Development of a Mushy State Simulated Annealing Algorithm for the Design of an Optimal Path Regulator Autopilot System

In this paper, initially the six degrees of freedom aircraft nonlinear equations of motion as well as the navigation relations are derived for a specified air vehicle in state space format. Subsequently through optimal formulation of the problem utilizing linear quadratic regulator (LQR) approach, optimal controls are determined for finite horizons in order to guide the vehicle on a pre-specified trajectory. In the proposed strategy the finite horizon forces and moments are taken as the six controls to be optimally determined using (LQR) and the receding horizon control (RHC) algorithm. These optimal forces and moments could be generated through the conventional existing vehicle mechanisms, namely the engines and the control surfaces. In essence, the engine commands and control surface deflections need to be determined in a fashion that would in turn produces these required optimal forces and moments, that are initially computed. To this end, the mushy state simulated annealing (MSSA) approach is utilized as a novel idea to perform the above-mentioned task that also shows the potential of this intelligent search engine for a practical aerospace problem of flight mechanics. With this idea, the optimal control commands are derived for consecutive time steps through inverted dynamics using algebraic equations in a closed loop fashion. Each time step resulting commands are applied to the vehicle through its nonlinear equations of motion in order to obtain the next updated states of the system. The loop iterates forward while the aircraft tries to track the desired path. It is shown that the proposed integrated closed loop scheme has good robustness properties against disturbances and thus could be potentially used for complex nonlinear control systems.