Sampled-data Networked Control Systems: A Lyapunov-Krasovskii Approach

The main goal of this thesis is to develop computationally efficient methods for stability analysis and controller synthesis of sampled-data networked control systems. In sampled-data networked control systems, the sensory information and feedback signals are exchanged among different components of the system (sensors, actuators, and controllers) through a communication network. Stabilization of sampled-data networked control systems is a challenging problem since the introduction of multirate sample and holds, time-delays, and packet losses into the system degrades its performance and can lead to instability. A diverse range of systems with linear, piecewise affine (PWA), and nonlinear vector fields are studied in this thesis. PWA systems are a class of state-based switched systems with affine vector field in each mode. Stabilization of PWA networked control systems are even more challenging since they simultaneously involve switches due to the hybrid vector fields (state-based switching) and switches due to the sample and hold devices in the network (event-based switching). The objectives of this thesis are: (a) to design controllers that guarantee exponential stability of the system for a desired sampling period; (b) to design observers that guarantee exponential convergence of the estimation error to the origin for a desired sampling period; and (c) given a controller, to find the maximum allowable network-induced delay that guarantees exponential stability of the sampled-data networked control system. Lyapunov-Krasovskii based approaches are used to propose sufficient stability and stabilization conditions for sampled-data networked control systems. Convex relaxation techniques are employed to cast the proposed stability analysis and controller synthesis criteria in terms of linear matrix inequalities that can be solved efficiently

On exponential stability of linear networked control systems

This paper addresses exponential stability of linear networked control systems. More specifically, the paper considers a continuous-time linear plant in feedback with a linear sampled-data controller with an unknown time varying sampling rate, the possibility of data packet dropout, and an uncertain time varying delay. The main contribution of this paper is the derivation of new sufficient stability conditions for linear networked control systems taking into account all of these factors. The stability conditions are based on a modified Lyapunov–Krasovskii functional. The stability results are also applied to the case where limited information on the delay bounds is available. The case of linear sampled-data systems is studied as a corollary of the networked control case. Furthermore, the paper also formulates the problem of finding a lower bound on the maximum network-induced delay that preserves exponential stability as a convex optimization program in terms of linear matrix inequalities. This problem can be solved efficiently from both practical and theoretical points of view. Finally, as a comparison, we show that the stability conditions proposed in this paper compare favorably with the ones available in the open literature for different benchmark problems

