Three-dimensional approximate cooperative integrated guidance and control with fixed-impact time and azimuth constraints

A novel three-dimensional (3D) approximate cooperative integrated guidance and control (ACIGC) scheme based on backstepping control (BC), sliding mode control (SMC), dynamic surface control (DSC), and a 3D reduced-order extended state observer (ESO) for multiple hypersonic skid-to-turn (STT) missiles simultaneously attacking ground-maneuver targets is proposed in this study, which considers a fixed-impact azimuth and time constraints. First, we established a novel integrated guidance and control (IGC) model that includes the missile-target relative distance and azimuth based on the missile-target engagement dynamics, attitude dynamics, and first-order delay dynamics of the rudder. It is a 3D fifth-order strict-feedback time-varying nonlinear model with mismatched uncertainties. Second, a 3D ACIGC scheme was designed, where a cooperative strategy was designed by transforming a fixed-impact time constraint into a nominal range-to-go constraint. The IGC model consists of seeker, guidance, angle-of-attack, attitude, and rudder subsystems based on the BC, and the SMC designs each subsystem. The DSC obtains the derivatives of virtual control commands, which solves the “differential explosion” caused by the BC. The unknown target acceleration, unmodeled parts of the system states, perturbations caused by time-varying parameters, and external disturbances are regarded as lumped disturbances, which are estimated and compensated for by the 3D reduced-order ESO to improve the robustness. Subsequently, the closed-loop system was proven to be stable, and the system states were ultimately uniformly bounded using Lyapunov theory. Finally, the simulation results of three missiles attacking a simultaneously ground-maneuvering target and Monte Carlo simulations demonstrated the effectiveness and robustness of the proposed ACIGC scheme.