Adaptive Output-Feedback Stabilization for PDE-ODE Cascaded Systems with Unknown Control Coefficient and Spatially Varying Parameter

This paper investigates the adaptive stabilization for a class of uncertain PDE-ODE cascaded systems. Remarkably, the PDE subsystem allows unknown control coefficient and spatially varying parameter, and only its one boundary value is measurable. This renders the system in question more general and practical, and the control problem more challenging. To solve the problem, an invertible transformation is first introduced to change the system into an observer canonical form, from which a couple of filters are constructed to estimate the unmeasurable states. Then, by adaptive technique and infinite-dimensional backstepping method, an adaptive controller is constructed which guarantees that all states of the resulting closed-loop system are bounded while the original system states converging to zero. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed method.

[1]  Miroslav Krstic,et al.  Backstepping boundary control for first order hyperbolic PDEs and application to systems with actuator and sensor delays , 2007, 2007 46th IEEE Conference on Decision and Control.

[2]  Stevan Dubljevic,et al.  Boundary optimal (LQ) control of coupled hyperbolic PDEs and ODEs , 2013, Autom..

[3]  Miroslav Krstic,et al.  Adaptive Boundary Control for Unstable Parabolic PDEs—Part I: Lyapunov Design , 2008, IEEE Transactions on Automatic Control.

[4]  Zhigang Ren,et al.  Stabilization of a general linear heat‐ODE system coupling at an intermediate point , 2017 .

[5]  Delphine Bresch-Pietri,et al.  Adaptive trajectory tracking despite unknown input delay and plant parameters , 2009, Autom..

[6]  Henrik Anfinsen,et al.  Disturbance rejection in general heterodirectional 1-D linear hyperbolic systems using collocated sensing and control , 2017, Autom..

[7]  Bao-Zhu Guo,et al.  The active disturbance rejection control approach to stabilisation of coupled heat and ODE system subject to boundary control matched disturbance , 2015, Int. J. Control.

[8]  Iasson Karafyllis,et al.  Exponential Stability Analysis of Sampled-Data ODE–PDE Systems and Application to Observer Design , 2016, IEEE Transactions on Automatic Control.

[9]  Zaihua Xu,et al.  Adaptive boundary stabilization for first‐order hyperbolic PDEs with unknown spatially varying parameter , 2016 .

[10]  Wenwu Cao,et al.  Applied Numerical Methods Using MATLAB®: Yang/Applied Numerical MATLAB , 2005 .

[11]  Miroslav Krstic,et al.  Boundary observer design for hyperbolic PDE-ODE cascade systems , 2016, Autom..

[12]  Wŏn-yŏng Yang,et al.  Applied Numerical Methods Using MATLAB , 2005 .

[13]  Jun-Jun Liu,et al.  Boundary stabilization of a cascade of ODE‐wave systems subject to boundary control matched disturbance , 2017 .

[14]  Andrey Smyshlyaev,et al.  Adaptive Control of Parabolic PDEs , 2010 .

[15]  Yungang Liu,et al.  Adaptive stabilization for ODE systems via boundary measurement of uncertain diffusion‐dominated actuator dynamics , 2014 .

[16]  R. Colombo,et al.  On the coupling of systems of hyperbolic conservation laws with ordinary differential equations , 2010 .

[17]  Miroslav Krstic,et al.  Compensating actuator and sensor dynamics governed by diffusion PDEs , 2009, Syst. Control. Lett..

[18]  Delphine Bresch-Pietri,et al.  Delay-Adaptive Predictor Feedback for Systems With Unknown Long Actuator Delay $ $ , 2010, IEEE Transactions on Automatic Control.

[19]  Jian Li,et al.  Adaptive control of the ODE systems with uncertain diffusion-dominated actuator dynamics , 2012, Int. J. Control.

[20]  Miroslav Krstic,et al.  PDE Boundary Control of Multi-Input LTI Systems With Distinct and Uncertain Input Delays , 2018, IEEE Transactions on Automatic Control.

[21]  Beibei Ren,et al.  Sliding mode control to stabilization of cascaded heat PDE-ODE systems subject to boundary control matched disturbance , 2015, Autom..

[22]  Huai-Ning Wu,et al.  Static output feedback control via PDE boundary and ODE measurements in linear cascaded ODE-beam systems , 2014, Autom..

[23]  Miroslav Krstic,et al.  Adaptive global stabilization of uncertain multi-input linear time-delay systems by PDE full-state feedback , 2018, Autom..

[24]  Miroslav Krstic,et al.  Control of Transport PDE/Nonlinear ODE Cascades With State-Dependent Propagation Speed , 2017, IEEE Transactions on Automatic Control.

[25]  Bao-Zhu Guo,et al.  Stabilization of ODE with hyperbolic equation actuator subject to boundary control matched disturbance , 2019, Int. J. Control.