Inverse optimal sliding mode guidance law against maneuvering targets

In this paper, two composite inverse optimal guidance laws against maneuvering targets have been proposed and the stability analysis is also presented. The first guidance law is constructed through a combination of Sontag’s formula and first order sliding mode control. In order to mitigating the undesired chattering caused by the discontinuous sign function, another robust guidance law is then synthesized using adaptive super-twisting algorithm. By virtue of the proposed adaptive law, the second guidance law only requires the time derivatives of the lumped uncertainties are bounded, but their upper bounds can be unknown. An important feature of the proposed adaptive algorithm is in non-overestimating the values of the control gains, which is achieved by introducing a ‘detector’ term in the updating law. Finally, some numerical simulations are carried out to demonstrate the effectiveness of the proposed formulations.