基于粒子群优化算法的的分数阶系统二次型最优控制算法

目前，利用分数阶变分法和分数阶非变分法，解决分数阶系统的二次型最优控制问题时，存在数值算法的收敛效果不够好，近似化的步骤过于繁琐，且计算耗时长，以及在使用传统的梯度迭代优化算法解决分数阶系统的二次型最优控制问题时，对于优化函数要求较高等问题。本文针对一类Caputo定义下的确定性线性分数阶系统，首先，设计一种状态反馈控制器，考虑从优化角度去解决分数阶系统的二次型最优控制问题，然后，利用PSO求二次型性能指标的最优值，即系统的最优控制增益，最终，得到系统的最优控制律。仿真结果表明，PSO比传统的梯度迭代优化算法收敛效果更佳，通用性更好，获得的性能指标更小，验证了该算法有效可行。

Quadratic Optimal Control Algorithm for Fractional Order Systems Based on PSO

At present, when using the fractional order variation method and the fractional order non-variational method to solve the quadratic optimal control problem of the fractional order system, the convergence effect of the numerical algorithm is not good enough, the approximation step is too cumbersome, and the calculation takes a long time. And when using the traditional gradient iterative optimization algorithm to solve the quadratic optimal control problem of the fractional order system, the optimization function requires higher problems. In this paper, for a class of deterministic linear fractional systems under the definition of Caputo, firstly, a state feedback controller is designed to solve the quadratic optimal control problem of fractional order systems from the optimization point of view, and then use PSO to find the second time. The optimal value of the type performance index, that is, the optimal control gain of the system, finally, the optimal control law of the system is obtained. The simulation results show that PSO has better convergence effect and better generality than traditional gradient iterative optimization algorithm, and the performance index is smaller. The algorithm is valid and feasible.