Observer-based Control For Nonlinear Systems Research Articles

Resilient event-triggered observer-based control of non-linear systems under denial-of-service attacks with actuator saturation

This paper studies the control problem for a continuous-time networked system with non-linearity in the state equation as well as in the input, as saturation. The system is considered under denial-of-service (DoS), attacks which cause the blockage of input and/or output components in the overall closed-loop model. An event-triggering scheme that is resilient in nature, along with an observer-based control, has been considered under DoS attacks. The resultant scheme ensures efficient network resources and excludes Zeno behavior naturally due to the presence of a minimum positive interevent delay. Then, an event-based switched non-linear model is presented to address both the event-triggering scheme and the presence of DoS blocking attacks. A piece-wise Lyapunov–Krasovskii functional method on the described non-linear model, resulting in the switched system, is considered for achieving an exponentially stable response by driving the required feasibility conditions. In the presence of a non-linear system with saturation in the actuator, the presented design establishes quantitative relationships among the exponential decay rate, active/sleeping intervals of attacks, parameters of the event-triggering condition, and sampling period of the system. After that, linear matrix inequalities are presented for designing an event-triggered controller with an observer, while the design also includes the region of convergence for dealing with the input non-linearity. Finally, comparative results for an offshore structure model with non-linearity in states as well as in actuator, are demonstrated to verify the results of the control scheme that is developed. It has been verified that our design is less conservative than the previous designs, and can handle the non-linearities in the dynamics of plant and actuator saturation more efficiently, while DoS attacks are also present. By applying our proposed method, the overshoot and undershoot are less than ±2.5 percent, while system states converge to the origin within 55 s.

Delay-range-dependent observer-based control of nonlinear systems under input and output time-delays

The problem of designing observer-based controller for a class of nonlinear time-delay systems subjected to input and output time-varying delays is addressed in this paper. More incisively, a delay-range-dependent criterion, incorporating variation of delays between known lower and upper bounds, is established for control of nonlinear time-delay systems. The proposed methodology ensures asymptotic stability of the closed-loop system's state and the estimation error between states of the system and observer. By application of a Lyapunov–Krasovskii functional, Jensen's inequality, standard matrix inequality procedures, Luenberger-type observer, delay-interval bounds and delay-derivative limits, observer-based controller synthesis approach using nonlinear matrix inequalities for the nonlinear time-delay systems is provided. Further, a decoupling approach is employed to render a simpler condition for the observer and the controller synthesis. A novel observer-based control scheme for the linear time-delay systems with interval time-varying input as well as output lags is derived from the proposed control strategy. The traditional delay-dependent controller design, incorporating zero lower bound of the delay, for the time-delay systems is a particular scenario of the projected delay-range-dependent approach. The proposed decoupled observer-based controller synthesis condition is cast into linear matrix inequalities by means of the cone complementary linearization approach. Finally, a numerical simulation example of control of one-link flexible joint robotic arm is provided to verify the proposed design methodology.

Observer-based controller for nonlinear analytical systems

In this paper, we propose to design a polynomial observer-based control for nonlinear systems and to determine sufficient linear matrix inequality (LMI) global stabilisation conditions of the polynomial controlled system augmented by its observer. The design of the observer-based control leverages some notations from the Kronecker product and the power of matrices properties for the state space description of polynomial systems. The stability study of the polynomial controlled system augmented by its observer is based on the Lyapunov stability direct method. Intensive simulations are performed to illustrate the validity and the effectiveness of the polynomial approach used to design the control.