Open-loop and feedback bounded control in linear systems

The classical PID regulators technique gives infinite control time duration and the constraints usually imposed on control do not take into consideration. The saturating linear feedback (SLF) meets the imposed control constraints but the control time is also infinite and the known difficulties restrict implementation of SLF. It is also known that the time-optimal bounded control steers the system to a terminal state in finite time. However, it is not easy to fabricate the switching surface if the dimension of the system is high. Therefore, in most applications, the time-optimal feedback has not been used. We attempt to design a nonlinear bounded feedback that gives the finite control time duration and is not complicated. This technique provides the control with the following properties: the control is presented in closed-loop form, can be calculated online, and meet the imposed constraints; the control is, to some degree, suboptimal and robust. An example is given to illustrate the proposed control technique