property of fractional models, Monte Carlo simulations prove the efficiency of our proposed algorithm. Then, when the differentiation orders are unknown, two-stage algorithms are necessary for both parameter and differentiation-order estimation. The performances of the new proposed recursive algorithm are studied through Monte Carlo simulations. Finally, the proposed algorithm is validated on a biological example where heat transfers in lungs are modeled by using thermal two-port network formalism with fractional models.