High‐order internal model‐based iterative learning control design for nonlinear distributed parameter systems

Abstract

SummaryThis article deals with the problem of iterative learning control algorithm for a class of nonlinear parabolic distributed parameter systems (DPSs) with iteration‐varying desired trajectories. Here, the variation of the desired trajectories in the iteration domain is described by a high‐order internal model. According to the characteristics of the systems, the high‐order internal model‐based P‐type learning algorithm is constructed for such nonlinear DPSs, and furthermore, the corresponding convergence theorem of the presented algorithm is established. It is shown that the output trajectory can converge to the desired trajectory in the sense of (L2,λ)‐norm along the iteration axis within arbitrarily small error. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.

Spatiotemporal adaptive state feedback control of a linear parabolic partial differential equation

“…In this area, an active issue is the stabilization of PDEs via boundary or in-domain control. [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] These results are established under an assumption that all parameters in the PDEs are exactly known. This assumption is strong for physical systems due to that the system parameters usually vary with operating conditions and their exact value is hard to obtain.…”

“…This is because most physical phenomena are spatiotemporally variant in nature and could be described by a mathematical model of PDE form, 1‐4 for example, fluid, thermal diffusion, concentration, and flexible vibration. In this area, an active issue is the stabilization of PDEs via boundary or in‐domain control 5‐24 . These results are established under an assumption that all parameters in the PDEs are exactly known.…”

Iterative Learning Tracking Control for a Vehicle-Manipulator System With Input Constraint

“…The initial conditions are given as z(x, 0) = 0.0004x 2 , ż(x, 0) = 0.001, θ(0) = θ(0) = 0, s(0) = ṡ(0) = 0. For showing the control performance of proposed control algorithm (20) for the mobile flexible manipulator system with saturation constraint and uncertain disturbances ( 11)- (17) in this paper, the simulations are divided into different four cases.…”

A unified adaptive control approach of nonlinear continuous non‐parameterized systems with asymmetric control gains for trajectory tracking in different domains

“…For trajectory tracking tasks of dynamical systems repetitively over a finite time interval, iterative learning control (ILC) is an intelligent control strategy that updates control inputs iteratively after each cycle by utilizing the control experience at past cycles such that the current tracking performance is improved progressively. Recent three decades have witnessed considerable ILC achievements in terms of theoretical development and experimental applications 1–6 …”

“…Recent three decades have witnessed considerable ILC achievements in terms of theoretical development and experimental applications. [1][2][3][4][5][6] The ILC methods in early period have been mainly investigated under the strict repeatability assumptions that the initial state, reference trajectory, time length of trail, and model parameters and so forth of the controlled system are invariant with iterations. 6,7 Nevertheless, in many practical ILC applications, initial system outputs at different iterations often deviate irregularly from the initial value of the reference trajectory due to inaccurate initial localization of the controlled system.…”