Optimization Algorithms for Predictive Control Approach to Networked Bilinear Systems
-
Abstract: This paper is concerned with the networked predictive control of discrete-time bilinear systems. To deal with the network-induced communication delay that exists in both forward channel (controller to actuator) and feedback channel (sensor to controller), a bilinear networked predictive control scheme is proposed. Then a non-convex optimization problem of solving the predictive control sequence is presented, for which two gradually-optimized algorithms are proposed based on the special structure of bilinear system dynamics model. The numerical simulation indicates that the resulting predictive control sequence can compensate for the network-induced issues actively, which proves the effectiveness of the proposed predictive control strategy.
-
Key words:
- Bilinear systems /
- networked control systems (NCSs) /
- non-convex optimization /
- predictive control
-
-
Table 1
Algorithm 1 Stepwise iterative algorithm Step 1. Given an initial predictive control sequence $\overline{U}_0$ and a threshold $\lambda$. Step 2. Calculate $J_{\rm old}(k)$ by using $\overline{U}_0$. Step 3. Determine the communication delay $k_t$ in the feedback channel. For the forward communication delay $i=0, 1, \ldots, \overline{M}$: Step 3.1 Calculate $K_i$ according to (12); Step 3.2 Calculate $V_i$ according to (13); Step 3.3 Calculate $u^{\star}_{t+i|t-k_t}$ according to (15). Step 4. Calculate $J_{\rm new}(k)$ by using the obtained $\overline{U}^{\star}_{t+\overline{M}}$. Step 5. If $[J_{\rm old}(k)-J_{\rm new}(k)]/J_{\rm old}(k)>\lambda$, let $J_{\rm old}(k)=J_{\rm new}(k), $ $\overline{U}_0=\overline{U}^{\star}_{t+\overline{M}}$, and go to Step 3; Otherwise, stop iterating and let $\overline{U}^{\star}_{t+\overline{M}}$ as the final optimal predictive control sequence. 
下载: 导出CSV
Table 2
Algorithm 2 Approximate forward stagewise algorithm Step 1. Calculate $u^{\star}_{t|t-k_t}$ according to Remark 8 for the case of no delay in the forward channel. Step 2. For the forward communication delay $i_t=1, 2, \ldots, \overline{M}$: Step 2.1 Add $\hat{x}^T_{t+i_t+1|t-k_t}$ into state vector $\overline{X}$; Step 2.2 Add $u_{t+i_t|t-k_t}$ into input vector $\overline{U}$; Step 2.3 Extend matrixes $Q_{k_t, 0}$ and $R_{k_t, 0}$ to the corresponding dimensions; Step 2.4 Calculate $\overline{K}_{i_t}$ and $\overline{V}_{i_t}$ according to (17) and (18); Step 2.5 Obtain $\overline{U}^{\star}_{k_t, i_t}$ according to (20). Step 3. Take $\overline{U}^{\star}_{\overline{N}, \overline{M}}$ as the final predictive control sequence and send it to the actuator via the forward channel.
下载: 导出CSV
-
[1] R. A. Gupta and M. Y. Chow, "Networked control system:overview and research trends, " IEEE Trans. Ind. Electron., vol.57, no.7, pp.2527-2535, Nov.2010. https://www.researchgate.net/publication/224076713_Networked_Control_System_Overview_and_Research_Trends [2] W. P. M. H. Heemels, A. R. Teel, N. van de Wouw, and D. Nesic, "Networked control systems with communication constraints:tradeoffs between transmission intervals, delays and performance, " IEEE Trans. Autom. Control, vol.55, no. 8, pp.1781-1796, Feb.2010. https://www.researchgate.net/publication/224112751_Networked_Control_Systems_With_Communication_Constraints_Tradeoffs_Between_Transmission_Intervals_Delays_and_Performance [3] R. N. Yang, P. Shi, G. P. Liu, and H. J. Gao, "Network-based feedback control for systems with mixed delays based on quantization and dropout compensation, " Automatica, vol.47, no.12, pp.2805-2809, Dec.2011. http://www.sciencedirect.com/science/article/pii/S000510981100433X [4] M. F. Ren, J. H. Zhang, M. Jiang, and J. L. Xu, "Minimum (h, φ)-entropy control for non-Gaussian stochastic networked control systems and its application to a networked DC motor control system, " IEEE Trans. Control Syst. Technol., vol.23, no.1, pp.406-411, Jan.2015. https://www.researchgate.net/publication/280235329_Minimum_Entropy_Control_for_Non-Gaussian_Stochastic_Networked_Control_Systems_and_Its_Application_to_a_Networked_DC_Motor_Control_System [5] G. Nikolakopoulos, L. Dritsas, and S. S. Delshad, "Combined networked switching output feedback control with D-region stability for performance improvement, " Int. J. Control, vol.87, no.6, pp.1172-1180, Jun.2014. https://www.researchgate.net/publication/263495014_Combined_networked_switching_output_feedback_control_with_Inline_graphic-region_stability_for_performance_improvement [6] R. Luck and A. Ray, "Experimental verification of a delay compensation algorithm for integrated communication and control systems, " Int. J. Control., vol.59, no.6, pp.1357-1372, 