H_∞ Static Output-Feedback Gain-Scheduled Control for Discrete LPV Time-Delay Systems^⁎

This paper proposes new synthesis conditions to design H∞ static output-feedback controllers for discrete-time linear systems affected by time-varying parameters and time-varying delays. The design conditions are provided in terms of sufficient parameter-dependent linear matrix inequalities with a scalar parameter, being capable of synthesizing either robust or gain-scheduled controllers. The main motivations to deal with such problem are that many real-world plants can be modeled in terms of discrete-time linear parameter-varying (LPV) time-delay models and the lack of methods to deal with such systems considering an output-feedback based approach. The technique presented in this paper is quite generalist, allowing an arbitrary structure for the measured output matrix. Numerical examples are provided to illustrate the effectiveness of the synthesis conditions, tractable in terms of LMI relaxations, for robust or gain-scheduled H∞ output-feedback for LPV time-delayed systems

Frequency-domain controller design by linear programming

In this thesis, a new framework to design controllers in the frequency domain is proposed. The method is based on the shaping of the open-loop transfer function in the Nyquist diagram. A line representing a lower approximation for the crossover frequency and a line representing a new linear robustness margin guaranteeing lower bounds for the classical robustness margins are defined and used as constraints. A linear programming approach is proposed to tune fixed-order linearly parameterized controllers for stable single-input single-output linear time-invariant plants. Two optimization problems are proposed and solved by linear programming. In the first one, the new robustness margin is maximized given a lower approximation of the crossover frequency, whereas in the second one, the closed-loop performance in terms of load disturbance rejection, output disturbance rejection and tracking is maximized subject to constraints on the new robustness margin. The method can directly consider multi-model systems. Moreover, this new framework can be used directly with frequency-domain data. Thus, it can also consider systems with frequency-domain uncertainties. Using the same framework, an extension of the method is proposed to tune fixed-order linearly parameterized gain-scheduled controllers for stable single-input single-output linear parameter varying plants. This method directly computes a linear parameter varying controller from a linear parameter varying model or from a set of frequency-domain data in different operating points and no interpolation is needed. In terms of closed-loop performance, this approach leads to extremely good results. However, the global stability cannot be guaranteed for fast parameter variations and should be analyzed a posteriori. Nevertheless, for certain classes of switched systems and linear parameter varying systems, it is also possible to guarantee the stability within the design framework. This can be accomplished by adding constraints based on the phase difference of the characteristic polynomials of the closed-loop systems. This frequency-domain methodology has been tested on numerous simulation examples and implemented experimentally on a high-precision double-axis positioning system. The results show the effectiveness and simplicity of the proposed methodologies

A non-uniform multi-rate control strategy for a Markov chain-driven Networked Control System

[EN] In this work, a non-uniform multi-rate control strategy is applied to a kind of Networked Control System (NCS) where a wireless path tracking control for an Unmanned Ground Vehicle (UGV) is carried out. The main aims of the proposed strategy are to face time-varying network-induced delays and to avoid packet disorder. A Markov chain-driven NCS scenario will be considered, where different network load situations, and consequently, different probability density functions for the network delay are assumed. In order to assure mean-square stability for the considered NCS, a decay-rate based sufficient condition is enunciated in terms of probabilistic Linear Matrix Inequalities (LMIs). Simulation results show better control performance, and more accurate path tracking, for the scheduled (delay-dependent) controller than for the non-scheduled one (i.e. the nominal controller when delays appear). Finally, the control strategy is validated on an experimental test-bed.This work was supported in part by Grants TEC2012-31506 from the Spanish Ministry of Education, DPI2011-28507-C02-01 by the Spanish Ministry of Economy, and PAID-00-12 from Technical University of Valencia (Spain). In addition, this research work has been developed as a result of a mobility stay funded by the Erasmus Mundus Programme of the European Commission under the Transatlantic Partnership for Excellence in Engineering (TEE Project).Cuenca Lacruz, ÁM.; Ojha, U.; Salt Llobregat, JJ.; Chow, M. (2015). A non-uniform multi-rate control strategy for a Markov chain-driven Networked Control System. Information Sciences. 321:31-47. https://doi.org/10.1016/J.INS.2015.05.035S314732

