Augmented Lagrange Based Particle Swarm Optimization for Missile Interception Guidance

Abstract

By raising a practical problem in missile interception guidance with detailed system dynamic equations, along with several constraints on initial states and terminal states, the optimal control problem will be converted to a parameter optimization problem by using implicit integration Hermite-Simpson method, which approximates states and control using piecewise continuous polynomials to simplify the involved integration calculations, will be used to discretize the time domain with steps of duration. Furthermore, augmented Lagrangian method (ALM) will be introduced to convert constrained problem (i.e. primal problem) into unconstrained one (i.e. barrier problem) and penalty term will be added to cost function. Meanwhile, particle swarm optimization (PSO) will be applied to optimize the parameter vector, including system states, control inputs and Lagrangian multipliers, evaluating the cost function at each iteration during the simulation until reaching the minimum value of cost function, which also suggests that the particles are converged, and the parameter vector is optimized. The main contribution of the study is to propose a hybrid optimal solver for the constrained optimization problem, an augmented Lagrangian particle swarm optimization (ALPSO), and comparison results between the self-build ALPSO solver, MATLAB built-in fmincon function, and the theoretical ones, verifying the correctness of the self-build solver for constrained optimization problems with accuracy of 15.49 m maximum error during the whole one thousand meters of flight.