Robust iterative learning control for uncertain continuous‐time system with input delay and random iteration‐varying uncertainties

Abstract

Abstract This study deals with the problem of robust iterative learning control (ILC) for linear continuous‐time systems with input delay subject to uncertainties in input delay, plant dynamic, reference trajectory, initial conditions and disturbances. Using the internal model control (IMC) structure in the frequency domain, an ILC scheme is proposed in which the IMC structure is responsible for coping with uncertainties in both delay time and plant dynamic. Sufficient conditions are derived to ensure that the tracking error expectation is bounded and converges monotonically to a small neighbourhood of zero (in the L2‐norm sense) when uncertainties in reference trajectory, initial conditions and disturbances vary randomly from trial to trial. It is shown that the derived conditions are still valid to guarantee both boundedness and monotonic convergence of the tracking error variance (in the L2‐norm sense). Illustrative examples are provided to demonstrate the effectiveness of the proposed method.

Keywords

• Control system analysis and synthesis methods
• Stability in control theory
• Discrete control systems
• Self‐adjusting control systems
• Nonlinear control systems
• Interpolation and function approximation (numerical analysis)