Output feedback stabilization for nonholonomic systems with unknown unmeasured states-dependent growth
Corresponding Author
Jiangbo Yu
School of Control Science and Engineering, Shandong University, Jinan, China
School of Science, Shandong Jianzhu University, Jinan, China
Jiangbo Yu, School of Control Science and Engineering, Shandong University, Jinan 250061, China; or School of Science, Shandong Jianzhu University, Jinan 250101, China.
Email: [email protected]
Search for more papers by this authorYungang Liu
School of Control Science and Engineering, Shandong University, Jinan, China
Search for more papers by this authorYuqiang Wu
Institute of Automation, Qufu Normal University, Qufu, China
Search for more papers by this authorCorresponding Author
Jiangbo Yu
School of Control Science and Engineering, Shandong University, Jinan, China
School of Science, Shandong Jianzhu University, Jinan, China
Jiangbo Yu, School of Control Science and Engineering, Shandong University, Jinan 250061, China; or School of Science, Shandong Jianzhu University, Jinan 250101, China.
Email: [email protected]
Search for more papers by this authorYungang Liu
School of Control Science and Engineering, Shandong University, Jinan, China
Search for more papers by this authorYuqiang Wu
Institute of Automation, Qufu Normal University, Qufu, China
Search for more papers by this authorSummary
This paper is concerned with the global output feedback stabilization for a class of nonholonomic systems with unknown parameter, polynomial-of-output, and unmeasurable states dependent growth. A dynamic high-gain observer is first designed to reconstruct the unmeasurable system states and, in addition, to compensate the serious parameter unknowns in nonlinear drifts. Then, we design a compact adaptive controller without invoking the backstepping technique, which reduces the complexity of controller. Additionally, a switching control strategy is employed to overcome the smooth feedback obstacle associated with nonholonomic systems. It is shown that the proposed control laws guarantee that all closed-loop system states are globally bounded and ultimately converge to zero. The simulation results demonstrate the effectiveness of the proposed control strategy.
REFERENCES
- 1Murray RM, Sastry S. Nonholonomic motion planning: steering using sinusoids. IEEE Trans Autom Control. 1993; 38(5): 700-716.
- 2Brockett RW. Asymptotic stability and feedback stabilization. Differ Geom Control Theory. 1983; 27(1): 181-191.
- 3Huang J, Chen J, Fang H, Dou LH. An overview of recent progress in high-order nonholonomic chained system control and distributed coordination. J Control Decis. 2015; 2(1): 64-85.
10.1080/23307706.2015.1004803 Google Scholar
- 4Astolfi A. Discontinuous control of nonholonomic systems. Syst Control Lett. 1996; 27(1): 37-45.
- 5Jiang Z-P. Robust exponential regulation of nonholonomic systems with uncertainties. Automatica. 2000; 36(2): 189-209.
- 6Ge SS, Wang ZP, Lee TH. Adaptive stabilization of uncertain nonholonomic systems by state and output feedback. Automatica. 2003; 39(8): 1451-1460.
- 7Xi ZR, Feng G, Jiang ZP, Cheng DZ. Output feedback exponential stabilization of uncertain chained systems. J Frankl Inst. 2007; 344(1): 36-57.
- 8Liu Y-G, Zhang J-F. Output feedback adaptive stabilization control design for nonholonomic systems with strong nonlinear drifts. Int J Control. 2005; 78(7): 474-490.
- 9Wu YQ, Zhao Y, Yu JB. Global asymptotic stability controller of uncertain nonholonomic systems. J Frankl Inst. 2013; 350(5): 1248-1263.
- 10Gao F, Wu Y, Yuan F. Semi-global finite-time stabilization of uncertain nonholonomic systems via output feedback. Trans Inst Meas Control. 2015; 37(1): 1-9.
- 11Wu K, Sun C-Y. Output feedback control for nonholonomic systems with non-vanishing disturbances. Int J Control. 2019. https://doi.org/10.1080/00207179.2019.1566633
10.1080/00207179.2019.1566633 Google Scholar
- 12Li F, Liu Y. Global stabilization via time-varying output-feedback for stochastic nonlinear systems with unknown growth rate. Syst Control Lett. 2015; 39(2): 123-131.
- 13Qian C, Lin W. Output feedback control of a class of nonlinear systems: a nonseparation principle paradigm. IEEE Trans Autom Control. 2002; 47(10): 1710-1715.
- 14Lei H, Lin W. Universal adaptive control of nonlinear systems with unknown growth rate by output feedback. Automatica. 2006; 42(10): 1783-1789.
- 15Lei H, Lin W. Adaptive regulation of uncertain nonlinear systems by output feedback: a universal control approach. Syst Control Lett. 2007; 56(7-8): 529-537.
- 16Lei H, Lin W. Robust control of uncertain systems with polynomial nonlinearity by output feedback. Int J Robust Nonlinear Control. 2009; 19(6): 692-723.
- 17Krishnamurthy P, Khorrami F. Dual high-gain-based adaptive output-feedback control for a class of nonlinear systems. Int J Adapt Control Signal Process. 2008; 22(1): 23-42.
- 18Liu YG. Global asymptotic regulation via time-varying output feedback for a class of uncertain nonlinear systems. SIAM J Control Optim. 2013; 51(6): 4318-4342.
