Research On Optimal Control With Two Kinds Of Stochastic System

Optimal Control Theory has increasingly wide range of applications, its rich theoretical foundation and advanced technologies provide lots of useful tools to solve today’s social and technological control issues. Control systems can be divided into deterministic and stochastic control systems. Over the years, many scholars have done a lot of researches on deterministic systems, but researches on stochastic control system are relatively small.However, in reality, there are many random factors in the systems, for solving practical problems effectively, it is necessary to select the appropriate control variable and establish performance indicators. First, this paper mainly studies the stochastic optimal control for a class of capital accumulation system, its conclusion is the expansion of the deterministic one. Then, we study the near-optimality of the stochastic population system, for the optimal control needs strict conditions relatively, and also not any one has its own optimal control. To this end, we provide the necessary and sufficient conditions for optimal control of stochastic systems with Poisson jumps.