# American Institute of Mathematical Sciences

2016, 6(2): 127-151. doi: 10.3934/naco.2016004

## Output feedback overlapping control design of interconnected systems with input saturation

 1 Distributed Control Research Lab, Systems Engineering Department, KFUPM, P. O. Box 5067, Dhahran 31261, Saudi Arabia

Received  March 2015 Revised  April 2016 Published  June 2016

In this paper, we establish new results to the problem of output feedback control design for a class of nonlinear interconnected continuous-time systems subject to input saturation. New schemes based on overlapping design methodology are developed for both static and dynamic output feedback control structures. The theoretical developments are illustrated by numerical simulations of a linearized nuclear power plant model.
Citation: Magdi S. Mahmoud. Output feedback overlapping control design of interconnected systems with input saturation. Numerical Algebra, Control & Optimization, 2016, 6 (2) : 127-151. doi: 10.3934/naco.2016004
##### References:
 [1] H. Akkurt, Development of a Control Model for a PWR,, M. Sc. Thesis, (1996). [2] Atomic Energy Agency, Modern Instrumentation and Control for Nuclear Power Plants: A Guidebook,, Vienna, (1999). [3] L. Backule and J. Rodellar, Decentralized control and overlapping decomposition of mechanical systems. part 1: System decomposition. part 2: Decentralized stabilization,, Int. J. Control, 61 (1995), 559. doi: 10.1080/00207179508921918. [4] L. Backule, F. Paulet-Crainiceanu, J. Rodellar and J. M. Rossell, Overlapping reliable control for a cable-stayed bridge benchmark,, IEEE Trans. Control Systems Technology, 13 (2005), 663. [5] D. S. Bernstein and A. N. Michel, A Chronological bibliography on saturating actuators,, Int. J. Robust Nonlinear Control, 5 (1995), 375. doi: 10.1002/rnc.4590050502. [6] D. Dai, T. Hu, A. R. Teel and L. Zaccarian, Control of saturated linear plants via output feedback containing an internal dead zone loop,, Proc. American Control Conference, (2006), 5239. [7] B. Frogner and H. S. Rao, Control of nuclear power plants,, IEEE Trans. Automat. Control, 23 (1978), 405. [8] P. Gahinet and P. Apkarian, A linear matrix inequality approach to H∞ control,, Int. J. Robust and Nonlinear Control, 4 (1994), 421. doi: 10.1002/rnc.4590040403. [9] T. Hua and Z. Lin, Control Systems with Actuator Saturation: Analysis and Design,, Birkhauser, (2001). [10] M. Ikeda, D. D. Siljak and D. E. White, Decentralized control with overlapping information set,, J. Optimization Theory and Applications, 34 (1981), 279. doi: 10.1007/BF00935477. [11] M. Ikeda and D. D. Siljak, Overlapping decentralized control with input, state and output inclusion,, Control-Theory and Advanced Technol., 2 (1986), 155. [12] K. Kalsi, J. Lian and S. H. Zak, Decentralized dynamic output feedback control of Nonlinear interconnected systems,, IEEE Trans on Autom Control, 55 (2010), 1964. doi: 10.1109/TAC.2010.2050715. [13] V. Kapilla and K. Grigoriadis, Actuator Saturation Control,, Marcel Dekker, (2002). [14] T. A. Kendi and F. J. Doyle, Nonlinear control of a fluidized bed reactor using approximate feedback linearization,, Ind. Eng. Chem. Res., 35 (1996), 746. [15] T. W. Kerlin, E. M. Katz and J. G. Thakkar, Theoretical and experimental dynamic analysis of the H. B. Robinson nuclear plant,, Nuclear Technology, 30 (1976), 299. [16] Z. Lin, Low Gain Feedback,, Springer-Verlag, (1998). [17] L. Lu, Z. Lin and A. Bateman, Decentralized state feedback