Abstract: From the perspective of optimal control, parameter dynamic optimization of particle swarm optimization (PSO) is addressed in this paper. This work is based on a type of simplified PSO and corresponding convergence conditions. First, to overcome the ``curse of dimensionality'', a novel swarm approximate dynamic programming (SADP) is proposed by introducing the heuristic stochastic search mechanism of swarm intelligence. Second, grounded on SADP, parameter dynamic optimization and computation are studied in detail for a deterministic PSO feedback system and a stochastic PSO system, respectively. Further, numerical experiments are performed to show the effectiveness of SADP in parameter dynamic optimization of PSO systems through computing optimal dynamics of acceleration coefficients, as well as comparing the optimized strategies with a time-varying acceleration coefficients (TVAC) strategy based on several benchmarks.