Event-triggered control cannot improve the ℓ2\ell_2 gain of h∞h_\infty optimal periodic control and transmit at a smaller average rate

We consider a standard discrete-time event-triggered control setting by which a scheduler collocated with the plant's sensors decides when to transmit sensor data to a remote controller collocated with the plant's actuators. When the scheduler transmits periodically with period larger than or equal to one, the $h_\infty$ optimal controller guarantees an optimal attenuation bound ($\ell_2$ gain) from any square-summable disturbance input to a plant's output. We show that, under mild assumptions, there does not exist a controller and scheduler pair that strictly improves the optimal attenuation bound of periodic control with a smaller average transmission rate. Equivalently, given any controller and scheduler pair, there exists a square-summable disturbance such that either the attenuation bound or the average transmission rate are larger than or equal to those of optimal periodic control

Estimation over Communication Networks: Performance Bounds and Achievability Results

This paper considers the problem of estimation over communication networks. Suppose a sensor is taking measurements of a dynamic process. However the process needs to be estimated at a remote location connected to the sensor through a network of communication links that drop packets stochastically. We provide a framework for computing the optimal performance in the sense of expected error covariance. Using this framework we characterize the dependency of the performance on the topology of the network and the packet dropping process. For independent and memoryless packet dropping processes we find the steady-state error for some classes of networks and obtain lower and upper bounds for the performance of a general network. Finally we find a necessary and sufficient condition for the stability of the estimate error covariance for general networks with spatially correlated and Markov type dropping process. This interesting condition has a max-cut interpretation

Optimal sampling schedules for h2h_2 and h∞h_\infty state-feedback control

We consider a discrete-time linear system for which the control input is updated at every sampling time, but the state is measured at a slower rate. We allow the state to be sampled according to a periodic schedule, which dictates when the state should be sampled along a period. Given a desired average sampling interval, our goal is to determine sampling schedules that are optimal in the sense that they minimize the $h_2$ or the $h_\infty$ closed-loop norm, under an optimal state-feedback control law. Our results show that, when the desired average sampling interval is an integer, the optimal state sampling turns out to be evenly spaced. This result indicates that, for the $h_2$ and $h_\infty$ performance metrics, there is relatively little benefit to go beyond constant-period sampling

Group Chase and Escape

We describe here a new concept of one group chasing another, called "group chase and escape", by presenting a simple model. We will show that even a simple model can demonstrate rather rich and complex behavior. In particular, there are cases in which an optimal number of chasers exists for a given number of escapees (or targets) to minimize the cost of catching all targets. We have also found an indication of self-organized spatial structures formed by both groups.Comment: 13 pages, 12 figures, accepted and to appear in New Journal of Physic

