Sliding Mode Reference Coordination of Constrained Feedback Systems

[EN] This paper addresses the problem of coordinating dynamical systems with possibly different dynamics (e.g., linear and nonlinear, different orders, constraints, etc.) to achieve some desired collective behavior under the constraints and capabilities of each system. To this end, we develop a new methodology based on reference conditioning techniques using geometric set invariance and sliding mode control: the sliding mode reference coordination (SMRCoord). The main idea is to coordinate the systems references. Starting from a general framework, we propose two approaches: a local one through direct interactions between the different systems by sharing and conditioning their own references and a global centralized one, where a central node makes decisions using information coming from the systems references. In particular, in this work we focus in implementation on multivariable systems like unmanned aerial vehicles (UAVs) and robustness to external perturbations. To show the applicability of the approach, the problem of coordinating UAVs with input constraints is addressed as a particular case of multivariable reference coordination with both global and local configuration.Research in this area is partially supported by Argentine government (ANPCyT PICT 2011-0888 and CONICET PIP 112-2011-00361), Spanish government (FEDER-CICYT DPI2011-28112-C04-01), and Universitat Politecnica de Valencia (Grant FPI/2009-21)Vignoni, A.; Garelli, F.; Picó, J. (2013). Sliding Mode Reference Coordination of Constrained Feedback Systems. Mathematical Problems in Engineering. 2013:1-11. https://doi.org/10.1155/2013/764348S1112013Information consensus in multivehicle cooperative control. (2007). IEEE Control Systems, 27(2), 71-82. doi:10.1109/mcs.2007.338264Cao, Y., Yu, W., Ren, W., & Chen, G. (2013). An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination. IEEE Transactions on Industrial Informatics, 9(1), 427-438. doi:10.1109/tii.2012.2219061Interconnected dynamic systems: An overview on distributed control. (2013). IEEE Control Systems, 33(1), 76-88. doi:10.1109/mcs.2012.2225929Olfati-Saber, R., Fax, J. A., & Murray, R. M. (2007). Consensus and Cooperation in Networked Multi-Agent Systems. Proceedings of the IEEE, 95(1), 215-233. doi:10.1109/jproc.2006.887293He, W., & Cao, J. (2011). Consensus control for high-order multi-agent systems. IET Control Theory & Applications, 5(1), 231. doi:10.1049/iet-cta.2009.0191Liu, L. (2012). Robust cooperative output regulation problem for non-linear multi-agent systems. IET Control Theory & Applications, 6(13), 2142-2148. doi:10.1049/iet-cta.2011.0575Pitarch, J. L., Sala, A., & Arino, C. V. (2014). Closed-Form Estimates of the Domain of Attraction for Nonlinear Systems via Fuzzy-Polynomial Models. IEEE Transactions on Cybernetics, 44(4), 526-538. doi:10.1109/tcyb.2013.2258910Nuñez, S., De Battista, H., Garelli, F., Vignoni, A., & Picó, J. (2013). Second-order sliding mode observer for multiple kinetic rates estimation in bioprocesses. Control Engineering Practice, 21(9), 1259-1265. doi:10.1016/j.conengprac.2013.03.003Wu, L., Su, X., & Shi, P. (2012). Sliding mode control with bounded gain performance of Markovian jump singular time-delay systems. Automatica, 48(8), 1929-1933. doi:10.1016/j.automatica.2012.05.064Cao, Y., Ren, W., & Meng, Z. (2010). Decentralized finite-time sliding mode estimators and their applications in decentralized finite-time formation tracking. Systems & Control Letters, 59(9), 522-529. doi:10.1016/j.sysconle.2010.06.002Cortés, J. (2006). Finite-time convergent gradient flows with applications to network consensus. Automatica, 42(11), 1993-2000. doi:10.1016/j.automatica.2006.06.015Rao, S., & Ghose, D. (2011). Sliding mode control-based algorithms for consensus in connected swarms. International Journal of Control, 84(9), 1477-1490. doi:10.1080/00207179.2011.602834Guo, P., Zhang, J., Lyu, M., & Bo, Y. (2013). Sliding Mode Control for Multiagent System with Time-Delay and Uncertainties: An LMI Approach. Mathematical Problems in Engineering, 2013, 1-12. doi:10.1155/2013/805492Garelli, F., Mantz, R. J., & De Battista, H. (2006). Limiting interactions in decentralized control of MIMO systems. Journal of Process Control, 16(5), 473-483. doi:10.1016/j.jprocont.2005.09.001Garelli, F., Mantz, R. J., & De Battista, H. (2007). Sliding mode compensation to preserve dynamic decoupling of stable systems. Chemical Engineering Science, 62(17), 4705-4716. doi:10.1016/j.ces.2007.05.020Picó, J., Garelli, F., De Battista, H., & Mantz, R. J. (2009). Geometric invariance and reference conditioning ideas for control of overflow metabolism. Journal of Process Control, 19(10), 1617-1626. doi:10.1016/j.jprocont.2009.08.007Revert, A., Garelli, F., Pico, J., De Battista, H., Rossetti, P., Vehi, J., & Bondia, J. (2013). Safety Auxiliary Feedback Element for the Artificial Pancreas in Type 1 Diabetes. IEEE Transactions on Biomedical Engineering, 60(8), 2113-2122. doi:10.1109/tbme.2013.2247602Gracia, L., Sala, A., & Garelli, F. (2012). A supervisory loop approach to fulfill workspace constraints in redundant robots. Robotics and Autonomous Systems, 60(1), 1-15. doi:10.1016/j.robot.2011.07.008Gracia, L., Garelli, F., & Sala, A. (2013). Integrated sliding-mode algorithms in robot tracking applications. Robotics and Computer-Integrated Manufacturing, 29(1), 53-62. doi:10.1016/j.rcim.2012.07.007Vignoni, A., Garelli, F., & Picó, J. (2013). Coordinación de sistemas con diferentes dinámicas utilizando conceptos de invarianza geométrica y modos deslizantes. Revista Iberoamericana de Automática e Informática Industrial RIAI, 10(4), 390-401. doi:10.1016/j.riai.2013.09.001Hanus, R., Kinnaert, M., & Henrotte, J.-L. (1987). Conditioning technique, a general anti-windup and bumpless transfer method. Automatica, 23(6), 729-739. doi:10.1016/0005-1098(87)90029-xMareczek, J., Buss, M., & Spong, M. W. (2002). Invariance control for a class of cascade nonlinear systems. IEEE Transactions on Automatic Control, 47(4), 636-640. doi:10.1109/9.995041Blasco, X., García-Nieto, S., & Reynoso-Meza, G. (2012). Control autónomo del seguimiento de trayectorias de un vehículo cuatrirrotor. Simulación y evaluación de propuestas. Revista Iberoamericana de Automática e Informática Industrial RIAI, 9(2), 194-199. doi:10.1016/j.riai.2012.01.00

