Adaptive Control Of Uncertain Lower-Triangular Nonlinear Systems And Its Applications

In recent years, a lot of researchers are particularly interested in online approximation based adaptive control of uncertain lower-triangular nonlinear systems. This dissertation is concerned with neural networks based adaptive tracking control of uncertain lower-triangular nonlinear systems and trajectory tracking of autonomous underwater vehicle. The main contributions of the dissertation are as follows.First, a novel robust adaptive tracking control approach is presented for a class of uncertain lower-triangular nonlinear systems with known gains. By employing radial-basis-function neural network to account for system uncertainties, the proposed scheme is developed by combining "command filter" and "minimal learning parameter" techniques. The main advantages of the proposed controller are that:(1) the problem of "explosion of complexity" inherent in the conventional backstepping method is avoided; (2) the problem of "dimensionality curse" is solved and only one adaptive parameter that needs to be updated online. These advantages result in a much simpler adaptive control algorithm, which is convenient to implement in applications. Finally, stability analysis shows that uniform ultimate boundedness of the solution of the closed-loop system can be guaranteed.Second, in order to solve the problem of complexity completely, a novel adaptive neural network tracking control scheme is proposed for a class of uncertain lower-triangular nonlinear systems with unknown gains. In the controller design process, all the unknown functions at intermediate steps are passed down, and only one neural network is used to approximate the lumped unknown function of the system at the last step and then the norm of weight vector rather than the weight vector elements themselves is used as the estimated parameter. In this way, the presented adaptive control law contains only one adaptive parameter. Therefore, the computational burden is significantly alleviated and the control scheme is more implemented in practical applications. Stability analysis shows that the uniform ultimate boundedness of all the signals in the closed-loop system can be guaranteed, and the steady state tracking error can be made arbitrarily small by appropriately choosing control parameters.Third, two robust adaptive control approaches are presented for trajectory tracking of autonomous underwater vehicle with unknown mathematical model. The problem of "explosion of complexity" inherent in the conventional backstepping method is avoided by using the "command filter" and the "dynamic surface control" techniques respectively. In addition, by employing radial basic function neural network to account for modeling errors and the norm of weight vector rather than the weight vector elements themselves is used as the estimated parameter, so the presented adaptive control law contains only one adaptive parameter. Therefore, the computational burden is significantly alleviated and the control schemes are more implemented in practical applications. The proposed controllers guarantee that all the close-loop signals are uniform ultimate boundedness and that the tracking errors converge to a small neighborhood of the desired trajectory if the design parameters are appropriately chosen. Finally, simulation studies are given to illustrate the effectiveness of the proposed algorithms.