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. Practice, vol. 11, no. 10, pp. 1099–1111, 2003.T. Jia, Y. Niu, and X. Wang, “H ∞ control for networked systems with data packet dropout,” Int. J. Control, Autom., and Syst., vol. 8, no. 2, pp. 198–203, 2010.Y. Wang and G. Yang, “Robust H ∞ model reference tracking control for networked control systems with communication constraints,” Int. J. Control, Autom., and Syst., vol. 7, no. 6, pp. 992–1000, 2009.H. Gao and T. Chen, “Network-based H ∞ output tracking control,” IEEE Trans. Autom. Control, vol. 53, no. 3, pp. 655–667, 2008.H. Karimi, “Robust H ∞ filter design for uncertain linear systems over network with network-induced delays and output quantization,” Modeling, Identification and Control, vol. 30, no. 1, pp. 27–37, 2009.H. R. Karimi, “Delay-range-dependent linear matrix inequality approach to quantized H ∞ control of linear systems with network-induced delays and norm-bounded uncertainties,” Proc. of the Inst. of Mech. Eng., Part I: J. of Syst. and Control Eng., vol. 224, no. 6, pp. 689–700, 2010.K. Lee, S. Lee, and M. Lee, “Remote fuzzy logic control of networked control system via Profibus-DP,” IEEE Trans. Ind. Electron., vol. 50, no. 4, pp. 784–792, 2003.Y. Tipsuwan and M.-Y. Chow, “Gain scheduler middleware: a methodology to enable existing controllers for networked control and teleoperationpart I: networked Control,” IEEE Trans. on Industrial Electronics, vol. 51, no. 6, pp. 1218–1227, December 2004.A. Sala, A. Cuenca, and J. Salt, “A retunable PID multi-rate controller for a networked control system,” Inform. Sci., vol. 179, no. 14, pp. 2390–2402, June 2009.A. Cuenca, J. Salt, V. Casanova, and R. Piza, “An approach based on an adaptive multi-rate Smith predictor and gain scheduling for a networked control system: implementation over Profibus-DP,” Int. J. Control, Autom., and Syst., vol. 8, no. 2, pp. 473–481, April 2010.A. Cuenca, J. Salt, A. Sala, and R. Piza, “A delay-dependent dual-rate PID controller over an Ethernet network,” IEEE Trans. Ind. Informat., vol. 7, no. 1, pp. 18–29, Feb. 2011.Y. Tian and D. Levy, “Compensation for control packet dropout in networked control systems,” Inform. Sci., vol. 178, no. 5, pp. 1263–1278, 2008.Y. Zhao, G. Liu, and D. Rees, “Modeling and stabilization of continuous-time packet-based networked control systems.” IEEE Trans. Syst., Man, Cybern. B, vol. 39, no. 6, pp. 1646–1652, Dec. 2009.X. Zhao, S. Fei, and C. Sun, “Impulsive controller design for singular networked control systems with packet dropouts,” Int. J. Control, Autom., and Syst., vol. 7, no. 6, pp. 1020–1025, 2009.H. Gao and T. Chen, “H ∞ estimation for uncertain systems with limited communication capacity,” IEEE Trans. Autom. Control, vol. 52, no. 11, pp. 2070–2084, 2007.S. Oh, L. Schenato, P. Chen, and S. Sastry, “Tracking and coordination of multiple agents using sensor networks: System design, algorithms and experiments,” Proc. of the IEEE, vol. 95, no. 1, pp. 234–254, 2007.M. Moayedi, Y. Foo, and Y. Soh, “Optimal and suboptimal minimum-variance filtering in networked systems with mixed uncertainties of random sensor delays, packet dropouts and missing measurements,” Int. J. Control, Autom., and Syst., vol. 8, no. 6, pp. 1179–1188, 2010.W. Zhang, M. Branicky, and S. Phillips, “Stability of networked control systems,” IEEE Control Syst. Mag., vol. 21, no. 1, pp. 84–99, 2001.J. Hespanha, P. Naghshtabrizi, and Y. Xu, “A survey of recent results in networked control systems,” Proc. of the IEEE, vol. 95, no. 1, pp. 138–162, 2007.J. Baillieul and P. Antsaklis, “Control and communication challenges in networked real-time systems,” Proc. of the IEEE, vol. 95, no. 1, pp. 9–28, 2007.P. Garcia, P. Castillo, R. Lozano, and P. Albertos, “Robustness with respect to delay uncertainties of a predictor-observer based discrete-time controller,” Proc. of the 45th IEEE Conf. on Decision and Control, pp. 199–204, 2006.C. Lien, “Robust observer-based control of systems with state perturbations via LMI approach,” IEEE Trans. Autom. Control, vol. 49, no. 8, pp. 1365–1370, 2004.A. Sala, “Computer control under time-varying sampling period: an LMI gridding approach,” Automatica, vol. 41, no. 12, pp. 2077–2082, Dec. 2005.J. Li, Q. Zhang, Y. Wang, and M. Cai, “H ∞ control of networked control systems with packet disordering,” IET Control Theory Appl., vol. 3, no. 11, pp. 1463–1475, March 2009.Y. Zhao, G. Liu, and D. Rees, “Improved predictive control approach to networked control systems,” IET Control Theory Appl., vol. 2, no. 8, pp. 675–681, Aug. 2008.K. Astrom, “Event based control,” Analysis and Design of Nonlinear Control Systems, pp. 127–147, 2007.A. Cuenca, P. García, K. Arzén, and P. Albertos, “A predictor-observer for a networked control system with time-varying delays and non-uniform sampling,” Proc. Eur. Control Conf., pp. 946–951, 2009.J. Xiong and J. Lam, “Stabilization of linear systems over networks with bounded packet loss,” Automatica, vol. 43, no. 1, pp. 80–87, 2007.H. Song, L. Yu, and A. Liu, “H ∞ filtering for network-based systems with communication constraints and packet dropouts,” Proc. of the 7th Asian Control Conf., pp. 220–225, 2009.P. Garcia, A. Gonzalez, P. Castillo, R. Lozano, and P. Albertos, “Robustness of a discrete-time predictor-based controller for time-varying measurement delay,” Proc. of the 9th IFAC Workshop on Time Delay Systems, 2010.J. Sturm, “Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones,” Optimization methods and software, vol. 11, no. 1, pp. 625–653, 1999.T. Henningsson and K. Astrom, “Log-concave observers,” Proc. of the 17th Int. Symp. on Mathematical Theory of Networks and Systems, pp. 2163–2170, 2006.D. Davison and E. Hwang, “Automating radiotherapy cancer treatment: use of multirate observer-based control,” Proc. of American Control Conf., vol. 2, pp. 1194–1199, 2003