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. Sala is grateful to the financial support of Spanish Ministry of Economy research Grant DPI2011-27845-C02-01, and Generalitat Valenciana Grant PROMETEO/2008/088.Cuenca Lacruz, ÁM.; Pizá, R.; Salt Llobregat, JJ.; Sala Piqueras, A. (2012). Linear matrix inequalities in multirate control over networks. Mathematical Problems in Engineering. 2012(768212):1-22. doi:10.1155/2012/768212S1222012768212Tipsuwan, Y., & Chow, M.-Y. (2003). Control methodologies in networked control systems. Control Engineering Practice, 11(10), 1099-1111. doi:10.1016/s0967-0661(03)00036-4Halevi, Y., & Ray, A. (1988). Integrated Communication and Control Systems: Part I—Analysis. Journal of Dynamic Systems, Measurement, and Control, 110(4), 367-373. doi:10.1115/1.3152698Yang, T. C. (2006). Networked control system: a brief survey. IEE Proceedings - Control Theory and Applications, 153(4), 403-412. doi:10.1049/ip-cta:20050178Cuenca, Á., Salt, J., Sala, A., & Piza, R. (2011). A Delay-Dependent Dual-Rate PID Controller Over an Ethernet Network. IEEE Transactions on Industrial Informatics, 7(1), 18-29. doi:10.1109/tii.2010.2085007Tipsuwan, Y., & Chow, M.-Y. (2004). On the Gain Scheduling for Networked PI Controller Over IP Network. IEEE/ASME Transactions on Mechatronics, 9(3), 491-498. doi:10.1109/tmech.2004.834645Hu, J., Wang, Z., Gao, H., & Stergioulas, L. K. (2012). Robust Sliding Mode Control for Discrete Stochastic Systems With Mixed Time Delays, Randomly Occurring Uncertainties, and Randomly Occurring Nonlinearities. IEEE Transactions on Industrial Electronics, 59(7), 3008-3015. doi:10.1109/tie.2011.2168791Wing Shing Wong, & Brockett, R. W. (1999). Systems with finite communication bandwidth constraints. II. Stabilization with limited information feedback. IEEE Transactions on Automatic Control, 44(5), 1049-1053. doi:10.1109/9.763226Casanova, V., Salt, J., Cuenca, A., & Piza, R. (2009). Networked Control Systems: control structures with bandwidth limitations. International Journal of Systems, Control and Communications, 1(3), 267. doi:10.1504/ijscc.2009.024556Cuenca, A., García, P., Albertos, P., & Salt, J. (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/s12555-011-0621-5Tian, Y.-C., & Levy, D. (2008). Compensation for control packet dropout in networked control systems. Information Sciences, 178(5), 1263-1278. doi:10.1016/j.ins.2007.10.012Wang, Z., Shen, B., Shu, H., & Wei, G. (2012). Quantized $H_{\infty }$ Control for Nonlinear Stochastic Time-Delay Systems With Missing Measurements. IEEE Transactions on Automatic Control, 57(6), 1431-1444. doi:10.1109/tac.2011.2176362Wang, Z., Shen, B., & Liu, X. (2012). H∞ filtering with randomly occurring sensor saturations and missing measurements. Automatica, 48(3), 556-562. doi:10.1016/j.automatica.2012.01.008Ma, L., Wang, Z., Bo, Y., & Guo, Z. (2011). Finite-horizonℋ2/ℋ∞control for a class of nonlinear Markovian jump systems with probabilistic sensor failures. International Journal of Control, 84(11), 1847-1857. doi:10.1080/00207179.2011.627379Li, J.-N., Cai, M., Wang, Y.-L., & Zhang, Q.-L. (2009). H∞ control of networked control systems with packet disordering. IET Control Theory & Applications, 3(11), 1463-1475. doi:10.1049/iet-cta.2008.0416Time synchronization in a local area network. (2004). IEEE Control Systems, 24(2), 61-69. doi:10.1109/mcs.2004.1275432Sala, A., Cuenca, Á., & Salt, J. (2009). A retunable PID multi-rate controller for a networked control system. Information Sciences, 179(14), 2390-2402. doi:10.1016/j.ins.2009.02.017Sala, A. (2005). Computer control under time-varying sampling period: An LMI gridding approach. Automatica, 41(12), 2077-2082. doi:10.1016/j.automatica.2005.05.017Salt, J., & Albertos, P. (2005). Model-based multirate controllers design. IEEE Transactions on Control Systems Technology, 13(6), 988-997. doi:10.1109/tcst.2005.857410Cuenca, Á., Salt, J., & Albertos, P. (2006). Implementation of algebraic controllers for non-conventional sampled-data systems. Real-Time Systems, 35(1), 59-89. doi:10.1007/s11241-006-9001-2Lall, S., & Dullerud, G. (2001). An LMI solution to the robust synthesis problem for multi-rate sampled-data systems. Automatica, 37(12), 1909-1922. doi:10.1016/s0005-1098(01)00167-4Shi, Y., Fang, H., & Yan, M. (2009). Kalman filter-based adaptive control for networked systems with unknown parameters and randomly missing outputs. International Journal of Robust and Nonlinear Control, 19(18), 1976-1992. doi:10.1002/rnc.1390Li, D., Shah, S. L., & Chen, T. (2002). Analysis of dual-rate inferential control systems. Automatica, 38(6), 1053-1059. doi:10.1016/s0005-1098(01)00295-3Boyd, S., El Ghaoui, L., Feron, E., & Balakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory. doi:10.1137/1.9781611970777Yun-Bo Zhao, Guo-Ping Liu, & Rees, D. (2009). Modeling and Stabilization of Continuous-Time Packet-Based Networked Control Systems. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 39(6), 1646-1652. doi:10.1109/tsmcb.2009.2027714Salt, J., Casanova, V., Cuenca, A., & Pizá, R. (2008). Sistemas de Control Basados en Red Modelado y Diseño de Estructuras de Control. Revista Iberoamericana de Automática e Informática Industrial RIAI, 5(3), 5-20. doi:10.1016/s1697-7912(08)70157-2Yang Shi, & Bo Yu. (2009). Output Feedback Stabilization of Networked Control Systems With Random Delays Modeled by Markov Chains. IEEE Transactions on Automatic Control, 54(7), 1668-1674. doi:10.1109/tac.2009.2020638Shi, Y., & Yu, B. (2011). Robust mixed H2/H∞ control of networked control systems with random time delays in both forward and backward communication links. Automatica, 47(4), 754-760. doi:10.1016/j.automatica.2011.01.022Van Loan, C. (1978). Computing integrals involving the matrix exponential. IEEE Transactions on Automatic Control, 23(3), 395-404. doi:10.1109/tac.1978.1101743Khargonekar, P., Poolla, K., & Tannenbaum, A. (1985). Robust control of linear time-invariant plants using periodic compensation. IEEE Transactions on Automatic Control, 30(11), 1088-1096. doi:10.1109/tac.1985.1103841Marti, P., Yepez, J., Velasco, M., Villa, R., & Fuertes, J. M. (2004). Managing Quality-of-Control in Network-Based Control Systems by Controller and Message Scheduling Co-Design. IEEE Transactions on Industrial Electronics, 51(6), 1159-1167. doi:10.1109/tie.2004.837873Tipsuwan, Y., & Chow, M.-Y. (2004). Gain Scheduler Middleware: A Methodology to Enable Existing Controllers for Networked Control and Teleoperation—Part I: Networked Control. 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Nonlinear Tracking Control Using a Robust Differential-Algebraic Approach.

