Abstract
To solve trajectory tracking problem of switched system with sensor saturation, an iterative learning control algorithm is proposed. The method uses actual measurement error to modify the control variable of system on the premise that switched rule does not change along iteration axis, but it randomly changes along time axis. Moreover, by dealing with the saturation via diagonal matrix method, the convergence of the algorithm is strictly proved in the sense of λ‐norm, and the convergence condition is derived. The algorithm can achieve complete tracking of desired trajectory in the finite time interval under the random switched rule, as iterations increase. The simulation example verifies the validity of the proposed algorithm.
Highlights
The switched system is one of the important hybrid systems, which consists of a set of continuous-time or discrete-time subsystems and switched logics on these subsystems [1], because it can describe many complex systems in the engineering field which cannot be described by any single model
Researchers mostly adopt the method of the dwell time and the average dwell time, the multiple Lyapunov function method, and the common Lyapunov function method to analyze the stability for the switched system [6,7,8,9]
The application of the multiple Lyapunov function can improve the flexibility of system analysis and design; the multiple Lyapunov function method needs to construct one or more Lyapunov functions for each subsystem and compare the Lyapunov function values of switched time points [19, 20], such that it needs some certain solution information of switched system, which is contrary to the thought of the Lyapunov direct method
Summary
The switched system is one of the important hybrid systems, which consists of a set of continuous-time or discrete-time subsystems and switched logics on these subsystems [1], because it can describe many complex systems in the engineering field which cannot be described by any single model. The proposed algorithm can enable the system output to completely track the desired trajectory in a finite time interval, rather than asymptotic tracking (ii) Compared with [27,28,29,30], the algorithm in this paper considers the saturation constraint of the sensor in practical engineering and modifies the control input by using the actual measurement error with saturation constraint instead of the tracking error, and the iterative learning control problem of switched systems with sensor saturation constraints is solved (iii) In [29, 30], the convergence condition of linear matrix inequality form is derived by constructing Lyapunov function, while in this paper, the convergence condition of norm form is obtained by using contraction mapping method based on the idea of [27, 28], which avoids constructing the Lyapunov function and solving linear matrix inequality.
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