On Adaptive Control Of Nonlinear Systems With Constraints And Unmodeled Dynamics

There exist many kinds of constraints in the practical nonlinear systems,such as physical stoppages,saturation,as well as performance and safety specifications.Violation of the constraints may bring about performance deterioration or even make the system unstable and fail to work properly.In addition to the constraints,there are also various uncertainties in the nonlinear systems due to the influence of measurement noise,model error,model simplification,disturbances and so on.The uncertainties from inside or outside of the system,which are collectively referred to as unmodeled dynamics,have a great impact on the stability of the control system.In recent years,driven by practical needs and theoretical challenges,more attention has been paid to the control problem of nonlinear systems with constrained and unmodeled dynamics,which has become one of the hotspots and difficult issues in the field of control theory.In this dissertation,some kinds of controller design methods are proposed for the nonlinear systems with the constraints and unmodeled dynamics.The auxiliary dynamic signal and Lyapunov function are used to dispose of the unmodeled dynamics and the integral barrier Lyapunov function is applied to deal with the state constraints.Nonlinear invertible mapping is introduced to handle the state constraints,which converts the constrained systems into the unconstrained systems.Combining the backstepping with DSC,the adaptive control schemes are presented through the neural networks.The detailed description and innovations are shown as follows:1.Adaptive control problem is considered for a class of pure feedback nonlinear constrained systems with dynamic uncertainties.The new method to deal with state constraints is proposed through introducing invertible asymmetric nonlinear mapping.It eliminates the unreasonable assumption that the upper bound of virtual control should be known in the course of the stability analysis by using barrier Lyapunov function to design controllers in existing literature.On the basis of the nonlinear mapping,the constrained system is transformed into an equivalent unconstrained system to employ the traditional control method while preventing the constraint from being violated simultaneously.Nussbaum function to deal with unknown high-frequency gain sign,the dynamic signal to handle the unmodeled dynamics,the adaptive control methods are presented on the modified DSC.The designed control scheme weakens the requirements that the lower bound and upper bound of the virtual control should be known.Two numerical examples illustrate the effectiveness of the proposed approach.2.The control problem is studied for a class of full state constrained nonlinear systems with time-delay,distributed time-delay and unmodeled dynamics.The Lyapunov-Krasovskii is constructed to compensate the time-delay term and the invertible nonlinear mapping method is extended to full state constrained nonlinear systems with time-delay,distributed time-delay and unmodeled dynamics.An adaptive control method is proposed on the backstepping and the dynamic signal is used to deal with unmodeled dynamics.The RBF neural network is applied to approximate unknown nonlinear function.Through estimating the norm of weight vector in the neural network,the number of the adaptive parameters is decreased,the complexity and calculation are reduced and the on-line control performance of the system is improved simultaneously.The simulation results demonstrate the effectiveness of the proposed method.3.For a class of stochastic nonlinear pure feedback systems with input and state unmodeled dynamics,the new adaptive neural control strategy is proposed for the first time on the modified DSC method with non-linear transformation replacing the median theorem and the sufficient condition is established to guarantee semi-globally uniformly ultimately bounded of stochastic closed-loop system simultaneously.Lyapunov function description is used to deal with state unmodeled dynamics and input unmodeled dynamics is handled by introducing normalization signal.Through introducing a first-order filter,the DSC method avoids the drawback of backstepping which is called as 'explosion of complexity' and the complexity of design is reduced.Through the theoretical analysis,all the signals in the closed-loop system are bounded in probability.The simulation of inverted pendulum system further verifies the effectiveness of the proposed control strategy4.For a class of full state constrained stochastic nonlinear systems with unmodeled dynamics,the definition of the stochastic state constraints in probability is proposed and applied to the stability analysis of the stochastic system.Using DSC technique,invertible nonlinear mapping,Ito formula and Chebyshev's inequality,the adaptive neural control method is explored to solve the problem of adaptive control for all-state constrained stochastic systems with unmodeled dynamics effectively.The proposed strategy can ensure that all the signals in the closed-loop system are bounded in probability.The validity of the control scheme is further illustrated by the simulation of numerical example and the inverted pendulum system.5.Adaptive tracking control is developed for a class of MIMO stochastic nonlinear systems with full state constraints and unmodeled dynamics.The stochastic adaptive DSC scheme is presented to the controller design of the block-structure MIMO stochastic nonlinear system and the definition of the stochastic state constraints in probability is extended to the MIMO stochastic systems with full state constraints.The states are constrainted in probability.Based on the proposed strategy,the requirement for nonsingularity of control gain matrix is deleted through the compact set introduced in the stability analysis of DSC.The simulation result illustrates the effectiveness of the control scheme.6.The control problem is investigated for a class of MIMO constrained stochastic nonlinear systems with quantized inputs and multiple dynamic uncertainties.The new adaptive control strategy is constructed by using nonlinear invertible mapping and dynamic surface control technology,which can guarantee the stability of the system and the stochastic constraints in probability for the state.The quantized input signal is generated from the hysteretic quantizer,which is decomposed into continuous and discontinuous parts.The RBF neural networks are used to approximate the unknown nonlinear functions together with some functions resulting from theoretical deduction,so the number of on-line adjusting parameters are reduced.Lyapunov function is designed for each block,which simplifies the design process.The simulation illustrates the effectiveness of the control method.