Abstract
A PD-type iterative learning control algorithm is applied to a class of linear discrete-time switched systems for tracking desired trajectories. The application is based on assumption that the switched systems repetitively operate over a finite time interval and the switching rules are arbitrarily prespecified. By taking advantage of the super-vector approach, a sufficient condition of the monotone convergence of the algorithm is deduced when both the model uncertainties and the external noises are absent. Then the robust monotone convergence is analyzed when the model uncertainties are present and the robustness against the bounded external noises is discussed. The analysis manifests that the proposed PD-type iterative learning control algorithm is feasible and effective when it is imposed on the linear switched systems specified by the arbitrarily preset switching rules. The attached simulations support the feasibility and the effectiveness.
Highlights
A switched system consists of finite subsystems described by differential equations or difference equations and a switching rule which specifies a subsystem being activated during a certain time subinterval [1, 2]
The application is based on assumption that the switched systems repetitively operate over a finite time interval and the switching rules are arbitrarily prespecified
Assume that the switched systems repetitively operate over a finite time interval and the switching rules are arbitrarily
Summary
A switched system consists of finite subsystems described by differential equations or difference equations and a switching rule which specifies a subsystem being activated during a certain time subinterval [1, 2]. Main reason may be that the arbitrary switching rules will result in indeterminate dynamical behaviors of the controlled switched systems, which does not meet requirement of trajectory tracking problem. According to ILC’s mechanism, the activated subsystems running over a certain time subinterval in different iterations are required to be identical This means that the dynamics of the controlled system is iteration-invariant. When the ILC strategies are used on the switched systems, a key assumption should be made that the switching rule which specifies activated subsystems at different time subintervals is iteration-invariant. In [3], a P-type ILC scheme has been applied to a class of linear discrete-time switched systems, where the convergence property is analyzed by the super-vector approach.
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