Distributed control of a class of flexible mechanical systems with global constraint

References

• Aoustin, Y., Chevallereau, C., Glumineau, A., & Moog, C. (1994). Experimental results for the end-effector control of a single flexible robotic arm. IEEE Transactions on Control Systems Technology, 2(4), 371–381.
   Google Scholar
• Armaou, A., & Christofides, P. (2000). Wave suppression by nonlinear finite-dimensional control. Chemical Engineering Science, 55(14), 2627–2640.
   Web of Science ®Google Scholar
• Balas, M.J. (1978). Active control of flexible systems. Journal of Optimization Theory and Applications, 25, 415–436.
   Web of Science ®Google Scholar
• Bamieh, B., Paganini, F., & Dahleh, M. (2002). Distributed control of spatially invariant systems. IEEE Transactions on Automatic Control, 47(7), 1091–1107.
   Web of Science ®Google Scholar
• Bhikkaji, B., Moheimani, S., & Petersen, I. (2012). A negative imaginary approach to modeling and control of a collocated structure. IEEE/ASME Transactions on Mechatronics, 17(4), 717–727.
   Web of Science ®Google Scholar
• Christofides, P., & Armaou, A. (2000). Global stabilization of the Kuramoto–Sivashinsky equation via distributed output feedback control. Systems and Control Letters, 39(4), 283–294.
   Web of Science ®Google Scholar
• D’Andrea, R., & Dullerud, G.E. (2003). Distributed control design for spatially interconnected systems. IEEE Transactions on Automatic Control, 48, 1478–1495.
   Web of Science ®Google Scholar
• Dubljevic, S., El Farra, N.H., Mhaskar, P., & Christofides, P.D. (2006). Predictive control of parabolic PDEs with state and control constraints. International Journal of Robust and Nonlinear Control, 16(16), 749–772.
   Web of Science ®Google Scholar
• El Farra, N.H., Armaou, A., & Christofides, P.D. (2003). Analysis and control of parabolic PDE systems with input constraints. Automatica, 39(4), 715–725.
   Web of Science ®Google Scholar
• Endo, T., Matsuno, F., & Kawasaki, H. (2009). Simple boundary cooperative control of two one-link flexible arms for grasping. IEEE Transactions on Automatic Control, 54(10), 2470–2476.
   Web of Science ®Google Scholar
• Ge, S.S., Hang, C.C., Lee, T.H., & Zhang, T. (2001). Stable adaptive neural network control. Boston, MA: Kluwer Academic.
   Google Scholar
• Ge, S.S., Lee, T.H., & Zhu, G. (1997a). A nonlinear feedback controller for a single-link flexible manipulator based on a finite element model. Journal of Robotic Systems, 14(3), 165–178.
   Web of Science ®Google Scholar
• Ge, S.S., Lee, T.H., & Zhu, G. (1997b). Non-model-based position control of a planar multi-link flexible robot. Mechanical Systems and Signal Processing, 11(5), 707–724.
   Web of Science ®Google Scholar
• Ge, S.S., Lee, T.H., & Zhu, G. (1998). Asymptotically stable end-point regulation of a flexible SCARA/Cartesian robot. IEEE/ASME Transactions on Mechatronics, 3(2), 138–144.
   Web of Science ®Google Scholar
• Ge, S.S., Zhang, S., & He, W. (2011). Vibration control of an Euler–Bernoulli beam under unknown spatiotemporally varying disturbance. International Journal of Control, 84(5), 947–960.
   Web of Science ®Google Scholar
• Guo, B.-Z., & Jin, F.-F. (2013). The active disturbance rejection and sliding mode control approach to the stabilization of the Euler–Bernoulli beam equation with boundary input disturbance. Automatica, 49(9), 2911–2918.
   Web of Science ®Google Scholar
• Guo, B.-Z., & Jin, F.-F. (2015). Output feedback stabilization for one-dimensional wave equation subject to boundary disturbance. IEEE Transactions on Automatic Control, 60(3), 824–830.
   Web of Science ®Google Scholar
• Guo, B.-Z., & Zhou, H.-C. (2015). The active disturbance rejection control to stabilization for multi-dimensional wave equation with boundary control matched disturbance. IEEE Transactions on Automatic Control, 60(1), 143–157.
   Web of Science ®Google Scholar
• He, W., Chen, Y., & Yin, Z. (2015). Adaptive neural network control of an uncertain robot with full-state constraints. IEEE Transactions on Cybernetics. doi:10.1109/TCYB.2015.2411285
   Web of Science ®Google Scholar
• He, W., & Ge, S.S. (2012). Robust adaptive boundary control of a vibrating string under unknown time-varying disturbance. IEEE Transactions on Control Systems Technology, 20(1), 48–58.
   Web of Science ®Google Scholar
• He, W., & Ge, S.S. (2015). Vibration control of a flexible beam with output constraint. IEEE Transactions on Industrial Electronics, 62(8), 5023–5030.
   Web of Science ®Google Scholar
• He, W., Ge, S.S., & Huang, D. (2015). Modeling and vibration control for a nonlinear moving string with output constraint. IEEE/ASME Transactions on Mechatronics. doi:10.1109/TMECH.2014.2358500.
   Google Scholar
• He, W., Sun, C., & Ge, S.S. (2015). Top tension control of a flexible marine riser by using integral-barrier Lyapunov function. IEEE/ASME Transactions on Mechatronics, 20(2), 497–505.
   Web of Science ®Google Scholar
• He, W., Zhang, S., & Ge, S.S. (2014). Adaptive control of a flexible crane system with the boundary output constraint. IEEE Transactions on Industrial Electronics, 61(8), 4126–4133.
   Web of Science ®Google Scholar
• He, W., Zhang, S., Ge, S.S., & Liu, C. (2014). Adaptive boundary control for a class of inhomogeneous Timoshenko beam equations with constraints. IET Control Theory and Applications, 8(14), 1285–1292.
   Web of Science ®Google Scholar
• Hewitt, E., & Stromberg, K. (1929). Real and abstract analysis: A modern treatment of the theory of functions of a real variable. Berlin: Springer-Verlag.
   Google Scholar
• Ho, M.T., & Lin, C.Y. (2003). PID controller design for robust performance. IEEE Transactions on Automatic Control, 48(8), 1404–1409.
   Web of Science ®Google Scholar
• Huang, D., Xu, J.X., Li, X., Xu, C., & Yu, M. (2013). D-type anticipatory iterative learning control for a class of inhomogeneous heat equations. Automatica, 49(8), 2397–2408.
   Web of Science ®Google Scholar
• Khalil, H.K. (2002). Nonlinear systems. New Jersey, NJ: Prentice Hall.
   Google Scholar
• Krstic, M., Kanellakopoulos, I., & Kokotovic, P. (1995). Nonlinear and adaptive control design. New York, NY: Wiley.
   Google Scholar
• Krstic, M., & Smyshlyaev, A. (2008). Boundary control of PDEs: A course on backstepping designs. Philadelphia, PA: Society for Industrial and Applied Mathematics.
   Google Scholar
• Logan, J.D. (2006). Applied mathematics (3rd ed.). New York, NY: Wiley.
   Google Scholar
• Lu, L., Chen, Z., Yao, B., & Wang, Q. (2013). A two-loop performance-oriented tip-tracking control of a linear-motor-driven flexible beam system with experiments. IEEE Transactions on Industrial Electronics, 60(3), 1011–1022.
   Web of Science ®Google Scholar
• Luo, B., & Wu, H.N. (2012). Approximate optimal control design for nonlinear one-dimensional parabolic PDE systems using empirical eigenfunctions and neural network. IEEE Transactions on Systems, Man, Cybernetics – Part B: Cybernetics, 42(6), 1538–1549.
   PubMed Web of Science ®Google Scholar
• Meirovitch, L., & Baruh, H. (1983). On the problem of observation spillover in self-adjoint distributed systems. Journal of Optimization Theory and Applications, 30(2), 269–291.
   Web of Science ®Google Scholar
• Pereira, E., Aphale, S., Feliu, V., & Moheimani, S. (2011). Integral resonant control for vibration damping and precise tip-positioning of a single-link flexible manipulator. IEEE/ASME Transactions on Mechatronics, 16(2), 232–240.
   Web of Science ®Google Scholar
• Ren, B., Ge, S.S., Tee, K.P., & Lee, T.H. (2010). Adaptive neural control for output feedback nonlinear systems using a barrier Lyapunov function. IEEE Transactions on Neural Networks, 21(8), 1339–1345.
   PubMed Web of Science ®Google Scholar
• Ren, B., Wang, J.M., & Krstic, M. (2013). Stabilization of an ODE–Schrödinger cascade. Systems and Control Letters, 62(6), 503–510.
   Web of Science ®Google Scholar
• Sakawa, Y., Matsuno, F., & Fukushima, S. (1985). Modeling and feedback control of a flexible arm. Journal of Robotic Systems, 2(4), 453–472.
   Web of Science ®Google Scholar
• Tee, K.P., Ge, S.S., & Tay, E.H. (2009). Barrier Lyapunov functions for the control of output-constrained nonlinear systems. Automatica, 45, 918–927.
   Web of Science ®Google Scholar
• Tee, K.P., Ren, B., & Ge, S.S. (2011). Control of nonlinear systems with time-varying output constraints. Automatica, 47, 2511–2516.
   Web of Science ®Google Scholar
• Wang, J.-M., Liu, J.-J., Ren, B., & Chen, J. (2015). Sliding mode control to stabilization of cascaded heat PDE–ODE systems subject to boundary control matched disturbance. Automatica, 52, 23–34.
   Web of Science ®Google Scholar
• Wang, J.M., Ren, B., & Krstic, M. (2012). Stabilization and Gevrey regularity of a Schrödinger equation in boundary feedback with a heat equation. IEEE Transactions on Automatic Control, 57(1), 179–185.
   Web of Science ®Google Scholar
• Wang, J.-W., Wu, H.-N., & Li, H.-X. (2012). Distributed proportional–spatial derivative control of nonlinear parabolic systems via fuzzy PDE modeling approach. IEEE Transactions on Systems, Man, Cybernetics – Part B: Cybernetics, 42(3), 927–938.
   PubMed Web of Science ®Google Scholar
• Wu, F. (2003). Distributed control for interconnected linear parameter-dependent systems. IEE Proceedings – Control Theory and Applications, 150, 518.
   Google Scholar
• Wu, H.-N., & Li, H.-X. (2007). Finite-dimensional constrained fuzzy control for a class of nonlinear distributed process systems. IEEE Transactions on Systems, Man, Cybernetics – Part B: Cybernetics, 37(5), 1422–1430.
   PubMed Web of Science ®Google Scholar
• Wu, H.N., Wang, J.W., & Li, H.X. (2012). Design of distributed H∞ fuzzy controllers with constraint for nonlinear hyperbolic PDE systems. Automatica, 48(10), 2535–2543.
   Web of Science ®Google Scholar
• Xu, G.Q., Han, Z.J., & Yung, S.P. (2007). Riesz basis property of serially connected Timoshenko beams. International Journal of Control, 80(3), 470–485.
   Web of Science ®Google Scholar
• Xu, G.Q., & Wang, H. (2013). Stabilisation of Timoshenko beam system with delay in the boundary control. International Journal of Control, 86(6), 1165–1178.
   Web of Science ®Google Scholar