Quantum mechanics

Controllability

Adaptive control

Algorithm

Control (management)

Applied mathematics

Convergence (economics)

Stability (learning theory)

Economics

Computer science

Projection (relational algebra)

Tracking error

Physics

Nonlinear system

Trajectory

Mathematics

Astronomy

Underactuation

Lyapunov function

Artificial intelligence

Economic growth

Control theory (sociology)

Artificial neural network

Machine learning

Nonlinear Dynamics

This paper studies neural network-based tracking control of underactuated systems with unknown parameters and with matched and mismatched disturbances. Novel adaptive control schemes are proposed with the utilization of multi-layer neural networks, adaptive control and variable structure strategies to cope with the uncertainties containing approximation errors, unknown base parameters and time-varying matched and mismatched external disturbances. Novel auxiliary control variables are designed to establish the controllability of the non-collocated subset of the underactuated systems. The approximation errors and the matched and mismatched external disturbances are efficiently counteracted by appropriate design of robust compensators. Stability and convergence of the time-varying reference trajectory are shown in the sense of Lyapunov. The parameter updating laws for the designed control schemes are derived using the projection approach to reduce the tracking error as small as desired. Unknown dynamics of the non-collocated subset is approximated through neural networks within a local region. Finally, simulation studies on an underactuated manipulator and an underactuated vibro-driven system are conducted to verify the effectiveness of the proposed control schemes.

Adaptive neural network tracking control for underactuated systems with matched and mismatched disturbances