Ultrasensitive Negative Feedback Control: A Natural Approach for the Design of Synthetic Controllers

This is the final version of the article. Available from Public Library of Science via the DOI in this record.Many of the most important potential applications of Synthetic Biology will require the ability to design and implement high performance feedback control systems that can accurately regulate the dynamics of multiple molecular species within the cell. Here, we argue that the use of design strategies based on combining ultrasensitive response dynamics with negative feedback represents a natural approach to this problem that fully exploits the strongly nonlinear nature of cellular information processing. We propose that such feedback mechanisms can explain the adaptive responses observed in one of the most widely studied biomolecular feedback systems—the yeast osmoregulatory response network. Based on our analysis of such system, we identify strong links with a well-known branch of mathematical systems theory from the field of Control Engineering, known as Sliding Mode Control. These insights allow us to develop design guidelines that can inform the construction of feedback controllers for synthetic biological systems.This work was funded by the UK Engineering and Physical Sciences Research Council (EPSRC), grant number EP/I017445/1

Reaction rate reconstruction from biomass concentration measurement in bioreactors using modified second-order sliding mode algorithms

This paper deals with the estimation of unknown signals in bioreactors using sliding observers. Particular attention is drawn to estimate the specific growth rate of microorganisms from measurement of biomass concentration. In a recent article, notions of high-order sliding modes have been used to derive a growth rate observer for batch processes. In this paper we generalize and refine these preliminary results. We develop a new observer with a different error structure to cope with other types of processes. Furthermore, we show that these observers are equivalent, under coordinate transformations and time scaling, to the classical super-twisting differentiator algorithm, thus inheriting all its distinctive features. The new observers’ family achieves convergence to timevarying unknown signals in finite time, and presents the best attainable estimation error order in the presence of noise. In addition, the observers are robust to modeling and parameter uncertainties since they are based on minimal assumptions on bioprocess dynamics. In addition, they have interesting applications in fault detection and monitoring. The observers performance in batch, fed-batch and continuous bioreactors is assessed by experimental data obtained from the fermentation of Saccharomyces Cerevisiae on glucose.This work was supported by the National University of La Plata (Project 2012-2015), the Agency for the Promotion of Science and Technology ANPCyT (PICT2007-00535) and the National Research Council CONICET (PIP112-200801-01052) of Argentina; the Technical University of Valencia (PAID-02-09), the CICYT (DPI2005-01180) and AECID (A/024186/09) of Spain; and by the project FEDER of the European Union.De Battista, H.; Picó Marco, JA.; Garelli, F.; Navarro Herrero, JL. (2012). Reaction rate reconstruction from biomass concentration measurement in bioreactors using modified second-order sliding mode algorithms. Bioprocess and Biosystems Engineering. 35(9):1-11. https://doi.org/10.1007/s00449-012-0752-yS111359Aborhey S, Williamson D (1978) State amd parameter estimation of microbial growth process. Automatica 14:493–498Bastin G, Dochain D (1986) On-line estimation of microbial specific growth rates. Automatica 22:705–709Bastin G, Dochain D (1990) On-line estimation and adaptive control of bioreactors. Elsevier, AmsterdamBejarano F, Fridman L (2009) Unbounded unknown inputs estimation based on high-order sliding mode differentiator. In: Proceedings of the 48th IEEE conference on decision and control, pp 8393–8398Corless M, