Both state and input constrained optimization of a pedestal positioning system

The optimization of a control system with a quadratic performance index subjected to both input and state constraints is a very complicated task. To the authorʹs best knowledge, the general theoretical researches as well as the practical applications are quite few, because there exist many difficult or even more formidable obstacles in the real work. From a practical point of view based on security consideration, these constraints are very important and should be observed strictly without exception, otherwise the whole system might be destroyed and all control laws become nothing! This paper is devoted to the study of this complicated but very important problem: to find the optimal control with both state and input constrained.