Delay-range-dependent control of nonlinear time-delay systems under input saturation
Summary This paper describes a delay‐range‐dependent local state feedback controller synthesis approach providing estimation of the region of stability for nonlinear time‐delay systems under input saturation. By employing a Lyapunov–Krasovskii functional, properties of nonlinear functions, local sec...
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| Published in | International journal of robust and nonlinear control Vol. 26; no. 8; pp. 1647 - 1666 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Bognor Regis
Blackwell Publishing Ltd
25.05.2016
Wiley Subscription Services, Inc |
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| Abstract | Summary
This paper describes a delay‐range‐dependent local state feedback controller synthesis approach providing estimation of the region of stability for nonlinear time‐delay systems under input saturation. By employing a Lyapunov–Krasovskii functional, properties of nonlinear functions, local sector condition and Jensen's inequality, a sufficient condition is derived for stabilization of nonlinear systems with interval delays varying within a range. Novel solutions to the delay‐range‐dependent and delay‐dependent stabilization problems for linear and nonlinear time‐delay systems, respectively, subject to input saturation are derived as specific scenarios of the proposed control strategy. Also, a delay‐rate‐independent condition for control of nonlinear systems in the presence of input saturation with unknown delay‐derivative bound information is established. And further, a robust state feedback controller synthesis scheme ensuring L2 gain reduction from disturbance to output is devised to address the problem of the stabilization of input‐constrained nonlinear time‐delay systems with varying interval lags. The proposed design conditions can be solved using linear matrix inequality tools in connection with conventional cone complementary linearization algorithms. Simulation results for an unstable nonlinear time‐delay network and a large‐scale chemical reactor under input saturation and varying interval time‐delays are analyzed to demonstrate the effectiveness of the proposed methodology. Copyright © 2015 John Wiley & Sons, Ltd. |
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| AbstractList | Summary
This paper describes a delay‐range‐dependent local state feedback controller synthesis approach providing estimation of the region of stability for nonlinear time‐delay systems under input saturation. By employing a Lyapunov–Krasovskii functional, properties of nonlinear functions, local sector condition and Jensen's inequality, a sufficient condition is derived for stabilization of nonlinear systems with interval delays varying within a range. Novel solutions to the delay‐range‐dependent and delay‐dependent stabilization problems for linear and nonlinear time‐delay systems, respectively, subject to input saturation are derived as specific scenarios of the proposed control strategy. Also, a delay‐rate‐independent condition for control of nonlinear systems in the presence of input saturation with unknown delay‐derivative bound information is established. And further, a robust state feedback controller synthesis scheme ensuring L2 gain reduction from disturbance to output is devised to address the problem of the stabilization of input‐constrained nonlinear time‐delay systems with varying interval lags. The proposed design conditions can be solved using linear matrix inequality tools in connection with conventional cone complementary linearization algorithms. Simulation results for an unstable nonlinear time‐delay network and a large‐scale chemical reactor under input saturation and varying interval time‐delays are analyzed to demonstrate the effectiveness of the proposed methodology. Copyright © 2015 John Wiley & Sons, Ltd. This paper describes a delay-range-dependent local state feedback controller synthesis approach providing estimation of the region of stability for nonlinear time-delay systems under input saturation. By employing a Lyapunov-Krasovskii functional, properties of nonlinear functions, local sector condition and Jensen's inequality, a sufficient condition is derived for stabilization of nonlinear systems with interval delays varying within a range. Novel solutions to the delay-range-dependent and delay-dependent stabilization problems for linear and nonlinear time-delay systems, respectively, subject to input saturation are derived as specific scenarios of the proposed control strategy. Also, a delay-rate-independent condition for control of nonlinear systems in the presence of input saturation with unknown delay-derivative bound information is established. And further, a robust state feedback controller