Optimal Control for Aperiodic Dual-Rate Systems With Time-Varying Delays

[EN] In this work, we consider a dual-rate scenario with slow input and fast output. Our objective is the maximization of the decay rate of the system through the suitable choice of the n-input signals between two measures (periodic sampling) and their times of application. The optimization algorithm is extended for time-varying delays in order to make possible its implementation in networked control systems. We provide experimental results in an air levitation system to verify the validity of the algorithm in a real plant.This work was supported in part by the Spanish Ministry of Economy and Competitiveness (MINECO) under the Projects DPI2012-31303 and DPI2014-55932-C2-2-R.Aranda-Escolástico, E.; Salt Llobregat, JJ.; Guinaldo, M.; Chacon, J.; Dormido, S. (2018). Optimal Control for Aperiodic Dual-Rate Systems With Time-Varying Delays. Sensors. 18(5):1-19. https://doi.org/10.3390/s18051491S119185Mansano, R., Godoy, E., & Porto, A. (2014). The Benefits of Soft Sensor and Multi-Rate Control for the Implementation of Wireless Networked Control Systems. Sensors, 14(12), 24441-24461. doi:10.3390/s141224441Shao, Q. M., & Cinar, A. (2015). System identification and distributed control for multi-rate sampled systems. Journal of Process Control, 34, 1-12. doi:10.1016/j.jprocont.2015.06.010Albertos, P., & Salt, J. (2011). Non-uniform sampled-data control of MIMO systems. Annual Reviews in Control, 35(1), 65-76. doi:10.1016/j.arcontrol.2011.03.004Cuenca, A., & Salt, J. (2012). RST controller design for a non-uniform multi-rate control system. Journal of Process Control, 22(10), 1865-1877. doi:10.1016/j.jprocont.2012.09.010Cuenca, Á., Ojha, U., Salt, J., & Chow, M.-Y. (2015). A non-uniform multi-rate control strategy for a Markov chain-driven Networked Control System. Information Sciences, 321, 31-47. doi:10.1016/j.ins.2015.05.035Kalman, R. E., & Bertram, J. E. (1959). 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IEEE Transactions on Control Systems Technology, 13(6), 988-997. doi:10.1109/tcst.2005.857410Nemani, M., Tsao, T.-C., & Hutchinson, S. (1994). Multi-Rate Analysis and Design of Visual Feedback Digital Servo-Control System. Journal of Dynamic Systems, Measurement, and Control, 116(1), 45-55. doi:10.1115/1.2900680Sim, T. P., Lim, K. B., & Hong, G. S. (2002). Multirate predictor control scheme for visual servo control. IEE Proceedings - Control Theory and Applications, 149(2), 117-124. doi:10.1049/ip-cta:20020238Xinghui Huang, Nagamune, R., & Horowitz, R. (2006). A comparison of multirate robust track-following control synthesis techniques for dual-stage and multisensing servo systems in hard disk drives. IEEE Transactions on Magnetics, 42(7), 1896-1904. doi:10.1109/tmag.2006.875353Wu, Y., Liu, Y., & Zhang, W. (2013). A Discrete-Time Chattering Free Sliding Mode Control with Multirate Sampling Method for Flight Simulator. Mathematical Problems in Engineering, 2013, 1-8. doi:10.1155/2013/865493Salt, J., & Tomizuka, M. (2014). Hard disk drive control by model based dual-rate controller. Computation saving by interlacing. Mechatronics, 24(6), 691-700. doi:10.1016/j.mechatronics.2013.12.003Salt, J., Casanova, V., Cuenca, A., & Pizá, R. (2013). Multirate control with incomplete information over Profibus-DP network. International Journal of Systems Science, 45(7), 1589-1605. doi:10.1080/00207721.2013.844286Liu, F., Gao, H., Qiu, J., Yin, S., Fan, J., & Chai, T. (2014). Networked Multirate Output Feedback Control for Setpoints Compensation and Its Application to Rougher Flotation Process. IEEE Transactions on Industrial Electronics, 61(1), 460-468. doi:10.1109/tie.2013.2240640Khargonekar, P. P., & Sivashankar, N. (1991). 2 optimal control for sampled-data systems. Systems & Control Letters, 17(6), 425-436. doi:10.1016/0167-6911(91)90082-pTornero, J., Albertos, P., & Salt, J. (2001). Periodic Optimal Control of Multirate Sampled Data Systems. IFAC Proceedings Volumes, 34(12), 195-200. doi:10.1016/s1474-6670(17)34084-3Kim, C. H., Park, H. J., Lee, J., Lee, H. W., & Lee, K. D. (2015). Multi-rate optimal controller design for electromagnetic suspension systems via linear matrix inequality optimization. Journal of Applied Physics, 117(17), 17B506. doi:10.1063/1.4906588LEE, J. H., GELORMINO, M. S., & MORARIH, M. (1992). Model predictive control of multi-rate sampled-data systems: a state-space approach. International Journal of Control, 55(1), 153-191. doi:10.1080/00207179208934231Mizumoto, I., Ikejiri, M., & Takagi, T. (2015). Stable Adaptive Predictive Control System Design via Adaptive Output Predictor for Multi-rate Sampled Systems∗∗This work was partially supported by KAKENHI, the Grant-in-Aid for Scientific Research (C) 25420444, from the Japan Society for the Promotion of Science (JSPS). IFAC-PapersOnLine, 48(8), 1039-1044. doi:10.1016/j.ifacol.2015.09.105Carpiuc, S., & Lazar, C. (2016). Real-Time Multi-Rate Predictive Cascade Speed Control of Synchronous Machines in Automotive Electrical Traction Drives. IEEE Transactions on Industrial Electronics, 1-1. doi:10.1109/tie.2016.2561881Roshany-Yamchi, S., Cychowski, M., Negenborn, R. R., De Schutter, B., Delaney, K., & Connell, J. (2013). Kalman Filter-Based Distributed Predictive Control of Large-Scale Multi-Rate Systems: Application to Power Networks. IEEE Transactions on Control Systems Technology, 21(1), 27-39. doi:10.1109/tcst.2011.2172444Donkers, M. C. F., Tabuada, P., & Heemels, W. P. M. H. (2012). Minimum attention control for linear systems. Discrete Event Dynamic Systems, 24(2), 199-218. doi:10.1007/s10626-012-0155-xQuevedo, D. E., Ma, W.-J., & Gupta, V. (2015). Anytime Control Using Input Sequences With Markovian Processor Availability. 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A non-uniform predictor-observer for a networked control system

