Search

An important issue in the area of multi-operation systems is the observation of a discontinuous trajectory. In order to track a discontinuous output trajectory, we choose impulsive differential systems to generate a series of local continuous state trajectories, which become a set of output trajectories via the action of the output functions. Concerning impulsive differential control systems, we design proportional–derivative (PD-type) and proportional plus one order derivative and fractional order derivative (PDDα-type) iterative learning control laws with initial state learning. In particular, the PDDα-type law is more flexible due to the impact of a certain fractional order factor α. Thereafter, we give the associated convergence characteristics by establishing sufficient conditions on open-loop and closed-loop iterative learning schemes in the sense of λ-norm under mild assumptions. Finally, several numerical examples, including an application to robotic fish, are given to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, a new class of stochastic impulsive differential equations involving Bernoulli distribution is introduced. For tracking the random discontinuous trajectory, a modified tracking error associated with a piecewise continuous variable by zero-order holder is defined. In the sequel, a new random ILC scheme by adopting global and local iteration average operators is designed too. Sufficient conditions to guarantee the convergence of modified tracking error are obtained by using the tools of mathematical analysis via an impulsive Gronwall inequality. Finally, two illustrative examples are presented to demonstrate the performance and the effectiveness of the averaging ILC scheme to track the random discontinuous trajectory. [ABSTRACT FROM AUTHOR]