synthesis scheme ensuring L sub(2) gain reduction from disturbance to output is devised to address the problem of the stabilization of input-constrained nonlinear time-delay systems with varying interval lags. The proposed design conditions can be solved using linear matrix inequality tools in connection with conventional cone complementary linearization algorithms. Simulation results for an unstable nonlinear time-delay network and a large-scale chemical reactor under input saturation and varying interval time-delays are analyzed to demonstrate the effectiveness of the proposed methodology. Summary This paper describes a delay-range-dependent local state feedback controller synthesis approach providing estimation of the region of stability for nonlinear time-delay systems under input saturation. By employing a Lyapunov-Krasovskii functional, properties of nonlinear functions, local sector condition and Jensen's inequality, a sufficient condition is derived for stabilization of nonlinear systems with interval delays varying within a range. Novel solutions to the delay-range-dependent and delay-dependent stabilization problems for linear and nonlinear time-delay systems, respectively, subject to input saturation are derived as specific scenarios of the proposed control strategy. Also, a delay-rate-independent condition for control of nonlinear systems in the presence of input saturation with unknown delay-derivative bound information is established. And further, a robust state feedback controller synthesis scheme ensuring L2 gain reduction from disturbance to output is devised to address the problem of the stabilization of input-constrained nonlinear time-delay systems with varying interval lags. The proposed design conditions can be solved using linear matrix inequality tools in connection with conventional cone complementary linearization algorithms. Simulation results for an unstable nonlinear time-delay network and a large-scale chemical reactor under input saturation and varying interval time-delays are analyzed to demonstrate the effectiveness of the proposed methodology. Copyright © 2015 John Wiley & Sons, Ltd. |
| Author | Rehan, Muhammad Iqbal, Naeem Hong, Keum-Shik |
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| References | Yin S, Zhu X, Kaynak O. Improved PLS focused on key-performance-indicator-related fault diagnosis. IEEE Transactions on Industrial Electronics 2015; 62(3):1651-1658. Li T, Li R, Li J. Decentralized adaptive neural control of nonlinear interconnected large-scale systems with unknown time delays and input saturation. Neurocomputing 2011; 74(14-15):2277-2283. Zhang H, Shi Y, Mehr AS. Robust static output feedback control and remote PID design for networked motor systems. IEEE Transactions on Industrial Electronics 2011; 58(12):5396-5405. Dey R, Ghosh S, Ray G, Rakshit A. Improved delay-dependent stabilization of time-delay systems with actuator saturation. International Journal of Robust and Nonlinear Control 2014; 24(5):902-917. Thuan MV, Phat VN, Trinh HM. Dynamic output feedback guaranteed cost control for linear systems with interval time-varying delays in states and outputs. Applied Mathematics and Computation 2012; 218(18):10697-10707. Tarbouriech S, Prieur C, Gomes-da-Silva-Jr JM. Stability analysis and stabilization of systems presenting nested saturations. IEEE Transactions on Automatic Control 2006; 51(7):1364-1371. Zhao YB, Liu GP, Rees D. Design of a packet-based control framework for networked control systems. IEEE Transactions on Control Systems Technology 2009; 17(4):859-865. Yan H, Zhang H, Meng MQH. Delay-range-dependent robust H∞ control for uncertain systems with interval time-varying delays. Neurocomputing 2010; 73(7-9):1235-1243. Yin S, Li X, Gao H, Kaynak O. Data-based techniques focused on modern industry: an overview. IEEE Transactions on Industrial Electronics 2015; 62(1):657-667. Zhang L, Boukas EL, Haidar A. Delay-range-dependent control synthesis for time-delay systems with actuator saturation. Automatica 2008; 44(9):2691-2695. Shao H. New delay-dependent stability criteria for systems with interval delay. Automatica 2009; 45(3):744-749. Park JK, Choi CH, Choo H. Dynamic anti-windup method for a class of time-delay control systems with input saturation. Journal of Robust and Nonlinear Control 2000; 10(6):457-488. Kwon OM, Park JH. Delay-range-dependent stabilization of uncertain dynamic systems with interval time-varying delays. Applied Mathematics and Computation 2009; 208(1):58-68. Zhang J, Zhang H, Luo Y, Feng T. Model-free optimal control design for a class of linear discrete-time systems with multiple delays using adaptive dynamic programming. Robotics and Autonomous Systems 2014; 62(5):319-329. Peng C, Han QL. Delay-range-dependent robust stabilization for uncertain T-S fuzzy