design for large-scale linear systems subject to input saturation,, IET Control Theory Appl., 4 (2010), 206. doi: 10.1049/iet-cta.2008.0605. [18] M. S. Mahmoud, Decentralized reliable control of interconnected systems with time-varying delays,, J. Optimization Theory and Applications, 143 (2009), 497. doi: 10.1007/s10957-009-9571-y. [19] M. S. Mahmoud and N. B. Almutairi, Decentralized stabilization of interconnected systems with time-varying delays,, European J. Control, 15 (2009), 624. doi: 10.3166/ejc.15.624-633. [20] M. S. Mahmoud, Decentralized stabilization of interconnected nonlinear systems with time-varying delays,, IEEE Tran. Automatic Control, 54 (2009), 2663. doi: 10.1109/TAC.2009.2031572. [21] M. S. Mahmoud, Decentralized Control and Filtering in Interconnected Dynamical Systems,, CRC Press, (2010). [22] M. S. Mahmoud, Improved stability and stabilization approach to linear interconnected time-delay systems,, Optimal Control Applications and Methods, 31 (2010), 81. doi: 10.1002/oca.884. [23] M. S. Mahmoud and S. Elferik, New stability and stabilization methods for nonlinear systems with time-varying delays,, Optimal Control Applications and Methods, 31 (2010), 273. doi: 10.1002/oca.904. [24] M. S. Mahmoud, Decentralized Control with Design Constraints,, Springer-Verlag, (2011). [25] I. Ngamroo, Overlapping decompositions-based robust decentralized TABU search-optimized fixed structure H∞ frequency stabilizer design in interconnected power systems,, Int. J. Innovative Computing, 9 (2013). [26] C. Pittet, S. Tarbouriech and C. Burgat, Output feedback synthesis via the circle criterion for linear systems subject to saturating inputs,, Proc. the 37th IEEE Conference on Decision and Control, (1998), 401. [27] I. Postlethwaite, M. Turner and G. Herman, Robust control applications,, Annual Reviews in Control, 31 (2007), 27. [28] A. Saberi, Z. Lin, and A. R. Teel, Control of linear systems with saturating actuators,, IEEE Trans. Automat. Control, 41 (1996), 368. doi: 10.1109/9.486638. [29] C. Scherer, P. Gahinet and M. Chilali, Multiobjective output-feedback control via LMI optimization,, IEEE Trans. Automat. Control, 42 (1997), 896. doi: 10.1109/9.599969. [30] C. Scherer and S. Weiland, Linear Matrix Inequalities in Control,, Delft Center for Systems and Control, (2005). [31] D. M. Stankovic, G. Inalhan, R. Teo and C. J. Tomlin, Decentralized overlapping control of a formation of unmanned aerial vehicles,, Automatica, 40 (2004), 1285. doi: 10.1016/j.automatica.2004.02.017. [32] S. S. Stankovic and D. D. Siljak, Robust stabilization of nonlinear interconnected systems by decentralized dynamic output feedback,, Systems and Control Letters, 58 (2009), 271. doi: 10.1016/j.sysconle.2008.11.003. [33] A. A. Stoorvogel, J. Minteer and C. Deliu, Decentralized control with input saturation: a first step towards design,, Proc. American Control Conference, (2005), 2082. [34] F. Wu, Z. Lin and Q. Zheng, Output feedback stabilization of linear systems with actuator saturation,, IEEE Trans. Autom. Control, 52 (2007), 122. doi: 10.1109/TAC.2006.886498. [35] G. Zhai, M. Ikeda and Y. Fujikasi, Decentralized H∞ controller design: a matrix inequality approach using a homotopy method,, Automatica, 37 (2001), 565. doi: 10.1016/S0005-1098(00)00190-4. [36] Y. Zhu and P. R. Pragilla, Decentralized output feedback control of a class of large scale systems,, IMA Journal of Mathematical Control and Info., 24 (2007), 57. doi: 10.1093/imamci/dnl007.

