Optimal Switching Control for Nonlinear Systems in A Finite Duration

这份报纸为一个将军建议一个最佳的控制问题非线性的系统与有限地许多可被考虑的控制设置并且与分到控制切换的费用。与动态编程和粘性解决方案理论，我们证明切换降低值的功能是伪变化的不平等(在这上下文的 Hamilton-Jacobi 方程的适当归纳) 的适当系统的一个粘性解决方案并且最小如此的开关存储函数等于连续切换为游戏降低值。与更低的价值功能，最佳的切换控制为最小化运用系统的费用被设计。

This paper proposes a optimal control problem for a general nonlinear systems with finitely many admissible control settings and with costs assigned to switching of controls. With dynamic programming and viscosity solution theory we show that the switching lower-value function is a viscosity solution of the appropriate systems of quasi-variational inequalities（the appropriate generalization of the Hamilton-Jacobi equation in this context） and that the minimal such switching-storage function is equal to the continuous switching lower-value for the game. With the lower value function a optimal switching control is designed for minimizing the cost of running the systems.