Control of a 2 × 2 coupled linear hyperbolic system sandwiched between 2 ODEs |
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| Authors: | Ji Wang Miroslav Krstic Yangjun Pi |
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| Affiliation: | 1. State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing, China;2. Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA, USA;3. School of Automotive Engineering, Chongqing University, Chongqing, China |
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| Abstract: | Motivated by an engineering application in cable mining elevators, we address a new problem on stabilization of 2×2 coupled linear first‐order hyperbolic PDEs sandwiched between 2 ODEs. A novel methology combining PDE backstepping and ODE backstepping is proposed to derive a state‐feedback controller without high differential terms. The well‐posedness and invertibility properties of the PDE backstepping transformation are proved. All states, including coupled linear hyperbolic PDEs and 2 ODEs, are included in the closed‐loop exponential stability analysis. Moreover, boundedness and exponential convergence of the designed controller are proved. The performance is investigated via numerical simulation. |
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| Keywords: | backstepping distributed parameter systems hyperbolic systems ODE‐PDE‐ODE |
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