Tracking control of chaotic spinning disks via nonlinear dynamic output feedback with input constraints

Abstract

In many control engineering applications, it is impossible or expensive to measure all the states of the dynamical system and only the system output is available for controller design. In this study, a new dynamic output feedback control algorithm is proposed to stabilize the unstable periodic orbit of chaotic spinning disks with incomplete state information. The proposed control structure is based on the T‐S fuzzy systems. This investigation also introduces a new design procedure to satisfy a constraint on the T‐S fuzzy dynamic output feedback control signal. This procedure is independent of the exact value of initial states. Finally, computer simulations are accomplished to illustrate the performance of the proposed control algorithm. © 2015 Wiley Periodicals, Inc. Complexity 21: 148–159, 2016

NON‐PDC Observer‐Based T‐S Fuzzy Tracking Controller Design and its Application in CHAOS Control

“…The results are given in Fig. , where the symbol “○” stands for the points that our methods lead to a feasible solution and the symbol “×” indicates the feasible points using the method of . From this figure, it is clear that the proposed method in this paper leads to a larger feasibility area due to employing the fuzzy Lyapunov function instead of the common quadratic Lyapunov function.…”

“…Suppose that the system matrices in the T‐S model (24) are perturbed as where a and b are two parameters that vary in the intervals [−100, 100] and [−50, 50], respectively. To show the effectiveness of the fuzzy Lyapunov function over the common quadratic Lyapunov function, we solve the LMIs of Theorem 1 and the LMIs proposed in for selected values of a and b in the abovementioned intervals. We set | x i | < 10 , i = 1 , .…”

“…Comparison of feasibility regions using Theorem 1 “o” and “×”. [Color figure can be viewed at wileyonlinelibrary.com]…”

“…Therefore, the main advantage of the proposed method in Theorem 1 in contrast with the methods in is that we removed the assumption that the s do not depend on the control signal. On the other hand, the authors of assume that grades of membership functions' derivatives do not depend on the system input , which is a major restriction and is not applicable to many T‐S systems such as the spinning disk system given in section II.Remark Recently, we proposed a solution to the problem of the chaos control of spinning disks in . The main differences between this paper and and the main novelties of this paper are summarized as follows:…”

“… The controller structure: In this paper, we have used a novel non‐PDC observer‐based tracking controller whereas in a dynamic output feedback controller was utilized. The Lyapunov function structure for the synthesis of the tracking controller: In this paper, we have employed the fuzzy Lyapunov function approach for the synthesis of the controller to derive less conservative conditions in contrast with the methods which are based on the common quadratic Lyapunov functions such as . Proposing a new method to tackle the problem of the appearance of the derivatives of grades of membership functions in the derivative of the fuzzy Lyapunov function, which was mentioned in the previous Remark. Remark It should be noted that the design conditions in Theorem 1 are valid when the norm of the difference between the initial conditions of the observer and the desired T‐S model is less than the prescribed value ; i.e. .…”