Adaptive Backstepping Control for Constrained Systems Using Nonlinear Mapping
-
摘要: 针对基于障碍Lyapunov函数的非线性约束系统反推控制中, 控制器结构复杂、约束量初值选取区间小、会引入额外参数等问题, 提出了一种新的基于非线性映射的自适应反推控制方案. 该方法扩大约束量的初值选取区间为整个约束区间, 增加了系统初值选取和控制器设计的便易性. 约束量被映射至实数空间中, 因此映射后的新系统可以直接应用反推法设计控制器, 简化了控制器结构且不会引入额外参数. 证明了映射前后系统具有一致的收敛性, 保证闭环系统所有信号一致有界, 并且跟踪误差渐近收敛于零. 仿真结果进一步验证了本文方法的有效性.
-
关键词:
- 约束系统 /
- 反推控制 /
- 非线性映射 /
- Lyapunov稳定性
Abstract: In this paper, a novel nonlinear mapping based adaptive backstepping control is presented for nonlinear systems with output constraint to overcome the problems faced by barrier Lyapunov function based backstepping control, such as complex controller structure, small set for initial value of constrained output and extra parameters employment. The constrained output can take any initial value within the output constrained space, so added flexibility is achieved in the control design. By mapping the constrained output into the real number set, the backstepping control design can be directly used for the transformed system, while simultaneously prevent the constraints from being violated. A similar convergence feature is proved between the system and its mapping, so that the stability of the closed-loop system is guaranteed in the sense that all closed-loop signals are uniformly bounded and the tracking error converges to zero asymptotically. Simulation results demonstrate the effectiveness of the proposed control.-
Key words:
- Constrained system /
- backstepping control /
- nonlinear mapping /
- Lyapunov stability
-
[1] Blanchini F. Set invariance in control. Automatica, 1999, 35(11): 1747-1767 [2] Mayne D Q, Rawlings J B, Rao C V, Scokaert P O M. Constrained model predictive control: stability and optimality. Automatica, 2000, 36(6): 789-814 [3] Bemporad A. Reference governor for constrained nonlinear systems. IEEE Transactions on Automatic Control, 1998, 43(3): 415-419 [4] Kogiso K, Hirata K. Reference governor for constrained systems with time-varying references. Robotics and Autonomous Systems, 2009, 57(3): 289-295 [5] Dehaan D, Guay M. Extremum-seeking control of state-constrained nonlinear systems. Automatica, 2005, 41(9): 1567-1574 [6] Adetola V, Guay M. Parameter convergence in adaptive extremum-seeking control. Automatica, 2007, 43(1): 105-110 [7] Kanellakopoulos I, Kokotovic P V, Morse A S. Systematic design of adaptive controllers for feedback linearizable systems. IEEE Transactions on Automatic Control, 1991, 36(11): 1241-1253 [8] Krstic M, KanellaKopulos I, Kokotovic P V. Nonlinear and Adaptive Control Design. New York: Wiley, 1995 [9] Ge S S, Hong F, Lee T H. Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients. IEEE Transactions on System, Man, and Cybernetics, Part B: Cybernetics, 2004, 34(1): 499-516 [10] Guo T, Liu G Y. Adaptive fuzzy control for unknown nonlinear time-delay systems with virtual control functions. International Journal of Control, Automation and Systems, 2011, 9(6): 1227-1234 [11] Deng H, Krstić M. Stochastic nonlinear stabilization —— I: a backstepping design. Systems and Control Letters, 1997, 32(3): 143-150 [12] Jain S, Khorrami F. Decentralized adaptive control of a class of large-scale interconnected nonlinear systems. IEEE Transactions on Automatic Control, 1997, 42(2): 136-154 [13] Chen W S, Li J M. Decentralized output-feedback neural control for systems with unknown interconnections. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 2008, 38(1): 258-266 [14] Liu Y J, Wang W. Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems. Information Sciences, 2007, 177(18): 3901-3917 [15] Ngo K B, Mahony R, Jiang Z P. Integrator backstepping using barrier functions for systems with multiple state constraints. In: Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference. Seville, Spain: IEEE, 2005. 8306-8312 [16] Tee K P, Ge S S, Tay E H. Barrier Lyapunov functions for the control of output-constrained nonlinear systems. Automatica, 2009, 45(4): 918-927 [17] Ren B, Ge S S, Tee K P, Lee T H. Adaptive control for parametric output feedback systems with output constraint. In: Proceedings of the Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference. Shanghai, China: IEEE, 2009. 6650-6655 [18] Ren B B, Ge S S, Tee K P, Lee T H. Adaptive neural control for output feedback nonlinear systems using a barrier Lyapunov function. IEEE Transactions on Neural Networks, 2010, 21(8): 1339-1345 [19] Sun W, Yeow J T W, Sun Z. Robust adaptive control of a one degree of freedom electrostatic microelectromechanical systems model with output-error-constrained tracking. IET Control Theory and Applications, 2012, 6(1): 111-119 [20] Tee K P, Ge S S. Control of nonlinear systems with full state constraint using a barrier Lyapunov function. In: Proceedings of the Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference. Shanghai, China: IEEE, 2009. 8618-8623 [21] Tee K P, Ge S S, Li H Z, Ren B B. Control of nonlinear systems with time-varying output constraints. In: Proceedings of the 2009 IEEE International Conference on Control and Automation. Christchurch, New Zealand: IEEE, 2009. 524-529 [22] Tee K P, Ren B B, Ge S S. Control of nonlinear systems with time-varying output constraints. Automatica, 2011, 47(11): 2511-2516 [23] Tee K P, Ge S S, Tay F E H. Adaptive control of electrostatic microactuators with bidirectional drive. IEEE Transactions on Control Systems Technology, 2009, 17(2): 340-352 [24] Tee K P, Yan R, Li H Z. Adaptive admittance control of a robot manipulator under task space constraint. In: Proceedings of the 2010 IEEE International Conference on Robotics and Automation. Anchorage, Alaska: IEEE, 2010. 5181-5186 [25] Yan F J, Wang J M. Fuel-assisted in-cylinder oxygen fraction transient trajectory shaping control for diesel engine combustion mode switching. In: Proceedings of the 2011 American Control Conference. San Francisco, CA: IEEE, 2011. 1573-1578 [26] Do K D, Nguyen D H, Nguyen T B. Nonlinear control of magnetic bearing. Journal of Measurement Science and Instrumentation, 2010, 1(1): 10-16 [27] Ge S S, Lee T H, Harris C J. Adaptive Neural Network Control of Robotic Manipulators. London: World Scientific, 1998 [28] Yang Y S, Feng G, Ren J S. A combined backstepping and small-gain approach to robust adaptive fuzzy control for strict-feedback nonlinear systems. IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans, 2004, 34(3): 406-420 [29] Chen B, Liu X P, Liu K F, Shi P, Lin C. Direct adaptive fuzzy control for nonlinear systems with time-varying delays. Information Sciences, 2010, 180(5): 776-792 [30] Tong S C, Cheng N. Adaptive fuzzy observer backstepping control for a class of uncertain nonlinear systems with unknown time-delay. International Journal of Automation and Computing, 2010, 7(2): 236-246
点击查看大图
计量
- 文章访问数: 1986
- HTML全文浏览量: 65
- PDF下载量: 1450
- 被引次数: 0