This dissertation presents the development and application of an inherently robust nonlinear trajectory tracking control design methodology which is based on linearization along a nominal trajectory. The problem of trajectory tracking is reduced to two separate control problems. The first is to compute the nominal control signal that is needed to place a nonlinear system on a desired trajectory. The second problem is one of stabilizing the nominal trajectory. The primary development of this work is the development of practical methods for designing error regulators for Linear Time Varying systems, which allows for the application of trajectory linearization to time varying trajectories for nonlinear systems. This development is based on a new Differential Algebraic Spectral Theory. The problem of robust tracking for nonlinear systems with parametric uncertainty is studied in relation to the Linear Time Varying spectrum. The control method presented herein constitutes a rather general control strategy for nonlinear dynamic systems. Design and simulation case studies for some challenging nonlinear tracking problems are considered. These control problems include: two academic problems, a pitch autopilot design for a skid-to-turn missile, a two link robot controller, a four degree of freedom roll-yaw autopilot, and a complete six degree of freedom Bank-to-turn planar missile autopilot. The simulation results for these designs show significant improvements in performance and robustness compared to other current control strategies

Multiobjective optimization and multivariable control of offshore wind turbine system

Renewable energy is a hot topic all over the world. Nowadays, there are several sustainable renewable power solutions out there; hydro, wind, solar, wave and biomass to name a few. Most countries have a tendency to want to become greener. According to the European Wind Energy Association (EWEA), the world wide capacity increased with 44.601 [MW] in 2012. From this number, 27 % accounts for new installed wind power, which is the second biggest contributor after solar (37 %). In the past, all new wind parks were installed onshore. During the last decade more and more wind parks were installed offshore, in shallow water (less than 30 [m]). Now, some of the issues related to onshore turbines can be avoided, such as the visual impact, noise and shadow flicker. If one is to speculate about what the future may hold, it is evident that the next step for companies is to install floating wind parks in deeper water (more than 30 [m]). Offshore conditions far from the shore provide with higher and more stable wind conditions. In such deep water, it is no longer economically viable to install bottom-fixed turbines. A solution is to use floating turbine. A floating turbine gives new and interesting challenges to the control community. This dissertation mainly deals with pitch control of a floating wind turbine. The modeling is also to some extend dealt with, e.g. it is the main topic of paper A. Paper A deals with the bond graph methodology as a graphical approach to model wind turbines. This is an alternative to the more classical Newtonian approach. The purpose is not to validate a specific wind turbine system, but rather explore how the bond graph can contribute with a model and give a better understanding ..

