The Recursive Method Based Controller Designs For Lower Triangular Nonlinear Systems

With the development of science and technology and the improvement of mechanical automation,the dynamic models of engineering systems become increasingly complicated.In addition,requirements on system performance are improved and the difficulty of the task is also strengthened.In a series of the engineering system models,the control problem for the representative lower triangular nonlinear systems has attracted many scholars' attention,and lots of results have been made.By the recursive method and based on the deterministic and stochastic systems Lyapunov stability theorems,this dissertation investigates the controller design for lower triangular deterministic nonlinear systems,lower triangular stochastic nonlinear systems and lower triangular nonlinear multiagent systems(MASs).The influence of many factors,such as unmodeled dynamics,dead-zone input,stochastic disturbance,uncertain parameters,time delays and so on,on the controller design and stability analysis is considered.In this dissertation,the main contents are summarized as follows.(1)Based on the recursive method,the decentralized finite time state feedback controller is constructed for interconnected nonlinear systems with unmodeled dynamics and dead-zone input,such that the state variables of the system converge to the equilibrium point in finite time.The robust control method and changing supply function are used to address the dead-zone input and unmodeled dynamics,respectively,and some restrictive conditions are given.In addition,based on the fixed time stability theorem,some conditions are given,under which the state variables can converge to equilibrium point in fixed time;(2)Further,by considering the influence of stochastic disturbances and the uncertain parameters,the adaptive state feedback controller is designed for a class of p-normal form switched stochastic nonlinear systems with arbitrary switching based on the stochastic systems Lyapunov stability theorem.The adaptation law is designed by the tuning function method.Both the constructed controller and the adaptation law are independent of the switching law.When there is no disturbance or uncertain parameters,two finite time stability theorems are given for the p-normal form nonlinear systems;(3)Considering the influence of the time delay on the controller design and stability analysis,theorems on existence and uniqueness of the solution and time delay stochastic system stability are given under the case that there exists dynamic gain in the studied systems.Based on these theorems,by the recursive method and dynamic gain technique,the adaptive state feedback tracking controller is designed for p-normal form time delay stochastic nonlinear systems to guarantee boundness of the expectation of the tracking error.Specially,if the reference signal is zero,all the state variables will converge to equilibrium point in probability;(4)For the lower triangular nonlinear MASs,the reduced order dynamic gain observer is constructed first to estimate the unmeasured state variables based on the dynamic gain technique.Then,by the recursive method,the output feedback distributed containment controller is designed to make the outputs of the followers converge to the convex hull spanned by the outputs of the leaders.The designed observer relaxes the traditional Lipschitz condition,and the proposed method allows the MASs to be heterogeneous,which also makes the method have a wider class of application;(5)Finally,considering the influence the stochastic disturbance on the MASs,the leader-following controller is designed based on the stochastic system stability theorem and the recursive method,to guarantee the boundness of the expectation of the tracking error and the other state variables in probability.The designed controller of each agent only needs the neighbors' outputs information.