Learning Control Methods Of Continuous-Time Nonlinear Systems

The existing researches are mainly concerned about nonlinear system with constant parametric and matched uncertainties. Challenges in the controller design arise when dealing with time-varying parametric and unmatched uncertainties. Iterative learning control is quite suitable for plants with repetitive dynamic characteristic. This method features the achieved complete tracking for the output trajectory. Through Lyapunov-like synthesis, this thesis presents several learning control schemes for typical classes of nonlinear systems. Our work mainly focuses on the following aspects:Firstly, design procedures of adapative control are presented for time-invariant strictly feedback nonlinear systems. And the strict feedback form of a class of time-varying nonlinear systems is derived by coordinate transformation.Secondly, for dealing with nonlinear systems with time-varying parametric and unmatched uncertainties, the time-varying parameters are expanded into Fourier series, by which adaptive back-stepping control for both minimum phase and 'weak' non-minimum phase systems are presented.Thirdly, for the non-minimum systems, output-redefinition technique is applied to handle the non-minimum phase characteristics, and both iterative learning control and repetitive learning control are developed.Fourthly, for the time-varying robot systems, when there exists the initial repositioning errors, iterative learning control is presented to achieve the complete tracking by modifying the desired trajectory. And a mixed repetitive learning scheme is give for tracking the periodic trajectoris.Finally, the boundedness of all the signals in the close loop systems and the convergence of the tracking error are guaranteed through rigorous analyses. Numerical simulations are conducted to demonstrate the effectiveness of the proposed learning control algorithms.