Inverse optimal control for linearizable nonlinear systems with input delays

Cai, Xiushan ; Wu, Jie ; Zhan, Xisheng ; Zhang, Xianhe

Kybernetika, Tome 55 (2019) no. 4, pp. 727-739

Abstract (VO)

We consider inverse optimal control for linearizable nonlinear systems with input delays based on predictor control. Under a continuously reversible change of variable, a nonlinear system is transferred to a linear system. A predictor control law is designed such that the closed-loop system is asymptotically stable. We show that the basic predictor control is inverse optimal with respect to a differential game. A mechanical system is provided to illustrate the effectiveness of the proposed method.

Détail

DOI : 10.14736/kyb-2019-4-0727

Classification : 93Cxx, 93Dxx
Keywords: nonlinear systems; inverse optimality; predictor control; input delays

Bibliographie

[1] Bekiaris-Liberis, N., Krstic, M.: Compensation of time-varying input and state delays for nonlinear systems. J. Dynamic Systems, Measurement Control 134 (2012), 1-14. | DOI | MR

[2] Bekiaris-Liberis, N., Krstic, M.: Robustness of nonlinear predictor feedback laws to time-and state-dependent delay perturbations. Automatica 49 (2013), 1576-1590. | DOI | MR

[3] Bekiaris-Liberis, N., Krstic, M.: Compensation of wave actuator dynamics for nonlinear systems. IEEE Trans. Automat. Control 59 (2014), 1555-1570. | DOI | MR

[4] Bullo, F., Lewis, A.: Reduction, linearization, and stability of relative equilibria for mechanical systems on riemannian manifolds. Acta Applicandae Mathematicae 99 (2007), 53-95. | DOI | MR

[5] Cai, X., Bekiaris-Liberis, N., Krstic, M.: Input-to-state stability and inverse optimality of linear time-varying-delay predictor feedbacks. IEEE Trans. Automat. Control 63 (2018), 233-240. | DOI | MR

[6] Cai, X., Bekiaris-Liberis, N., Krstic, M.: Input-to-state stability and inverse optimality of predictor feedback for multi-input linear systems. Automatica 103 (2019), 549-557. | DOI | MR

[7] Cai, X., Krstic, M.: Nonlinear control under wave actuator dynamics with time- and state-dependent moving boundary. Int. J. Robust. Nonlinear Control 25 (2015), 222-253. | DOI | MR | Zbl

[8] Cai, X., Krstic, M.: Nonlinear stabilization through wave PDE dynamics with a moving uncontrolled boundary. Automatica 68 (2016), 27-38. | DOI | MR

[9] Cai, X., Liao, L., Zhang, J., Zhang, W.: Oberver design for a class of nonlinear system in cascade with counter-convecting transport dynamics. Kybernetika 52 (2016), 76-88. | DOI | MR

[10] Cai, X., Lin, Y., Liu, L.: Universal stabilisation design for a class of non-linear systems with time-varying input delays. IET Control Theory Appl. 9 (2015), 1481-1490. | DOI | MR

[11] Cai, X., Lin, C., Liu, L., Zhan, X.: Inverse optimal control for strict-feedforward nonlinear systems with input delays. Int. J. Robust. Nonlinear Control 28 (2018), 2976-2995. | DOI | MR

[12] Jankovic, M.: Control Lyapunov Razumikhin functions and robust stabilization of time delay systems. IEEE Trans. Automat. Control 46 (2001), 1048-1060. | DOI | MR

[13] Jankovic, M.: Control of nonlinear systems with time delay. In: Proc. 42nd IEEE conference on Decision and Control, Maui 2003, pp. 4545-4550. | DOI

[14] Karafyllis, I., Krstic, M.: Predictor Feedback for Delay Systems: Implementations and Approximations. Springer, 2016. | DOI | MR

[15] Krstic, M.: Feedback linearizability and explicit integrator forwarding controllers for classes of feedforward systems. IEEE Trans. Automat. Control 49 (2004), 1668-1681. | DOI | MR

[16] Krstic, M.: Integrator forwarding control laws for some classes of linearizable feedforward systems. In: Proc. American Control Conference, Boston, Massachusetts 2004, 4360-4365. | DOI

[17] Krstic, M.: Lyapunov tools for predictor feedbacks for delay systems: Inverse optimality and robustness to delay mismatch. Automatica 44 (2008), 2930-2935. | DOI | MR

[18] Krstic, M.: Input delay compensation for forward complete and feed forward nonlinear systems. IEEE Trans. Automat. Control 55 (2010), 287-303. | DOI | MR

[19] Krstic, M., Li, Z.: Inverse optimal design of input-to-state stabilizing nonlinear controllers. IEEE Trans. Automat. Control 43 (1998), 336-350. | DOI | MR

[20] Respondek, W., Ricardo, S.: On linearization of mechanical control systems. In: Proc. 4th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Bertinoro 2012. | DOI

[21] Tall, I.: Linearizable feedforward systems: A special class. In: Proc. IEEE Multi-conference on Systems and Control, Texas 2008. | DOI | MR

[22] Schaft, A. van der: Linearization of Hamiltonian and gradient systems. IMA J. Math. Control Inform. 1 (1994), 185-198. | DOI

[23] Zhan, X., Cheng, L., Wu, J., Yang, Q.: Optimal modified performance of MIMO networked control systems with multi-parameter constraints. ISA Trans. 84 (2019), 111-117. | DOI

[24] Zhan, X., Z.Guan, Zhang, X., Yuan, F.: Optimal tracking performance and design of networked control systems with packet dropout. J. the Franklin Inst. 350 (2013), 3205-3216. | DOI | MR

[25] Zhan, X., Wu, J., Jiang, T., Jiang, X.: Optimal performance of networked control systems under the packet dropouts and channel noise. ISA Trans. 58 (2015), 214-221. | DOI

[26] Zhang, Z., Xu, S., Zhang, B.: Asymptotic tracking control of uncertain nonlinear systems with unknown actuator nonlinearity. IEEE Trans. Automatic Control 59 (2014), 1336-1341. | DOI | MR

[27] Zhang, Z., Xu, S., Zhang, B.: Exact tracking control of nonlinear systems with time delays and dead-zone input. Automatica 52 (2015), 272-276. | DOI | MR