【摘要】 本文研究了一类带有终端约束的切换系统在有限时间内的最优控制问题.终端约束的出现使得最优控制问题的值函数不再是处处可微的,甚至是不连续的.因此,原来关于无穷时间域上的值函数是Bensoussan-Lions拟变分不等式(QVI)的粘性解的这一结论已不再适用.本文采用了动态规划方法和生存定理将QVI的解延拓到了下半连续的情形,并且得到了有限时间最优切换控制问题的值函数是QVI的下半连续解的重要结论.更多还原

【Abstract】 A class of deterministic switched control problems with end-point constraint in finite horizon is addressed.An end-point constraint makes the value-functions being not differentiable everywhere or even discontinuous.As a result,the former conclusion that the value-functions for infinite horizon are the unique viscosity solutions to a Bensoussan-Lions type quasi-variational inequality(QVI) is no longer valid.We extend the viscosity solutions to the lower semi-continuous case by using the dynamic programming and the viability theory.更多还原