- 19Wu Y-Q, Yu J-B, Zhao Y. Further results on global asymptotic regulation control for a class of nonlinear systems with iISS inverse dynamics. IEEE Trans Autom Control. 2011; 56(4): 941-946.
- 20Wu Y-Q, Yu J-B, Zhang Z. Output feedback regulation control for a class of cascade nonlinear systems by time-varying Kalman observer. Int J Robust Nonlinear Control. 2019; 29(7): 2149-2170.
- 21Qian C, Du H. Global output feedback stabilization of a class of nonlinear systems via linear sampled-data control. IEEE Trans Autom Control. 2012; 57(11): 2934-2939.
- 22Lin W, Wei W. Robust control of a family of uncertain nonminimum-phase systems via continuous-time and sampled-data output feedback. Int J Robust Nonlinear Control. 2017; 28(4): 1440-1455.
- 23Liu YG. Global output-feedback tracking for nonlinear systems with unknown polynomial-of-output growth rate. J Control Theory Appl. 2014; 31(7): 921-933.
- 24Zhang X, Lin Y. Robust adaptive tracking of uncertain nonlinear systems by output feedback. Int J Robust Nonlinear Control. 2016; 26(10): 2187-2200.
- 25Yu J-B, Zhao Y, Wu Y-Q. Global robust output tracking control for a class of uncertain cascaded nonlinear systems. Automatica. 2018; 93(7): 274-281.
- 26Man Y, Liu Y. Global adaptive stabilization and practical tracking for nonlinear systems with unknown powers. Automatica. 2019; 100(2): 171-181.
- 27Zhai J, Karimi HR. Global output feedback control for a class of nonlinear systems with unknown homogenous growth condition. Int J Robust Nonlinear Control. 2019; 29(7): 2082-2095.
- 28Zhai J. Dynamic output feedback control for nonlinear time-delay systems and applications to chemical reactor systems. IEEE Trans Circuits Syst II Exp Br. 2018. https://doi.org/10.1109/TCSII.2018.2890654
- 29Liu Z, Xue L, Sun W, Sun Z. Robust output feedback tracking control for a class of high-order time-delay nonlinear systems with input dead-zone and disturbances. Nonlinear Dynamics. 2019. https://doi.org/10.1007/s11071-019-05018-1
- 30Liu Y-L, Wu Y-Q. Output feedback control for stochastic nonholonomic systems with growth rate restriction. Asian J Control. 2011; 13(1): 177-185.
- 31Ju G, Wu Y, Sun W. Output-feedback control for nonholonomic systems with linear growth condition. J Syst Sci Complex. 2011; 24(5): 862-874.
- 32Chen X, Zhang X. Output-feedback control strategies of lower-triangular nonlinear nonholonomic systems in any prescribed finite time. Int J Robust Nonlinear Control. 2019; 29(4): 904-918.
- 33Praly L, Jiang ZP. Linear output feedback with dynamic high gain for nonlinear systems. Syst Control Lett. 2004; 53(2): 107-116.
- 34Huang Y, Liu Y. A compact design scheme of adaptive output-feedback control for uncertain nonlinear systems. Int J Control. 2019; 92(2): 261-269.
- 35Wu Y, Wu Y. Robust stabilization of delayed nonholonomic systems with strong nonlinear drifts. Nonlinear Anal Real World Appl. 2010; 11(5): 3620-3627.
- 36Wu Y-Q, Liu Z-G. Output feedback stabilization for time-delay nonholonomic systems with polynomial conditions. ISA Transactions. 2015; 58(9): 1-10.
- 37Zhao Y, Yu J, Wu Y. State-feedback stabilization for a class of more general high order stochastic nonholonomic systems. Int J Adapt Control Signal Process. 2011; 25(8): 687-706.
- 38Gao F, Wu Y, Liu Y. Finite-time stabilization for a class of switched stochastic nonlinear systems with dead-zone input nonlinearities. Int J Robust Nonlinear Control. 2018; 28(9): 3239-3257.
- 39Li G-J, Xie X-J. Adaptive state feedback stabilization of more general stochastic high-order nonholonomic systems. Int J Adapt Control Signal Process. 2018; 32(8): 1222-1242.
- 40Wang H, Zhu Q. Adaptive output feedback control of stochastic nonholonomic systems with nonlinear parameterization. Automatica. 2018; 98(12): 247-255.
- 41Du H, Wen G, Yu X, Li S, Chen MZQ. Finite-time consensus of multiple nonholonomic chained-form systems based on recursive distributed observer. Automatica. 2015; 62(12): 236-242.
- 42Cheng Y, Jia R, Du H, Wen G, Zhu W. Robust finite-time consensus formation control for multiple nonholonomic wheeled mobile robots via output feedback. Int J Robust Nonlinear Control. 2017; 28(6): 2082-2096.
- 43Anggraeni P, Defoort M, Djemai M, Zou Z. Control strategy for fixed-time leaderCfollower consensus for multi-agent systems with chained-form dynamics. Nonlinear Dynamics. 2019; 96(4): 2693-2705.
- 44Qian C, Schrader CB, Lin W. Global regulation of a class of uncertain nonlinear systems using output feedback. In: Proceedings of the 2003 American Control Conference; 2003; Denver, CO.
- 45Hale JK. Ordinary Differential Equations. 2nd ed. New York, NY: Wiley-Interscience; 1980.
- 46Khalil HK. Nonlinear Systems. 3rd ed. Upper Saddle River, NJ: Prentice-Hall; 2002.