The final publication is available at Springer via http://dx.doi.org/10.1007/s12555-011-0621-5This paper presents a Non-Uniform Predictor-Observer (NUPO) based control approach in order to deal with two of the main problems related to Networked Control Systems (NCS) or Sensor Networks (SN): time-varying delays and packet loss. In addition, if these delays are longer than the sampling period, the packet disordering phenomenon can appear. Due to these issues, a (scarce) nonuniform, delayed measurement signal could be received by the controller. But including the NUPO proposal in the control system, the delay will be compensated by the prediction stage, and the nonavailable data will be reconstructed by the observer stage. So, a delay-free, uniformly sampled controller design can be adopted. To ensure stability, the predictor must satisfy a feasibility problem based on a time-varying delay-dependent condition expressed in terms of Linear Matrix Inequalities (LMI). Some aspects like the relation between network delay and robustness/performance trade-off are empirically studied. A simulation example shows the benefits (robustness and control performance improvement) of the NUPO approach by comparison to another similar proposal. © ICROS, KIEE and Springer 2011.This work was supported by the Spanish Ministerio de Ciencia y Tecnologia Projects DPI2008-06737-C02-01 and DPI2009-14744-C03-03, by Generalitat Valenciana Project GV/2010/018, by Universidad Politecnica de Valencia Project PAID06-08.Cuenca Lacruz, ÁM.; García Gil, PJ.; Albertos Pérez, P.; Salt Llobregat, JJ. (2011). A non-uniform predictor-observer for a networked control system. International Journal of Control, Automation and Systems. 9(6):1194-1202. doi:10.1007/s12555-011-0621-5S1194120296K. Ogata, Discrete-time Control Systems, Prentice-Hall, Inc., Upper Saddle River, NJ, USA, 1987.Y. Tipsuwan and M. Chow, “Control methodologies in networked control systems,” Control Eng. 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Spatiotemporal Fuzzy-Observer-based Feedback Control for Networked Parabolic PDE Systems

Assisted by the Takagi-Sugeno (T-S) fuzzy model- based nonlinear control technique, nonlinear spatiotemporal feedback compensators are proposed in this article for exponential stabilization of parabolic partial differential dynamic systems with measurement outputs transmitted over a communication network. More specifically, an approximate T-S fuzzy partial differential equation (PDE) model with C∞-smooth membership functions is constructed to describe the complex spatiotemporal dynamics of the nonlinear partial differential systems, and its approximation capability is analyzed via the uniform approximation theorem on a real separable Hilbert space. A spatiotemporally asynchronous sampled-data measurement output equation is proposed to model the transmission process of networked measurement outputs. By the approximate T-S fuzzy PDE model, fuzzy-observer-based nonlinear continuous-time and sampled- data feedback compensators are constructed via the spatiotemporally asynchronous sampled-data measurement outputs. Given that sufficient conditions presented in terms of linear matrix inequalities are satisfied, the suggested fuzzy compensators can exponentially stabilize the nonlinear system in the Lyapunov sense. Simulation results are presented to show the effectiveness and merit of the suggested spatiotemporal fuzzy compensators

Optimization approaches for controller and schedule codesign in networked control

We consider the offline optimization of a sequence for communication scheduling in networked control systems. Given a continuous-time Linear Quadratic Regulator (LQR) problem we design a sampled-data periodic controller based on the continuous time LQR controller that takes into account the limited communication medium and inter-sampling behavior. To allow for a Riccati equation approach, singularities in the weighting matrices and time-variance are accounted for using a lifting approach. Optimal scheduling can be obtained by solving a complex combinatorial optimization problem. Two stochastic algorithms will be proposed to find a (sub)optimal sequence and the associated optimal controller which is the result of a discrete algebraic Riccati equation for the given optimal sequence