control systems with interval time-varying delays. Information Sciences 2011; 181(16):4287-4299. Tarbouriech S, Turner MC. Anti-windup design: an overview of some recent advances and open problems. IET Control Theory and Applications 2009; 3(1):1-19. Tarbouriech S, Gomes Da Silva JM, Garcia G. Delay-dependent anti-windup strategy for linear systems with saturating inputs and delayed outputs. International Journal of Robust and Nonlinear Control 2004; 14(6):665-682. Yoo SJ, Park JB. Decentralized adaptive output-feedback control for a class of nonlinear large-scale systems with unknown time-varying delayed interactions. Information Sciences 2012; 186(1):222-238. De Souza CE, Coutinho D. Robust stability and control of uncertain linear discrete-time periodic systems with time-delay. Automatica 2014; 50(2):431-441. Rehan M, Hong KS. Decoupled-architecture-based nonlinear anti-windup design for a class of nonlinear systems. Nonlinear Dynamics 2013; 73(3):1955-1967. Gomes da Silva JM, Ghiggi I, Tarbouriech S. Non-rational dynamic output feedback for time-delay systems with saturating inputs. International Journal of Control 2008; 81(4):557-570. Hua CC, Wang QG, Guan XP. Adaptive tracking controller design of nonlinear systems with time delays and unknown dead-zone input. IEEE Transactions on Automatic Control 2008; 53(6):1753-1759. Wang HQ, Chen B, Lin C. Adaptive neural tracking control for a class of stochastic nonlinear systems. International Journal of Robust and Nonlinear Control 2014; 24(6):1262-1280. Ghaoui LE, Oustry F, AitRami M. A cone complementarity linearization algorithm for static output-feedback and related problems. IEEE Transactions on Automatic Control 1997; 42(7):1171-1176. Niculescu SI, Dion JM, Dugard L. Robust stabilization for uncertain time-delay systems containing saturating actuators. IEEE Transactions on Automatic Control 1996; 41(5):742-747. Yin S, Huang Z. Performance monitoring for vehicle suspension system via fuzzy positivistic C-means clustering based on accelerometer measurements. IEEE/ASME Transactions on Mechatronics 2014; PP(99):1-8. Botmart T, Niamsup P, Phat VN. Delay-dependent exponential stabilization for uncertain linear systems with interval non-differentiable time-varying delays. Applied Mathematics and Computation 2011; 217(18):8236-8247. Zhang XF, Liu L, Feng G, Zhang CH. Output feedback control of large-scale nonlinear time-delay systems in lower triangular form. Automatica 2013; 49(10):3476-3483. Yang R, Wang Y. Finite-time stability analysis and H∞ control for a class of nonlinear time-delay Hamiltonian systems. Automatica 2013; 49(2):390-401. Garcia E, Antsaklis PJ. Model-based event-triggered control for systems with quantization and time-varying network delays. IEEE Transactions on Automatic Control 2013; 58(2):422-434. Kim KB. Design of feedback controls supporting TCP based on the state-space approach. IEEE Transactions on Automatic Control 2006; 51(6):1086-1099. Li T, Li Z, Wang D, Chen CLP. Output-feedback adaptive neural control for stochastic nonlinear time-varying delays systems with unknown control directions. IEEE Transactions on Neural Networks and Learning Systems 2015; 26(6):1188-1201. Liu Y, Hu LS, Shi P. A novel approach on stabilization for linear systems with time-varying input delay. Applied Mathematics and Computation 2012; 218(9):5937-5947. Yin S, Ding DX, Xie X, Luo H. A review on basic data-driven approaches for industrial process monitoring. IEEE Transactions on Industrial Electronics 2014; 61(10):6418-6428. Ahmed A, Rehan M, Iqbal N. Delay-dependent anti-windup synthesis for stability of constrained state delay systems using pole-constraints. ISA Transactions 2011; 50(2):249-255. Li H, Shi Y. State-feedback H-infinity control for stochastic time-delay nonlinear systems with state and disturbance-dependent noise. International Journal of Control 2012; 85(9):1515-1531. Zhang BL, Hu YH, Tang GY. Stabilization control for offshore steel jacket platforms with actuator time-delays. Nonlinear Dynamics 2012; 70(2):1593-1603. Oucheriah S. Synthesis of controllers for time-delay systems subject to actuator saturation and disturbance. Journal of Dynamic Systems, Measurement, and Control 2003; 125(2):244-249. Liu K, Xie G, Wang L. Containment control for second-order multi-agent systems with time-varying delays. Systems & Control Letters 2014; 67:24-31. Rehan M. Synchronization and anti-synchronization of chaotic oscillators under input saturation. Applied Mathematical Modelling 2013; 37(10-11):6829-6837. Chen X, Yan P, Serrani A. On input-to-state stability-based design for leader/follower formation control with measurement delays. International Journal of Robust and Nonlinear Control 2013; 23(11):1433-1455. Li T, Wang D, Li J, Li Y. Adaptive decentralized NN control of nonlinear interconnected time-delay systems with input saturation. Asian Journal of Control 2013; 15(2):533-542. Kun Y. Robust synchronization in arrays of coupled networks with delay and mixed coupling. Neurocomputing 2009; 72(4-6):1026-1031. 2009; 45 2012; 186 2011; 217 2013; 49 2006; 51 1997; 42 2013; 23 2011; 74 2014; 24 2011; 58 2008; 53 2014; 62 2014; 61 2014; 67 2014; PP 2012; 70 2015; 26 2013; 15 2013; 37 2013; 58 2000 2015; 62 2009; 72 2000; 10 2013; 73 2004; 14 2011; 50 1996; 41 2011; 181 2008; 44 2009; 3 2003; 125 2014; 50 2009; 208 2008; 81 2010; 73 2012; 218 2012; 85 2009; 17 |
