Iterative Learning Control Design for Discrete-Time Stochastic Switched Systems
- PDF / 593,588 Bytes
- 15 Pages / 612 x 792 pts (letter) Page_size
- 7 Downloads / 236 Views
PICAL ISSUE
Iterative Learning Control Design for Discrete-Time Stochastic Switched Systems P. V. Pakshin∗,a and J. P. Emelianova∗,b ∗
Arzamas Polytechnic Institute of R.E. Alekseev Nizhny Novgorod State Technical University, Arzamas, Russia e-mail: a [email protected], b [email protected] Received March 2, 2020 Revised May 27, 2020 Accepted July 9, 2020
Abstract—Discrete-time linear systems with switching in the repetitive mode are considered. The systems are subjected to random disturbances, and the measurements are corrupted by additive noises. Two iterative learning control design methods are proposed. Both of the methods involve an auxiliary 2D model in the form of a discrete repetitive process. The first method is based on the dissipativity conditions established for the auxiliary model with a special choice of the supply rate and storage function. This choice allows finding a control law (in the general case, nonlinear) that ensures the convergence of the learning process. The second method adopts a linear iterative learning control update law of a given form, while the convergence of the learning process is ensured by the stability conditions of the auxiliary 2D model. The structure of both control laws includes a stationary Kalman filter. The stability conditions are obtained using the divergent method of vector Lyapunov functions. An example is given to demonstrate the capabilities and features of the new method. Keywords: iterative learning control, stochastic systems, switched systems, repetitive processes, 2D systems, stability, dissipativity, vector Lyapunov function DOI: 10.1134/S0005117920110053
1. INTRODUCTION Iterative learning control plays an important role in improving the accuracy of systems operating in a repetitive mode, in particular, in the design of high-precision gantry robots. Due to its high efficiency and relatively simple form, such control attracts wide interest of both theorists and practitioners. Since the late 1980s, the largest international conferences have organized regular sessions devoted to the problems of iterative learning control. Real systems are subjected to random disturbances, and the systems always contain systematic and random measurement errors. These factors reduce the accuracy of control; moreover, for each repetition (pass, trial) of the process, the initial conditions must be the same for making the iterative learning control approach effective. Thus, taking the random factors into account is essential. The basic principles of iterative learning control were proposed in the US patent with priority [1] registered in 1967. Later on, the concept of such control was formulated in the Japanese journal [2]. These ideas were not in demand until a series of publications [3–6] appeared, which aroused much interest of both researchers and engineers. Subsequently, a large number of papers were published on various issues of iterative learning control, including the monographs [7, 8], the surveys [9, 10] and special issues of international journals (International Jo
Data Loading...