Entwurf eines Beobachterbasierten Robusten Nichtlinearen Reglers

Due to observers ability in the estimation of internal system states, observers play an important role in the field of control and monitoring of dynamical systems. In reality, using sensors to measure the desired system states may be costly and/or affects the reliability of technical systems. Besides, some signals are impractical or inaccessible to be measured and using of sensors leads to significant errors such as stochastic noise. The solution of using observers is well-known since 1964. Besides the estimation of system states, some observers are able to estimate unknown inputs affecting the system dynamics such as disturbance forces or torques. These features are helpful for supervision and fault diagnosis tasks by monitoring the sensors and system components or for advanced control purposes by realizing observer-based control for practical systems. Among the state and disturbance observers, Proportional-Integral-Observer (PIO) is highly appreciated because of its simple structure and design procedure. Furthermore, using sufficiently high gain PIO, a robust estimation of system states and unknown inputs can be achieved. Besides taking the advantages of high gain design, the disadvantages of large overshoot and strong influence from measurement noise (as typical drawbacks of high gain utilization) in the control and estimation performance can not be neglected. Recently, some researches have been done to overcome the disadvantages of high gain observers and to adaptively adjust the gain of observer based on the resulting actual performance. Considering the advantages and disadvantages of high gain PIO besides the recent developments, it is evident that there are still open problems and questions to be solved in the area of optimal design of PIO and robust nonlinear control approaches based on PIO. On the other hand, the PI-Observer can be used in combination with linear/nonlinear control approaches (due to its simple structure and capability to estimate the system states and disturbances) to improve the performance and robustness of the closed-loop control results. Therefore, this thesis focuses on development and improvement of high gain Proportional-Integral-Observer as well as utilization of this observer in combination with well-known robust control approaches for possible general application in nonlinear systems. The Modified Advanced PIO (MAPIO) is introduced in this work as the extended version of Advanced PIO (APIO) to tune the gain of PIO according to the current situation. A cost function is defined so that the estimation performance and the related energy can be evaluated. Comparison between advanced observer design approaches has been done in the task of reconstructing the nonlinear characteristics and estimating the external inputs (contact forces) acting to elastic mechanical structures. Simulation results in open-loop and closed-loop cases verified that the performance of MAPIO in the task of unknown input estimation is more robust to different levels of measurement noise in comparison to previous methods e.g. APIO and standard high/low gain PIO. Furthermore, a new gain design approach of Proportional-Integral-Observer is proposed to overcome the disadvantages of high gain PIO and to realize the estimation of fast dynamical behaviors like unknown impact force. The dynamics of this force input is assumed as unknown. The idea of funnel control is taking into consideration to design the PIO gain. The important advantage of the proposed approach compared to previously published PIO gain design is the self-adjustment of observer gains according to the actual estimation situation inside the predefined funnel area. In this thesis it is shown that the proposed funnel PI-Observer algorithm allows adaptive PIO gain calculation, being able to be situatively adjusted even in the presence of measurement noise. Stability proof of funnel PI-Observer is investigated according to the switching observer condition and Lyapunov theory. The effectiveness of the proposed method is evaluated by simulation and experimental results using an elastic beam test rig. Furthermore, a nonlinear MIMO mechanical system is used to verify the effectiveness of the proposed method in the closed-loop context. Additionally, this thesis provides two new PI-Observer-based robust controllers as PIO-based sliding mode control and PIO-based backstepping control to improve the position tracking performance of a hydraulic differential cylinder system in the presence of uncertainties e.g. modeling errors, disturbances, and measurement noise. To use the linear PIO for estimation of system states and unknown inputs, the input-output feedback linearization approach is used to linearize the