This paper presents a new parametric optimization approach based on a modified particle swarm optimization (PSO) to design a class of impulsive-correction projectiles with discrete, flexible-time interval, and finite-energy control. In terms of optimal control theory, the task is described as the formulation of minimum working number of impulses and minimum control error, which involves reference model linearization, boundary conditions, and discontinuous objective function. These result in difficulties in finding the global optimum solution by directly utilizing any other optimization approaches, for example, Hp-adaptive pseudospectral method. Consequently, PSO mechanism is employed for optimal setting of impulsive control by considering the time intervals between two neighboring lateral impulses as design variables, which makes the briefness of the optimization process. A modification on basic PSO algorithm is developed to improve the convergence speed of this optimization through linearly decreasing the inertial weight. In addition, a suboptimal control and guidance law based on PSO technique are put forward for the real-time consideration of the online design in practice. Finally, a simulation case coupled with a nonlinear flight dynamic model is applied to validate the modified PSO control algorithm. The results of comparative study illustrate that the proposed optimal control algorithm has a good performance in obtaining the optimal control efficiently and accurately and provides a reference approach to handling such impulsive-correction problem.
Real-time energy management of an islanded microgrid using multi-objective Particle Swarm Optimization
