Linear feedback control for a nonlinear multirotor aerial vehicle model with stochastic parameter uncertainties
Mateus de Freitas Virgílio Pereira1; Davi Ferreira de Castro1; Igor Afonso Acampora Prado1; Davi Antônio dos Santos1; José Manoel Balthazar1
1 Instituto Tecnológico de Aeronáutica (ITA)
doi:10.20906/CPS/CON-2016-1237
Resumo
Applications of Multirotor aerial vehicles (MAVs) have been gaining in popularity in the last decade. A current topic of research is the design of control laws for nonlinear MAV models that guarantee both stability and robustness to uncertainties in the determination of the system parameters. In this paper, we present a polynomial chaos-based framework for designing optimal linear feedback control laws for the nonlinear MAV model with stochastic parameter uncertainty. The spectral decomposition in orthogonal polynomial basis, prescribed by the Wiener-Askey scheme, provides a deterministic framework from which the control design is derived. Optimality of the proposed control law is proved by solving the Hamilton-Jacobi-Bellman equation and asymptotically stability of the controlled nonlinear systems is guaranteed in the Lyapunov sense. Numerical simulations are carried out for an octocopter model that accounts for the coupling between the dynamical modes. The results are verified with Monte-Carlo simulations.
Palavras-chave: Polynomial chaos; Uncertainty; Multirotor aerial vehicles; Linear feedback control