Multirate control with incomplete information over Profibus-DP network

This is an Accepted Manuscript of an article published by Taylor & Francis in International Journal of Systems Science on 2014, available online:http://www.tandfonline.com/10.1080/00207721.2013.844286When a process ¿eld bus-decentralized peripherals (Pro¿bus-DP) network is used in an industrial environment, a deterministic behaviour is usually claimed. However, due to some concerns such as bandwidth limitations, lack of synchronisation among different clocks and existence of time-varying delays, a more complex problem must be faced. This problem implies the transmission of irregular and, even, random sequences of incomplete information. The main consequence of this issue is the appearance of different sampling periods at different network devices. In this paper, this aspect is checked by means of a detailed Pro¿bus-DP timescale study. In addition, in order to deal with the different periods, a delay-dependent dual-rate proportional-integral-derivative control is introduced. Stability for the proposed control system is analysed in terms of linear matrix inequalitiesThe authors are grateful to the financial support of the Spanish Ministry of Economy and Competitivity [Research Grant TEC2012-31506].Salt Llobregat, JJ.; Casanova Calvo, V.; Cuenca Lacruz, ÁM.; Pizá Fernández, R. (2014). Multirate control with incomplete information over Profibus-DP network. International Journal of Systems Science. 45(7):1589-1605. https://doi.org/10.1080/00207721.2013.844286S15891605457Alves, M., & Tovar, E. (2007). Real-time communications over wired/wireless PROFIBUS networks supporting inter-cell mobility. Computer Networks, 51(11), 2994-3012. doi:10.1016/j.comnet.2007.01.001Boyd, S., El Ghaoui, L., Feron, E., & Balakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory. doi:10.1137/1.9781611970777Bucher, R., & Balemi, S. (2006). Rapid controller prototyping with Matlab/Simulink and Linux. 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IEEE Transactions on Circuits and Systems I: Regular Papers, 53(10), 2306-2317. doi:10.1109/tcsi.2006.882824Moayedi, M., Foo, Y. K., & Soh, Y. C. (2011). Filtering for networked control systems with single/multiple measurement packets subject to multiple-step measurement delays and multiple packet dropouts. International Journal of Systems Science, 42(3), 335-348. doi:10.1080/00207720903513335Peñarrocha, I., Sanchis, R., & Romero, J. A. (2012). State estimator for multisensor systems with irregular sampling and time-varying delays. International Journal of Systems Science, 43(8), 1441-1453. doi:10.1080/00207721.2011.625482Piza, R., Salt, J., Sala, A., & Cuenca, A. (2014). Hierarchical Triple-Maglev Dual-Rate Control Over a Profibus-DP Network. IEEE Transactions on Control Systems Technology, 22(1), 1-12. doi:10.1109/tcst.2012.2222883Ray, A. (1989). Introduction to networking for integrated control systems. 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Decentralized event-triggered control of large-scale systems with saturated actuators

We consider a large-scale LTI system with multiple local communication networks connecting sensors, controllers, and actuators. The local networks operate asynchronously and independently of one another. The main novelty is that the decentralized controllers are subject to saturation. Our objective is to achieve a regional exponential stability providing a decentralized bound on the domain of attraction for each plant. We introduce a sampled-data event-Triggering mechanism from sensors to controllers to reduce the amount of transmitted signals. Using the time-delay approach to networked control systems and appropriate Lyapunov-Krasovskii functionals, we derive linear matrix inequalities that allow to find the decentralized bounds on the domains of attraction for each plant. Numerical example of coupled cart-pendulums illustrates the efficiency of the method

Linear matrix inequalities in multirate control over networks

This paper faces two of the main drawbacks in networked control systems: bandwidth constraints and timevarying delays. The bandwidth limitations are solved by using multirate control techniques. The resultant multirate controller must ensure closed-loop stability in the presence of time-varying delays. Some stability conditions and a state feedback controller design are formulated in terms of linear matrix inequalities. The theoretical proposal is validated in two different experimental environments: a crane-based test-bed over Ethernet, and a maglev based platform over Profibus. © 2012 Ángel Cuenca et al.The authors A. Cuenca, R. Piza, and J. Salt are grateful to the Spanish Ministry of Education research Grants DPI2011-28507-C02-01 and DPI2009-14744-C03-03, and Generalitat Valenciana Grant GV/2010/018. A. 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Time-and event-driven communication process for networked control systems: A survey

Copyright © 2014 Lei Zou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.In recent years, theoretical and practical research topics on networked control systems (NCSs) have gained an increasing interest from many researchers in a variety of disciplines owing to the extensive applications of NCSs in practice. In particular, an urgent need has arisen to understand the effects of communication processes on system performances. Sampling and protocol are two fundamental aspects of a communication process which have attracted a great deal of research attention. Most research focus has been on the analysis and control of dynamical behaviors under certain sampling procedures and communication protocols. In this paper, we aim to survey some recent advances on the analysis and synthesis issues of NCSs with different sampling procedures (time-and event-driven sampling) and protocols (static and dynamic protocols). First, these sampling procedures and protocols are introduced in detail according to their engineering backgrounds as well as dynamic natures. Then, the developments of the stabilization, control, and filtering problems are systematically reviewed and discussed in great detail. Finally, we conclude the paper by outlining future research challenges for analysis and synthesis problems of NCSs with different communication processes.This work was supported in part by the National Natural Science Foundation of China under Grants 61329301, 61374127, and 61374010, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany