Stability Analysis Of Model Free Adaptive Control With Applications In Multi-agent Systems

In the dissertation,the unknown single input single output(SISO)/multi input multi output(MIMO)nonlinear non-affine discrete-time systems are regarded as the research objects,and the stability and the tracking error convergence of the full-form dynamic linearization(FFDL)model-free adaptive control(MFAC)are proved rigorously.Further,based on the theory of FFDL-MFAC,the formation control problems of unknown heterogeneous multi-input multi-output(MIMO)nonlinear discrete multi-agent system with disturbances and with sensor faults as well are also investigated.The main contents of this work are summarized as follows:1.For a class of unknown SISO nonlinear non-affine discrete-time systems,the asymptotic convergence of the tracking error dynamics,the bounded-input bounded output(BIBO)stable and the internal stability of the closed-loop system controlled by FFDLMFAC algorithm are guaranteed by rigorous theoretical analysis based on the contraction mapping principle.The conventional model based adaptive control for linear timeinvariant systems and the well-known PID controller are clearly stated as a special case of the FFDL-MFAC algorithm.2.A FFDL-MFAC algorithm is designed for a class of MIMO system with unknown non-affine nonlinear dynamics.The asymptotic convergence of the tracking error of the closed-loop control system,the BIBO stability and the internal stability of the closed loop are proved rigorously by contraction mapping principle.Further,the multi-variable discrete-time incremental PID controller and the conventional adaptive control for MIMO linear time-invariant model are also proved as special cases of the FFDL-MFAC algorithm.The simulation and experiment results on the QRAS verify the effectiveness of the proposed algorithm.In addition,for a class of unknown nonlinear non-affine with input saturation,a quasi-Newton control algorithm with only using the saturation input and output data is designed,and the convergence of the closed-loop system is analyzed rigorously.3.For a class of unknown heterogenous MIMO nonlinear discrete-time multi-agent systems with measurable and unmeasurable disturbance,the distributed formation control algorithms are designed respectively based on the FFDL-MFAC theory.The boundedness of formation error driven by the proposed controllers is shown to be guaranteed by the contraction mapping principle,the virtual equivalent data modes and the inductive methods.4.For a class of unknown heterogeneous nonlinear non-affine discrete-time MIMO multi-agent system with sensor fault,a data-driven model free adaptive distributed formation control algorithm is proposed based on the FFDL-MFAC theory.By using the outputs of the well-trained RBFNN and the actual outputs of MAS with sensor fault case,the estimation laws of unknown fault and system parameters are designed,and then the model free adaptive formation fault-tolerant control algorithm is proposed.Finally,the boundedness of the formation error is proved by contraction mapping method and mathematical induction method.The effectiveness of the proposed distributed model free adaptive formation fault-tolerant control algorithm is illustrated by simulation examples.