Adaptive Control Of Uncertain Lower-Triangular Nonlinear Systems

In recent years, a lot of researchers are particularly interested in online approximation based adaptive control of uncertain nonlinear systems. This dissertation is concerned with neural networks based adaptive tracking control of uncertain lower-triangular nonlinear systems. The main contributions of the dissertation are as follows.First, a neural adaptive backstepping dynamic surface control design method is presented for a class of affine pure-feedback nonlinear systems with an unknown control gain. In the controller design, virtual control laws and actual control law are constructed recursively by approximating unknown nonlinear functions of the systems with neural networks. At each intermediate step, a dynamic surface control technique is used to eliminate the problem of "explosion of complexity". Furthermore, for a class of non-affine pure-feedback nonlinear systems, a neural adaptive backstepping dynamic surface control design method is developed. In the controller design, the subsystems are firstly changed into the affine-like forms. Then virtual control laws and actual control law are constructed by approximating unknown nonlinear functions of the subsystems with neural networks. A dynamic surface control technique is used to eliminate the problem of "explosion of complexity’’at each intermediate step. By the approaches, the structures of the designed controllers are simple, and the problem of circular construction of the controller can be solved. Stability analysis based on Lyapunov stability, Input-to-state practical stability and small gain theorem shows that all the closed-loop system signals are semiglobally ultimately bounded, and the steady state tracking error can be made arbitrarily small by appropriately choosing control parameters. Simulation results demonstrate the effectiveness of the proposed approaches.Second, for the first time, single neural network approximation based adaptive control design methods are presented for a class of uncertain strict-feedback nonlinear systems with known gains and a class of uncertain strict-feedback nonlinear systems with unknown gains, respectively. In the controller design, virtual control laws and desired control law are firstly given. Then by approximating the unknown function of the desired control law with a single neural network, an actual adaptive control law is constructed. Furthermore, for a class of non-affine pure-feedback nonlinear systems, a single neural network approximation based adaptive control design approach is developed. In the controller design, the forms of the subsystems are firstly changed, and then virtual control laws and desired control law are given. Then by using one neural network to approximate the unknown function of the desired control law, an actual adaptive control law is constructed. By the proposed approaches, the designed controller only contains one actual control law and one adaptive law, and can be given directly. Compared with existing methods, all the virtual control laws need not be implemented in the controller realization. Thus, the structure of the designed controller is much simpler. Lyapunov stability, input-to-state practical stability and small gain theorem are employed to analyze the stability of the closed-loop systems. It is shown that the semiglobal ultimate boundedness of all the closed-loop system signals can be guaranteed, and the steady state tracking error can be made arbitrarily small by appropriately choosing control parameters. The presented approaches are applied to the controllers design of some numerical examples and practical engineering systems. Simulation results demonstrate the effectiveness of the proposed approaches.Third, some robust adaptive control design methods are developed for uncertain lower-triangular nonlinear systems with unknown dead-zone and disturbances. For a class of uncertain strict-feedback nonlinear systems with known gains and a class of uncertain strict-feedback nonlinear systems with unknown gains, single neural network approximation based robust adaptive control design methods are presented, respectively. At the intermediate steps, the contained disturbances are firstly compensated, and then virtual robust control laws are given. At the last step, the contained disturbance and unknown dead-zone are compensated firstly, and then a desired robust control law is given. By approximating the unknown part of the desired control law with a single neural network, an actual robust adaptive control law is constructed. Furthermore, for a class of non-affine pure-feedback nonlinear systems, a single neural network robust adaptive controller is designed. At the intermediate steps, the contained disturbances are firstly compensated. After changing the subsystems into the affine-like forms, virtual robust control laws can be given. At the last step, the contained disturbance and unknown dead-zone are compensated firstly. Then a desired robust control law can be given after changing the last subsystem into the affinc-like form. By approximating the unknown part of the desired control law with a single neural network, an actual robust adaptive control law is constructed. Stability analysis shows that all the closed-loop system signals are semiglobally ultimately bounded, and the steady state tracking error can be made arbitrarily small by appropriately choosing control parameters. Simulation results based on numerical examples and actual systems demonstrate the effectiveness of the proposed approaches.