Monotonically convergent hybrid ILC for uncertain discrete-time switched systems with state delay

Abstract

This paper is mainly devoted to a monotonically convergent iterative learning control (ILC) design for a class of uncertain discrete-time switched systems with state delay (UDTSDSs). By taking advantage of output error and state information, a hybrid ILC law for a class of UDTSDSs is proposed. After the ILC process is transformed into a 2D system, sufficient conditions in terms of linear matrix inequalities (LMIs) are derived by using a multiple Lyapunov–Krasovskii-like functional approach and a quadratic performance function. It is shown that if certain LMIs are met, the tracking error 2-norm converges monotonically to zero along the iteration direction, while the learning gains could be determined directly by solving the LMIs. The simulation results are provided to illustrate the theoretical analysis.

Adaptive Iterative Learning Control of Switched Nonlinear Discrete-Time Systems With Unmodeled Dynamics

“…Further, the estimation errors δˆ k by the captured system inputs, outputs and the previous estimation as the learning mechanism is in the processing. In the existing literature [26]- [29], the P-type ILC, D-type ILC, PD-type ILC are hardly to determine the parameters of the learning gain. Thus, it is hopeful that the gradient-type learning gain in AILC (11) may improve the tracking performance.…”

“…It has the conclusion that the expectation of the tracking error is monotonically convergent to zero. (ii) Using (29) and 30gets…”

“…Thereafter, a PD-type ILC has been considered for a class of switched discrete-time linear systems with subsystems dynamics uncertain, and in the sense of sup-norm, the monotonic convergence is guaranteed [28]. Furthermore, reference [29] has proposed a hybrid ILC scheme for a class of switched discrete-time linear systems with the subsystems dynamics uncertainty and the state bounded delay. The analysis shows that the tracking is monotonic decay in the sense of 2-norm.…”

Adaptive iterative learning control for switched discrete-time systems with stochastic measurement noise

“…Then, in Yang (2015), it has been studied a PD-type ILC for a class of switched discrete-time linear systems with subsystems dynamics uncertain and the monotonic convergence is ensured in the sense of sup-norm. Further, Wang et al (2017) has explored a hybrid ILC scheme for a class of switched discrete-time linear systems with the subsystems dynamics uncertain and the state delay bounded, in which the monotone convergence is derived in the sense of 2-norm. Those achievements are no doubt valuable.…”

“…Those achievements are no doubt valuable. However, the traditional ILCs (Bu et al, 2013a, 2013b; Ouyang et al, 2006; Wang et al, 2017; Yang 2015) are to some extent conservative and are often difficult to determine the parameters of the learning gain as they did not make use of the dynamics information of systems. Thus, in order to improve the tracking performance, it is necessary to develop an effective ILC for switching systems, and its leaning gain is acquired by the system information.…”