Article
Full entry |
PDF
(2.1 MB)
Feedback
PDF
(2.1 MB)
Feedback
Keywords:
inverse optimality; adaptive boundary control; reaction-diffusion PDE; parameter update law; unknown coefficient
inverse optimality; adaptive boundary control; reaction-diffusion PDE; parameter update law; unknown coefficient
Summary:
We study adaptive inverse optimal boundary control for reaction-diffusion PDE system with unknown coefficient. First, an adaptive boundary control with parameter update rule is designed which no attempt is made to force parameter convergence. Next, it is proven through a non quadratic Lyapunov function that the closed-loop system is globally asymptotically stable. Further, it indicates that adaptive boundary control with parameter update law is optimal for a meaningful functional. Finally, the effectiveness of the proposed control design is demonstrated through an example.
References:
[1] 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
[2] 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
[3] Cai, X., Liao, L., Zhang, J., Zhang, W.: Observer design for a class of nonlinear system in cascade with counter-conveting transport dynamics. Kybernetika 52 (2016), 76-88. DOI
[4] Cai, X., Lin, Y., Lin, C., Liu, L.: Inverse optimality of adaptive control for Korteweg-de Vries-Burgers equation. Int. J. Dynamics Control 12 (2024), 486-493. DOI
[5] 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
[6] Cai, X., Lin, Y., Zhang, J., Lin, C.: Predictor control for wave PDE/nonlinear ODE cascaded system with boundary value-dependent propagation speed. Kybernetika 58 (2022), 400-425. DOI
[7] Cai, X., Wu, J., Zhan, X., Zhang, X.: Inverse optimal control for linearizable nonlinear systems with input delays. Kybernetika 55 (2019), 727-739. DOI
[8] Ding, K., Zhu, Q.: Intermittent static output feedback control for stochastic delayed-switched positive systems with only partially measurable information. IEEE Trans. Automat. Control 68 (2023), 8150-8157. DOI
[9] Freeman, A., Kokotovic, P. V.: Inverse optimality in robust stabilization. SIAM J. Control Optim. 34 (1996), 1365-1391. DOI
[10] Krstic, M.: On global stabilization of Burgers' equation by boundary control. Systems Control Lett. 37 (1999), 123-141. DOI
[11] Krstic, M.: Optimal adaptive control-contradiction in terms or a matter of choosing the right cost functional?. IEEE Trans. Automat. Control 53(2008), 1942-1947. DOI
[12] Krstic, M.: Control of an unstable reaction-diffusion PDE with long input delay. System Control Lett. 58 (2009), 773-782. DOI
[13] Krstic, M., Li, Z.: Inverse optimal design of input-to-state stabilizing nonlinear controllers. IEEE Tran. Automat. Control 43 (1998), 336-350. DOI
[14] Krstic, M., Smyshlyaev, A.: Adaptive boundary control for unstable parabolic PDEs-part I: Lyapunov design. IEEE Trans. Automat. Control 53 (2008), 1575-1591. DOI
[15] Lhachemi, H., Prieur, C.: Output feedback stabilization of reaction-diffusion PDEs with a non-collocated boundary condition. Systems Control Lett. 164 (2022), 105238. DOI
[16] Lu, K., Liu, Z., Yu, H., Chen, C. L. Philip, Zhang, Y.: Adaptive fuzzy inverse optimal fixed-time control of uncertain nonlinear systems. IEEE Trans. Fuzzy Systems 30 (2022), 3857-3868. DOI
[17] Prieur, C., Trelat, E.: Feedback stabilization of a 1-D linear reaction-diffusion equation with delay boundary control. IEEE Trans. Automat. Control 64 (2019), 1415-1425. DOI
[18] Smyshlyaev, A., Krstic, M.: Closed form boundary state feedbacks for a class of paratial integro-differential equations. IEEE Trans. Automat. Control 49 (2004), 2185-2202. DOI
[19] Sontag, E. D.: A 'universal' construction of Artsteins theorem on nonlinear stabilization. SIAM J. Control Optim. 13 (1989), 117-123. DOI
[20] Tang, J., Wang, J., Kang, W.: Boundary feedback stabilization of an unstable cascaded heat-heat system with different reaction coefficients. Systems Control Lett. 183 (2024), 105684. DOI
[21] Wang, J., Krstic, M.: Output feedback boundary control of a heat PDE sandwiched between two ODEs. IEEE Trans. Automat. Control 64 (2019), 4653-4660. DOI
[22] Wettlaufer, J. S.: Heat flux at the ice-ocean interface. J. Geophysical Res.: Oceans 96(1991), 7215-7236. DOI
[23] Xue, W., Kolaric, P., Fan, J., Lian, B., Chai, T., Lewis, F. L.: Inverse reinforcement learning in tracking control based on inverse optimal control. IEEE Trans. Cybernetics 52 (2022), 10570-10581. DOI
Search
Partner of