nonlinear model of hydraulic differential cylinder system. Thereupon the result of state and unknown input estimation is integrated into the structure of robust control design (here SMC and backstepping control) to eliminate the effects of uncertainties and disturbances. The introduced PIO-based robust controllers guarantee the ultimate boundness of the tracking error in the presence of uncertainties. The closed-loop stability is proved using Lyapunov theory in both cases. The proposed methods are experimentally validated and the results are compared with the standard SMC and industrial standard approach P-Controller in the presence of measurement noise, model uncertainties, and external disturbances. A general comparison of SMC and backstepping control approaches is provided in the last part of this work.Die Regelung und Überwachung dynamischer Systeme kann voraussetzen, dass Informationen über interne Systemzustände bekannt sind. Die Verwendung von Sensoren zur Erfassung aller Systemzustände kann erhöhte Kosten zur Folge haben und die Systemzuverlässigkeit negativ beeinflussen. Weitere Probleme ergeben sich dadurch, dass ggf. nicht jeder Systemzustand sensorisch erfasst werden kann. Der Beobachter erlaubt die Rekonstruktion aller Systemzustände auf Grundlage weniger Messungen. Neben Systemzuständen können externe Eingangsgrößen wie Reibmomente und Störungen geschätzt werden. Als Konsequenz ermöglicht der Beobachter eine gegenüber Störungen robuste Regelung und Fehlerdiagnose technischer Systeme. Der Proportional-Integral-Observer (PIO) kann mittels bestehender Entwurfsverfahren einfach implementiert werden. Durch Anpassen der Rückkopplungsmatrix eignet sich der PIO zur kombinierten Schätzung von Zuständen und unbekannten Eingangsgrößen. In diesem Zusammenhang spielt die Wahl einer betragsmäßig großen Rückkopplungsverstärkungsmatrix, als sogenannter High Gain Ansatz, eine entscheidende Rolle. Weiterhin hängt die Performance des PIO von der unbekannten Charakteristik der zu schätzenden Eingangsgröße ab. Diese Arbeit befasst sich mit der Entwicklung optimierter Entwurfsverfahren für den Proportional-Integral-Observer und der Entwicklung und Anwendung beobachterbasierter Konzepte zur robusten Regelung nichtlinearer Systeme. In dieser Arbeit wird der modifizierte Advanced PIO (MAPIO) als erweiterte Version des Advanced PIO (APIO) eingeführt. Der Schätzfehler von MAPIO wird über ein Gütefunktional abgebildet. Das Gütefunktional wird durch Anpassung der Rückkopplungsverstärkungsmatrix an die Charakteristik der unbekannten Eingangsgröße minimiert. Die Performance der modifizierten Beobachterentwurfsansätze wird anhand eines praktischen Beispiels bewertet. Geschätzt wird eine unbekannte Kontaktkraft mit nichtlinearer Charakteristik, die auf ein mechanisches System wirkt. Anhand eines Simulationsbeispiels im offenen und geschlossenen Regelkreis wird die Performance von MAPIO gegenüber vorherigen Verfahren APIO und PIO verifiziert. Basierend auf der Idee des Funnel Reglers wird ein neuartiges Entwurfskonzept für den Proportional-Integral-Observer vorgestellt. Die Nachteile des PIO-Konzeptes mit hohem Verstärkungsfaktor können überwunden werden und Schätzungen schneller dynamischer Verhaltensweisen lassen sich realisieren. Der Vorteil der neuartigen Funnel PIO Methode ist, dass der Schätzfehler in einem definierten Bereich, der sogenannten Funnel-Area, verbleibt. In dieser Arbeit wird gezeigt, dass der vorgeschlagene Funnel PIO Algorithmus eine adaptive PIO Verstärkungsberechnung ermöglicht, die auch in Gegenwart von Messrauschen situativ eingestellt werden kann. Der Stabilitätsnachweis von Funnel PIO wird mittels der Lyapunov Theorie untersucht. Die Wirksamkeit der vorgeschlagenen Methode wird durch Simulation und experimentelle Ergebnisse validiert. Eine auf einen elastischen Balken wirkende äußere Kraft mit nichtlinearer Charakteristik wird geschätzt. Ein nichtlineares MIMO System wird verwendet, um die Wirksamkeit der vorgeschlagenen Methode im geschlossenen Regelkreis zu verifizieren. In dieser Arbeit werden zwei neue PI-Observer basierte robuste Regelungen (PIO-basierte Sliding Mode und PIO-basierte Backstepping Regelung) vorgestellt. Die Positionsregelung eines hydraulischen Differentialzylinders in Gegenwart von Modellunsicherheiten, Störungen und Messrauschen wird untersucht. Zur Anwendung der PIO-basierten Störgrößenschätzung wird eine Ein-/Ausgangs-Linearisierung des nichtlinearen Modells vorgenommen. Die Stabilität des geschlossenen Regelkreises wird in beiden Fällen mit der Lyapunov Theorie bewiesen. Die vorgeschlagenen Methoden werden experimentell validiert und die Ergebnisse werden mit dem Standard Sliding Mode Regler und einem P-Regler in Gegenwart von Messrauschen, Modellunsicherheiten und externen Störungen verglichen