| References_xml | – reference: De Souza CE, Coutinho D. Robust stability and control of uncertain linear discrete-time periodic systems with time-delay. Automatica 2014; 50(2):431-441. – reference: Liu Y, Hu LS, Shi P. A novel approach on stabilization for linear systems with time-varying input delay. Applied Mathematics and Computation 2012; 218(9):5937-5947. – reference: Tarbouriech S, Gomes Da Silva JM, Garcia G. Delay-dependent anti-windup strategy for linear systems with saturating inputs and delayed outputs. International Journal of Robust and Nonlinear Control 2004; 14(6):665-682. – reference: Tarbouriech S, Turner MC. Anti-windup design: an overview of some recent advances and open problems. IET Control Theory and Applications 2009; 3(1):1-19. – reference: Rehan M, Hong KS. Decoupled-architecture-based nonlinear anti-windup design for a class of nonlinear systems. Nonlinear Dynamics 2013; 73(3):1955-1967. – reference: Yin S, Zhu X, Kaynak O. Improved PLS focused on key-performance-indicator-related fault diagnosis. IEEE Transactions on Industrial Electronics 2015; 62(3):1651-1658. – reference: Zhang XF, Liu L, Feng G, Zhang CH. Output feedback control of large-scale nonlinear time-delay systems in lower triangular form. Automatica 2013; 49(10):3476-3483. – reference: Yang R, Wang Y. Finite-time stability analysis and H∞ control for a class of nonlinear time-delay Hamiltonian systems. Automatica 2013; 49(2):390-401. – reference: Zhang H, Shi Y, Mehr AS. Robust static output feedback control and remote PID design for networked motor systems. IEEE Transactions on Industrial Electronics 2011; 58(12):5396-5405. – reference: Zhang BL, Hu YH, Tang GY. Stabilization control for offshore steel jacket platforms with actuator time-delays. Nonlinear Dynamics 2012; 70(2):1593-1603. – reference: Hua CC, Wang QG, Guan XP. Adaptive tracking controller design of nonlinear systems with time delays and unknown dead-zone input. IEEE Transactions on Automatic Control 2008; 53(6):1753-1759. – reference: Rehan M. Synchronization and anti-synchronization of chaotic oscillators under input saturation. Applied Mathematical Modelling 2013; 37(10-11):6829-6837. – reference: Yin S, Huang Z. Performance monitoring for vehicle suspension system via fuzzy positivistic C-means clustering based on accelerometer measurements. IEEE/ASME Transactions on Mechatronics 2014; PP(99):1-8. – reference: Tarbouriech S, Prieur C, Gomes-da-Silva-Jr JM. Stability analysis and stabilization of systems presenting nested saturations. IEEE Transactions on Automatic Control 2006; 51(7):1364-1371. – reference: Li T, Li R, Li J. Decentralized adaptive neural control of nonlinear interconnected large-scale systems with unknown time delays and input saturation. Neurocomputing 2011; 74(14-15):2277-2283. – reference: Kwon OM, Park JH. Delay-range-dependent stabilization of uncertain dynamic systems with interval time-varying delays. Applied Mathematics and Computation 2009; 208(1):58-68. – reference: Dey R, Ghosh S, Ray G, Rakshit A. Improved delay-dependent stabilization of time-delay systems with actuator saturation. International Journal of Robust and Nonlinear Control 2014; 24(5):902-917. – reference: Ghaoui LE, Oustry F, AitRami M. A cone complementarity linearization algorithm for static output-feedback and related problems. IEEE Transactions on Automatic Control 1997; 42(7):1171-1176. – reference: Li T, Wang D, Li J, Li Y. Adaptive decentralized NN control of nonlinear interconnected time-delay systems with input saturation. Asian Journal of Control 2013; 15(2):533-542. – reference: Li H, Shi Y. State-feedback H-infinity control for stochastic time-delay nonlinear systems with state and disturbance-dependent noise. International Journal of Control 2012; 85(9):1515-1531. – reference: Zhang L, Boukas EL, Haidar A. Delay-range-dependent control synthesis for time-delay systems with actuator saturation. Automatica 2008; 44(9):2691-2695. – reference: Zhang J, Zhang H, Luo Y, Feng T. Model-free optimal control design for a class of linear discrete-time systems with multiple delays using adaptive dynamic programming. Robotics and Autonomous Systems 2014; 62(5):319-329. – reference: Botmart T, Niamsup P, Phat VN. Delay-dependent exponential