Resilient nonlinear control for attacked cyber-physical systems

In this paper, the problem of resilient nonlinear control for cyber-physical systems (CPSs) over attacked networks is studied. The motivation for this paper comes from growing applications that demand the secure control of CPSs in industry 4.0. The nonlinear physical system considered can be attacked by changing the temporal characteristics of the network, causing fixed time or time-varying delays and changing the orders of received packets. The systems under attack can be destabilized if the controller is not designed to be robust with an adversarial attack. In order to cope with nonlinearity of the physical system, a nonlinear generalized minimum variance controller and a modified Kalman estimator are derived. A worst-case controller is presented for fixed-time delay. In the situations of time-varying delays and out-of-order transmissions, an opportunistic estimator and a resilient controller are designed through an on-line algorithm in the sense that it is calculated by using the information in the received packets immediately. The ability to use the received information immediately leads to the improvement of the controller's performance. Simulation results are provided to show the applicability and performance of control law developed.