Resource-Aware Design Of Wireless Control Systems

This work is motivated by modern monitoring and control infrastructures appearing in smart homes, urban environments, and industrial plants. These systems are characterized by multiple sensor and actuator devices at different physical locations, communicating wirelessly with each other. Desired monitoring and control performance requires efficient wireless communication, as the more information the sensors convey the more precise actuation becomes. However wireless communication is constrained by the inherent uncertainty of the wireless medium as well as resource limitations at the devices, e.g., limited power resources. The increased number of wireless devices in such environments further necessitates the management of the shared wireless spectrum with direct account of control performance. To address these challenges, the goal of this work is to provide control-aware and resource-aware communication policies. This is first examined in the fundamental problem of allocating transmit power resources for wireless closed loop control. Opportunistic online adaptation of power to plant and wireless channel conditions is shown to be essential in achieving the optimal tradeoff between control performance and power utilization. Optimal structural properties of channel access mechanisms are also considered for the problem of guaranteeing multiple control performance requirements over a shared wireless medium. This includes scheduling mechanisms implemented by central authorities, as well as decentralized mechanisms implemented independently by the wireless devices with emerging wireless interferences. Again the mechanisms exhibit an opportunistic adaptation to varying wireless channel conditions, especially designed to explore the tradeoffs between different communication links and meet control performance requirements. The structural characterization is augmented with tractable optimization algorithms to compute these channel access mechanisms. Finally, as control is naturally a dynamic task that requires a long term planning, appropriate dynamic algorithms adapting to the varying control system states are examined. Besides adapting dynamically, the proposed algorithms provide guarantees about long term control performance and resource utilization by construction