stabilization for uncertain linear systems with interval non-differentiable time-varying delays. Applied Mathematics and Computation 2011; 217(18):8236-8247. – reference: Kim KB. Design of feedback controls supporting TCP based on the state-space approach. IEEE Transactions on Automatic Control 2006; 51(6):1086-1099. – reference: Kun Y. Robust synchronization in arrays of coupled networks with delay and mixed coupling. Neurocomputing 2009; 72(4-6):1026-1031. – reference: Oucheriah S. Synthesis of controllers for time-delay systems subject to actuator saturation and disturbance. Journal of Dynamic Systems, Measurement, and Control 2003; 125(2):244-249. – reference: Liu K, Xie G, Wang L. Containment control for second-order multi-agent systems with time-varying delays. Systems & Control Letters 2014; 67:24-31. – reference: Peng C, Han QL. Delay-range-dependent robust stabilization for uncertain T-S fuzzy control systems with interval time-varying delays. Information Sciences 2011; 181(16):4287-4299. – reference: Thuan MV, Phat VN, Trinh HM. Dynamic output feedback guaranteed cost control for linear systems with interval time-varying delays in states and outputs. Applied Mathematics and Computation 2012; 218(18):10697-10707. – reference: Garcia E, Antsaklis PJ. Model-based event-triggered control for systems with quantization and time-varying network delays. IEEE Transactions on Automatic Control 2013; 58(2):422-434. – reference: Gomes da Silva JM, Ghiggi I, Tarbouriech S. Non-rational dynamic output feedback for time-delay systems with saturating inputs. International Journal of Control 2008; 81(4):557-570. – reference: Park JK, Choi CH, Choo H. Dynamic anti-windup method for a class of time-delay control systems with input saturation. Journal of Robust and Nonlinear Control 2000; 10(6):457-488. – reference: Yin S, Ding DX, Xie X, Luo H. A review on basic data-driven approaches for industrial process monitoring. IEEE Transactions on Industrial Electronics 2014; 61(10):6418-6428. – reference: Niculescu SI, Dion JM, Dugard L. Robust stabilization for uncertain time-delay systems containing saturating actuators. IEEE Transactions on Automatic Control 1996; 41(5):742-747. – reference: Li T, Li Z, Wang D, Chen CLP. Output-feedback adaptive neural control for stochastic nonlinear time-varying delays systems with unknown control directions. IEEE Transactions on Neural Networks and Learning Systems 2015; 26(6):1188-1201. – reference: Chen X, Yan P, Serrani A. On input-to-state stability-based design for leader/follower formation control with measurement delays. International Journal of Robust and Nonlinear Control 2013; 23(11):1433-1455. – reference: Shao H. New delay-dependent stability criteria for systems with interval delay. Automatica 2009; 45(3):744-749. – reference: Zhao YB, Liu GP, Rees D. Design of a packet-based control framework for networked control systems. IEEE Transactions on Control Systems Technology 2009; 17(4):859-865. – reference: Ahmed A, Rehan M, Iqbal N. Delay-dependent anti-windup synthesis for stability of constrained state delay systems using pole-constraints. ISA Transactions 2011; 50(2):249-255. – reference: Wang HQ, Chen B, Lin C. Adaptive neural tracking control for a class of stochastic nonlinear systems. International Journal of Robust and Nonlinear Control 2014; 24(6):1262-1280. – reference: Yan H, Zhang H, Meng MQH. Delay-range-dependent robust H∞ control for uncertain systems with interval time-varying delays. Neurocomputing 2010; 73(7-9):1235-1243. – reference: Yin S, Li X, Gao H, Kaynak O. Data-based techniques focused on modern industry: an overview. IEEE Transactions on Industrial Electronics 2015; 62(1):657-667. – reference: Yoo SJ, Park JB. Decentralized adaptive output-feedback control for a class of nonlinear large-scale systems with unknown time-varying delayed interactions. 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This paper describes a delay‐range‐dependent local state feedback controller synthesis approach providing estimation of the region of stability for... Summary This paper describes a delay-range-dependent local state feedback controller synthesis approach providing estimation of the region of stability for... This paper describes a delay-range-dependent local state feedback controller synthesis approach providing estimation of the region of stability for nonlinear... |
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| SubjectTerms | Control systems Controllers delay-range-dependency Dynamical systems input saturation Intervals Nonlinear dynamics Nonlinearity region of stability Saturation Stabilization state feedback control time-delay systems |
| Title | Delay-range-dependent control of nonlinear time-delay systems under input saturation |
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