Robust Adaptive Control Of Uncertain Nonlinear Systems

With the development of science and technology, the more effective control algorithms for the nonlinear system are required. In order to promote the progress in the nonlinear control theory, a set of robust adaptive control methods is presented for a class of nonlinear systems with mismatched uncertainties. The major contributions of this dissertation are:(1) A robust adaptive backstepping scheme with a dead zone modification is proposed for a class of uncertain nonlinear systems with unknown control direction, uncertain parameters and unmodeled dynamics. A priori knowledge of the sign of the control direction is not required. With priori knowledge of the bounds of the parametric uncertainties, the smooth projection method and the discontinuous projection method are incorporated into the adaptive laws to prevent parameter drifts respectively. The number of parameter estimates is minimal for the two cases. It is proved that under the proposed control law, all closed-loop signals are bounded and the tracking error converges to the any prescribed small interval around zero.(2) A robust adaptive design with a dead zone modification for the H_∞ control problem of the strict-feedback nonlinear system with external disturbances is presented. The algorithm can ensure not only the stability of the closed-loop system but also the given L₂ performance criterion of disturbance rejection. The closed-form solution is provided without solving the Hamiton-Jacobi inequality.(3) Robust control approach with a dead zone modification is extended to a class of time-varying uncertain strict-feedback nonlinear systems with completely unknown time-varying control directions, uncertain time-varying parameters and unknown time-varying bounded disturbances. The control design method requires no knowledge of the bounds of the uncertain time-varying control coefficients, the upper bounds of the uncertain parameters and the bounds of unknown time-varying disturbances. It is proved that under the proposed control, all the closed-loop signals are bounded and the tracking error converges to the any prescribed small interval around zero.(4) A robust adaptive output feedback control scheme is proposed for a class of nonlinear minimum phase system with unknown parameters, including the high-frequency gain and the external disturbances. The disturbances in the systems are assumed to be bounded, but the bounds are unknown. The control method does not require a priori knowledge of the sign of the unknown high-frequency gain, the bounds of the disturbances, and furthermore, the restrictive growth and matching conditions on system nonlinearities are removed. The number of parameter estimates is minimal in the adaptive systems. It is proved that under the proposed control scheme, all the closed-loop signals are bounded and the tracking error asymptotically converges to zero. When the unmodeled dynamics are considered, the other output feedback control scheme is presented. With priori knowledge of the bounds of the parametric uncertainties, the smooth projection method and the discontinuous projection method are incorporated into adaptive laws to prevent parameter drifts, respectively. It is proved that under the proposed control law, all the closed-loop signals are bounded and the output asymptotically converges to zero.(5) Based on the universal approximation property of neural networks, a class of robust adaptive neural network control scheme for the uncertain nonlinear systems is proposed. The neural networks are used to approximate the uncertain nonlinear functions in the system and the neural network parameter vectors are tuned online. Even if the control direction is unknown, the proposed algorithm can ensure the output of the system asymptoticallyconverges to zero. When the unmodeled dynamics in the system satisfy the property of input-output stability, the controller design and the stability analysis of the closed-loop system are given by employing the small-gain theory. We also prove that the output can be tuned to be any small value. When all the state variables in the system are obtainable, we give a multiple-surface sliding neural network control scheme. At every step, a sliding surface with a boundary layer is introduced. The algorithm can guarantee the tracking error converges to the given boundary layer.(6) By combining the testable information of the system with the linguistic information, we propose a class of highly precise robust adaptive fuzzy control algorithm. For the low order nonlinear system with mismatched uncertainties, the fuzzy logic systems are used to approximate the unknown functions and the robust terms are introduced to compensate the approximation errors. The fuzzy system parameter vectors and the estimates of the bounds of the approximation error functions are tuned online. For the high order system, the premise parts of the fuzzy logic systems as well as the nominal vectors are designed first and fixed according to a priori knowledge. Then design a robust term to compensate the approximation error by estimating its bounds online. The control laws have the adaptive mechanism with minimal learning parameterizations. The online computation burden is kept to minimum. Furthermore, the exponential tracking to the reference trajectory up to an ultimately bounded error is achieved. At last, we expand the proposed algorithm by introducing a low pass filter at each step in the design. The controllers do not need to satisfy the condition of smoothness.(7) Based on the proposed design methods, the application study for the multi-fingered robot hand is introduced. Firstly, the problem of four-fingered robot hand manipulation, while allowing one of the four fingers to slide on the object's surface, is discussed. An online optimization algorithm for grasping forces under the constraints of maximal static friction and dynamic friction at the grasping points is proposed. Based on the optimal solutions, a dynamic control law is then derived. The control laws ensure the tracking of the object trajectory together with the desired sliding motions along the surface of the object and realize the desired internal forces. Secondly, a robust manipulation algorithm is proposed for multi-fingered hand in the constrained environment when the uncertainties in the dynamic models and the external disturbances are considered. The algorithm can guarantee the position tracking error, the velocity error and the force error between the object and the environment have the property of globally exponential convergence when the parametric uncertainties are considered only. If the system is subject to external disturbances, it satisfies a given performance criterion of disturbance rejection. When the bounds functions of the uncertain terms are unknown, we present an adaptive neural network control method. The algorithm can guarantee the tracking errors converge to any small value. Furthermore, the robustness of the system rejecting external disturbance is improved by the robust optimization algorithm for the internal forces.