Physics

Nonlinear system

Tracking error

Mathematics

Ellipsoid

Agronomy

Biology

Gene

Adaptive control

Astronomy

Mathematical analysis

Artificial intelligence

Controller (irrigation)

Control (management)

Chemistry

Computer science

Quantum mechanics

Robust control

Bounded function

Control theory (sociology)

Biochemistry

Lyapunov function

Robustness (evolution)

International Journal of Systems Science

A type of high-order fully actuated (HOFA) systems with both nonlinear uncertainties and time-varying unknown parameters is considered, and a direct approach for the designs of robust adaptive stabilising controllers and robust adaptive tracking controllers is proposed based on the Lyapunov stability theory. The established controller is composed of three parts, the basic part cancels the known nonlinearities in the system and simultaneously assigns the linear dominant term in the closed-loop system, the robustness part overcomes the effects of the nonlinear uncertainties in the system, and the adaptation part adjusts online the controller to suit the effect of the unknown time-varying parameter vector. The proposed controller guarantees that the tracking error of the state to a given signal and the estimation error of the parameter vector finally converge globally into a bounded ellipsoid. Particularly, in the case that the unknown parameter vector is constant, an adaptive scheme that enables global asymptotical tracking is presented. An example demonstrates the effect of the proposed approach.

High-order fully actuated system approaches: Part V. Robust adaptive control