自治切换混杂系统优化控制研究与实现

An Approach to Optimal Control for Switched Systems with Autonomous Switching

研究了比受控切换具有更多参数约束的自治切换混杂系统优化控制问题.给出了优化控制的数学模型和计算泛函极值的必要条件,提出了一种可以解决多个切换时刻的综合极大值原理算法,能给出问题的全局最优解,可以使搜索尽可能好地指向极小点,同时避免直接求解目标函数偏导产生的大计算量,并对算法的收敛性进行了研究.仿真实例验证了该自治切换混杂系统优化策略的有效性.

The optimization for switched systems with autonomous switching is studied, which have more constraints than the controlled switching. The mathematical model and necessary conditions for the optimal control are presented. The Composite Maximum Principle algorithm for multiple autonomous switchings is proposed. This method can obtain the global optimal solution and provide a good direction for searching. It also avoids the enormous computation caused by solving the derivatives of the optimal cost function. Convergence analysis and numerical testing show the optimal control approach is effective and efficient.