1994. doi: 10.1080/00207179408923135 [7] H. J. Gao and T. W. Chen, "Network-based output tracking control, " IEEE Trans. Autom. Control, vol.53, no.3, pp.655-667, Apr.2008. https://www.researchgate.net/publication/3033073_Network-Based_Output_Tracking_Control [8] G. P. Liu, J. X. Mu, and D. Rees, "Networked predictive control of systems with random communication delay, " in Proc. UKACC Control, Bath, U. K. , 2004. [9] G. P. Liu, "Predictive controller design of networked systems with communication delays and data loss, " IEEE Trans. Circuits Syst. Ⅱ Exp. Briefs, vol.57, no.6, pp.481-485, Jun. 2010. https://www.researchgate.net/publication/224142479_Predictive_Controller_Design_of_Networked_Systems_With_Communication_Delays_and_Data_Loss [10] Y. Q. Xia, W. Xie, B. Liu, and X. Y. Wang, "Data-driven predictive control for networked control systems, " Inf. Sci., vol. 235, pp.45-54, Jun.2013. http://www.sciencedirect.com/science/article/pii/S0020025512000758 [11] Z. H. Pang, G. P. Liu, and D. H. Zhou, "Design and performance analysis of incremental networked predictive control systems, " IEEE Trans. Cyber., vol.46, no.6, pp.1400-1410, Jun. 2016. https://www.researchgate.net/publication/280116504_Design_and_Performance_Analysis_of_Incremental_Networked_Predictive_Control_Systems [12] J. H. Zhang, J. Lam, and Y. Q. Xia, "Output feedback delay compensation control for networked control systems with random delays, " Inf. Sci., vol.265, pp.154-166, May2014. http://www.sciencedirect.com/science/article/pii/S0020025513008712 [13] G. P. Liu, J. X. Mu, D. Rees, and S. C. Chai, "Design and stability analysis of networked control systems with random communication time delay using the modified MPC, " Int. J. Control, vol. 79, no. 4, pp. 288-297, 2006. doi: 10.1080/00207170500533288 [14] J. X. Mu, G. P. Liu, and D. Rees, "Design of robust networked predictive control systems, " in Proc. 2005 American Control Conf. , Portland, OR, USA, vol. 1, pp. 638-643, 2005. https://www.researchgate.net/publication/4151220_Design_of_robust_networked_predictive_control_systems?ev=sim_pub [15] R. R. Mohler, Bilinear Control Processes:with Applications to Engineering, Ecology and Medicine, Orlando:Academic Press, 1973. [16] G. Marchesini and S. K. Mitter, Mathematical Systems Theory, Berlin Heidelberg:Springer, 1976. [17] Y. B. Zhao, G. P. Liu, and D. Rees, "A predictive control-based approach to networked Hammerstein systems:design and stability analysis, " IEEE Trans. Syst. Man Cybern. B, Cybern., vol.38, no.3, pp.700-708, Jun.2008. https://www.ncbi.nlm.nih.gov/pubmed/18558535/# [18] Y. B. Zhao, G. P. Liu, and D. Rees, "A predictive control based approach to networked wiener systems, " Int. J. Innov. Comput. Inf. Control., vol.4, no.11, pp.2793-2802, Nov. 2008. https://www.researchgate.net/publication/264840709_A_predictive_control_based_approach_to_networked_wiener_systems [19] H. Ouyang, G. P. Liu, D. Rees, and W. Hu, "Predictive control of networked non-linear control systems, " Proc. Inst. Mech. Eng. J. Syst. Control Eng., vol.221, no.3, pp.453-463, May2007. https://www.researchgate.net/publication/245389365_Predictive_control_of_networked_non-linear_control_systems [20] G. Pin and T. Parisini, "Networked predictive control of uncertain constrained nonlinear systems:recursive feasibility and input-to-state stability analysis, " IEEE Trans. Autom. Control, vol.56, no.1, pp.72-87, Jan.2011. https://www.researchgate.net/publication/220387079_Networked_Predictive_Control_of_Uncertain_Constrained_Nonlinear_Systems_Recursive_Feasibility_and_Input-to-State_Stability_Analysis [21] G. P. Liu, "Design and analysis of networked non-linear predictive control systems, " IET Control Theory Appl., vol.9, no.11, pp.1740-1745, Jul.2015. [22] P. E. Gill and E. Wong, "Sequential quadratic programming methods", in Mixed Integer Nonlinear Programming, J. Lee and S. Leyffer, Eds. , New York, USA, Springer, 2012. [23] M. Hotz and C. Vogel, "Linearization of time-varying nonlinear systems using a modified linear iterative method, " IEEE Trans. Signal Process., vol.62, no.10, pp.2566-2579, May 2014. http://www.oalib.com/paper/4081839 [24] A. Bidram, F. L. Lewis, and A. Davoudi, "Synchronization of nonlinear heterogeneous cooperative systems using input-output feedback linearization, " Automatica., vol.50, no.10, pp.2578-2585, Oct.2014. http://dl.acm.org/citation.cfm?id=2941006.2941225 [25] Z. L. Mu, F. Liu, and Z. L. Qiu, "Analysis of stabilizing control of discrete bilinear system, " Control Theory Appl., vol.17, no.2, pp.267-269, Apr.2000. http://en.cnki.com.cn/Article_en/CJFDTOTAL-KZLY200002025.htm -
图(3) / 表(2)
计量
- 文章访问数: 2217
- HTML全文浏览量: 199
- PDF下载量: 632
- 被引次数: 0
