| Distributed parameter system whose state is not only dependent on the time,but also de-pendent on the space location,can model a larger range of practical system than the lumped parameter system.In recent years,since the development of computational techniques,the control of the distributed parameter system has become a more and more fascinating re-search,motivated by the practical needs of the control techniques,urgently.However,since many kinds of distributed parameter system owns completely different evolution dynamic-s,there is no a general effective control technique for all the distributed parameter system including the stabilization and trajectory tracking problem.Another challenging problem,from implementation viewpoint,is the location of the actuator which makes the control al-gorithms design become more complex.Besides,with the practical condition,the robust control for the distributed parameter systems with respect to disturbance and modelling un-certainties is still a challenge problem.Finally,except for the stabilization or synchroniza-tion of the distributed parameter systems,the tracking control for the distributed parameter system remains a topic to be further studied and there are few works to deal with it.There-fore,inspired by the challenges presented above,in this study,the author will address the boundary stabilization,synchronization and the trajectory tracking problem by proposing the novel control schemes for several classes of distributed parameter systems including the non-linearly coupled parabolic system,hyperbolic heat conduction system,first-order hyperbolic system with non-local terms and unknown nonlinear uncertainties,2×2 hyperbolic system with disturbance and uncertainties and the time-varying network of reaction-diffusion neural networks.The main works of this study are:1.For a class of nonlinearly coupled parabolic system,the decentralized boundary stabi-lization control is investigated,by using the backstepping techniques.Since the presence of the nonlinear term,the stability analysis and the state estimation will be a tough problem.Based on a Luenberger type observer where the sate estimation is performed in the decen-tralized,the decentralized boundary output feedback control scheme is proposed to address the stabilization of nonlinearly coupled parabolic system.Furthermore,the stability anal-ysis of the resulted closed-loop system is dealt with by using the Lyapunov theory where the nonlinearly coupled terms are dealt with by using some inequalities.Comparing with the existed boundary control schemes,the proposed decentralized boundary output feedback control generalizes the nonlinear distributed parameter system to some extent.With rigor-ous proof,the state of the original nonlinear system and the state estimation error are both locally exponentially stable.2.The boundary stabilization control for a new type of heat conduction model,named as hyperbolic heat conduction model,is addressed by using the backstepping transform.Firstly,the state feedback control is proposed.Comparing with the spectrum analysis method,the stability analysis is performed by constructing a Lyapunov function directly.Besides,the well-posedness of the classical solution of the closed-loop system is established.Secondly,to reduce the measurement costs,a Luenberger-type observer is constructed to estimate the state of the hyperbolic heat conduction model.Finally,an observer-based boundary output feedback control scheme is presented.Also,the stability and well-posedness of the closed-loop system are guaranteed,by rigorous analysis.3.The boundary regulation and disturbance rejection for the wave equation with a distur-bance generated by a linear ordinary differential equation and the unstable boundary condi-tion are addressed.Firstly,the boundary regulation is first considered for the wave equation with Neumann boundary condition.A boundary control,consisting of a state feedback and a feed-forward control is designed to regulate the boundary condition.An initial value prob-lem for an ordinary differential equation is derived to obtain the feed-forward gains.Besides,the estimation of the disturbance and the state of the unstable wave equation with Neumann condition is first considered by constructing an observer based on the collocated measure-ments.Thus,a boundary value problem derived from the Neumann condition is presented for the observer gains.Furthermore,the existence condition of this boundary value problem and the observability condition of this kind of observer are given,respectively.For the stabil-ity analysis,the boundary regulation error is proven to be exponentially stable with the state feedback and feed-forward control scheme.Also,with the separable principle,based on the observer designed,an output feedback control algorithm is presented and the exponential stability of the closed-loop system is guaranteed.4.The iterative learning control problem for a class of first-order hyperbolic equations with non-local terms is addressed.The output of the system is regulated to track the desired ref-erence signals over the repeatable finite time domain.By introducing the Volterra transform and the characteristic transform,the input output transform function is established.Based on the transform functions,the iterative learning controller is presented for the system with state independent unknown term and state dependent unknown nonlinear term,respectively.The iterative learning controller is consisting of a non-local feedback and an anticipatory proportional feedforward controller.What’s more,the convergence of the iterative learning control with respect to the initial states resetting errors and unknown disturbances,including iteration independent,iteration dependent and state dependent unknown terms,is proven via rigorous analysis.5.The robust iterative learning control is extended to study the output tracking of the 2×2nonlinear hyperbolic system with unknown time-varying disturbance and modelling uncer-tainties.Since the measurement limitation,the iterative learning control is actuated in a collocated form.That is the measurement and control is on the same side of the system.It is not necessary to estimate the unknown boundary disturbance and is easy in implemen-tation.With the initial states resetting errors,considering the complete dynamics of the nonlinear 2×2 hyperbolic system without any reduction order of the distributed parame-ter system,the convergence of the iterative learning control strategy is guaranteed and the control is bounded uniformly with respect to the iteration index.Furthermore,to implement the proposed iterative learning control,the actuator dynamic is considered,also.Finally,the proposed iterative learning control scheme is applied to the open-canal flow levels control and heave-induced pressure fluctuations reduction in the managed pressure drilling and the numerical simulations show the effectiveness of the iterative learning control with respect to the disturbance and nonlinear uncertainties.6.The dynamics of a time-varying strength network of reaction-diffusion system named as the reaction-diffusion neural networks is investigated via the iterative learning control.For the time-varying network structure,a discrete learning law is proposed to estimate the unknown time-varying coefficient.Based on this learning law,a hybrid synchronization feedback controller consisting of the discrete learning law and continuous adaptive law is presented.Comparing with the synchronization control scheme without learning law,the time-varying structure of the network is dealt with and a better performance is obtained.By constructing a series of Lyapunov function,the synchronization of an array of linearly coupled reaction-diffusion neural networks with time-varying strength is obtained.What’s more,from practical viewpoint,the disturbance attenuation control via the H_∞performance under the learning control framework is considered. |
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