show all references

##### References:
 [1] H. Akkurt, Development of a Control Model for a PWR,, M. Sc. Thesis, (1996). [2] Atomic Energy Agency, Modern Instrumentation and Control for Nuclear Power Plants: A Guidebook,, Vienna, (1999). [3] L. Backule and J. Rodellar, Decentralized control and overlapping decomposition of mechanical systems. part 1: System decomposition. part 2: Decentralized stabilization,, Int. J. Control, 61 (1995), 559. doi: 10.1080/00207179508921918. [4] L. Backule, F. Paulet-Crainiceanu, J. Rodellar and J. M. Rossell, Overlapping reliable control for a cable-stayed bridge benchmark,, IEEE Trans. Control Systems Technology, 13 (2005), 663. [5] D. S. Bernstein and A. N. Michel, A Chronological bibliography on saturating actuators,, Int. J. Robust Nonlinear Control, 5 (1995), 375. doi: 10.1002/rnc.4590050502. [6] D. Dai, T. Hu, A. R. Teel and L. Zaccarian, Control of saturated linear plants via output feedback containing an internal dead zone loop,, Proc. American Control Conference, (2006), 5239. [7] B. Frogner and H. S. Rao, Control of nuclear power plants,, IEEE Trans. Automat. Control, 23 (1978), 405. [8] P. Gahinet and P. Apkarian, A linear matrix inequality approach to H∞ control,, Int. J. Robust and Nonlinear Control, 4 (1994), 421. doi: 10.1002/rnc.4590040403. [9] T. Hua and Z. Lin, Control Systems with Actuator Saturation: Analysis and Design,, Birkhauser, (2001). [10] M. Ikeda, D. D. Siljak and D. E. White, Decentralized control with overlapping information set,, J. Optimization Theory and Applications, 34 (1981), 279. doi: 10.1007/BF00935477. [11] M. Ikeda and D. D. Siljak, Overlapping decentralized control with input, state and output inclusion,, Control-Theory and Advanced Technol., 2 (1986), 155. [12] K. Kalsi, J. Lian and S. H. Zak, Decentralized dynamic output feedback control of Nonlinear interconnected systems,, IEEE Trans on Autom Control, 55 (2010), 1964. doi: 10.1109/TAC.2010.2050715. [13] V. Kapilla and K. Grigoriadis, Actuator Saturation Control,, Marcel Dekker, (2002). [14] T. A. Kendi and F. J. Doyle, Nonlinear control of a fluidized bed reactor using approximate feedback linearization,, Ind. Eng. Chem. Res., 35 (1996), 746. [15] T. W. Kerlin, E. M. Katz and J. G. Thakkar, Theoretical and experimental dynamic analysis of the H. B. Robinson nuclear plant,, Nuclear Technology, 30 (1976), 299. [16] Z. Lin, Low Gain Feedback,, Springer-Verlag, (1998). [17] L. Lu, Z. Lin and A. Bateman, Decentralized state feedback design for large-scale linear systems subject to input saturation,, IET Control Theory Appl., 4 (2010), 206. doi: 10.1049/iet-cta.2008.0605. [18] M. S. Mahmoud, Decentralized reliable control of interconnected systems with time-varying delays,, J. Optimization Theory and Applications, 143 (2009), 497. doi: 10.1007/s10957-009-9571-y. [19] M. S. Mahmoud and N. B. Almutairi, Decentralized stabilization of interconnected systems with time-varying delays,, European J. Control, 15 (2009), 624. doi: 10.3166/ejc.15.624-633. [20] M. S. Mahmoud, Decentralized stabilization of interconnected nonlinear systems with time-varying delays,, IEEE Tran. Automatic Control, 54 (2009), 2663. doi: 10.1109/TAC.2009.2031572. [21] M. S. Mahmoud, Decentralized Control and Filtering in Interconnected Dynamical Systems,, CRC Press, (2010). [22] M. S. Mahmoud, Improved stability and stabilization approach to linear interconnected time-delay systems,, Optimal Control Applications and Methods, 31 (2010), 81. doi: 10.1002/oca.884. [23] M. S. Mahmoud and S. Elferik, New stability and stabilization methods for nonlinear systems with time-varying delays,, Optimal Control Applications and Methods, 31 (2010), 273. doi: 10.1002/oca.904. [24] M. S. Mahmoud, Decentralized Control with Design Constraints,, Springer-Verlag, (2011). [25] I. Ngamroo, Overlapping decompositions-based robust decentralized TABU search-optimized fixed structure H∞ frequency stabilizer design in interconnected power systems,, Int. J. Innovative Computing, 9 (2013). [26] C. Pittet, S. Tarbouriech and C. Burgat, Output feedback synthesis via the circle criterion for linear systems subject to saturating inputs,, Proc. the 37th IEEE Conference on Decision and Control, (1998), 401. [27] I. Postlethwaite, M. Turner and G. Herman, Robust control applications,, Annual Reviews in Control, 31 (2007), 27. [28] A. Saberi, Z. Lin, and A. R. Teel, Control of linear systems with saturating actuators,, IEEE Trans. Automat. Control, 41 (1996), 368. doi: 10.1109/9.486638. [29] C. Scherer, P. Gahinet and M. Chilali, Multiobjective output-feedback control via LMI optimization,, IEEE Trans. Automat. Control, 42 (1997), 896. doi: 10.1109/9.599969. [30] C. Scherer and S. Weiland, Linear Matrix Inequalities in Control,, Delft Center for Systems and Control, (2005). [31] D. M. Stankovic, G. Inalhan, R. Teo and C. J. Tomlin, Decentralized overlapping control of a formation of unmanned aerial vehicles,, Automatica, 40 (2004), 1285. doi: 10.1016/j.automatica.2004.02.017. [32] S. S. Stankovic and D. D. Siljak, Robust stabilization of nonlinear interconnected systems by decentralized dynamic output feedback,, Systems and Control Letters, 58 (2009), 271. doi: 10.1016/j.sysconle.2008.11.003. [33] A. A. Stoorvogel, J. Minteer and C. Deliu, Decentralized control with input saturation: a first step towards design,, Proc. American Control Conference, (2005), 2082. [34] F. Wu, Z. Lin and Q. Zheng, Output feedback stabilization of linear systems with actuator saturation,, IEEE Trans. Autom. Control, 52 (2007), 122. doi: 10.1109/TAC.2006.886498. [35] G. Zhai, M. Ikeda and Y. Fujikasi, Decentralized H∞ controller design: a matrix inequality approach using a homotopy method,, Automatica, 37 (2001), 565. doi: 10.1016/S0005-1098(00)00190-4. [36] Y. Zhu and P. R. Pragilla, Decentralized output feedback control of a class of large scale systems,, IMA Journal of Mathematical Control and Info., 24 (2007), 57. doi: 10.1093/imamci/dnl007.
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