CLF based design for attitude control of VTOL-UAVs: An inverse optimal control approach

Observer‐based robust optimal control for helicopter with uncertainties and disturbances

“…In this section, the effectiveness of the proposed observer-based robust optimal control method is demonstrated using numerical simulations. There is a close relation between the proposed controller and the inverse optimal control method, thereby the inverse optimal controller [21] is also carried out to compare their performance. The parameters of helicopter system (1) are specified as m = 798.5kg, g a = 9.8m∕s 2 , and J 0 = diag[358.4,777.9,601.4] kg•m 2 [17].…”

“…In this section, the effectiveness of the proposed observer‐based robust optimal control method is demonstrated using numerical simulations. There is a close relation between the proposed controller and the inverse optimal control method, thereby the inverse optimal controller [21] is also carried out to compare their performance. The parameters of helicopter system () are specified as $$$ m=798.5\kern0.1em \mathrm{kg},{g}_a=9.8\kern0.1em \mathrm{m}/{\mathrm{s}}^2 $$$, and $$$ {J}_0=\operatorname{diag}\left[\mathrm{358.4,777.9,601.4}\right]\kern0.1em \mathrm{kg}\cdotp {\mathrm{m}}^2 $$$ [17].…”

“…Figure 2 depicts the attitude angles and altitude responses for the helicopter with the proposed method compared with the inverse optimal controller [21]. Both two controllers have good control performance when there is no model uncertainties and external disturbances.…”

“…Let $$$ V $$$ be a Lyapunov function for the nominal system, then $$$ V $$$ is a CLF [21] if $$$ \forall x\ne 0 $$$, $$$$ {L}_GV=0\Rightarrow {L}_FV<0. $$$$ …”

“…A CLF-based control approach is developed to design a nonlinear optimal controller in Freeman and Primbs [20]. Guerrero-Castellanos et al [21] present an optimal control design using the relationship between Sontag's formula and the HJB equation for unmanned aerial vehicles. The study on designing optimal controllers for spacecrafts based on inverse optimal control and Sontag-type formula can be tracked to the work [22][23][24].…”