Optimal control in novel state derivative space system

There are two major problems that people usually have to face when they carry out optimal control designs in state space system or descriptor system. One is no state derivative considered in cost functional, the other is that some systems cannot easily design optimal control in either state space system or generalized system frameworks. To overcome the problems, a novel state derivative space system (SDS system) framework is proposed. In this novel framework, novel differential Lagrange multiplier should be used to adjoin SDS system constraint to the cost functional that is function of state derivative to straightforwardly carry out optimal control design. It showed that some singular systems with impulse mode can easily carry out optimal control in SDS system. The purpose of this research is to develop novel and simple optimal control algorithms in SDS system so that wider ranges of problems can be solved without much of mathematics overhead.