Stabilising feedback control schemes of dynamical systems with completely unknown saturated inputs: an adaptive design method

The objective of this paper is mainly to present a simple design method to synthesise the stabilising feedback control schemes for dynamical systems with input saturations. In this paper, such a simple design method, called an adaptive design method, is presented so that (i) the presented design method is easy to understand for the system designers; (ii) it is not necessary to know any information on the saturated input nonlinearities; and (iii) the resulting control schemes are simple and easy to implement in practical control problems. Here, a linear dynamical system with any unknown saturated input nonlinearities is used to describe this method. For such dynamical systems, by making use of the presented design method, the resulting feedback control schemes consist of a conventional optimal control law and an adaptive control gain, and the resulting closed-loop control dynamical systems are globally stable. By combining the presented adaptive design method with other control ones, a number of interesting results can be expected for a rather large class of dynamical systems with saturation in the actuators. Finally, some illustrative numerical examples are provided to demonstrate the validity of the presented adaptive design method.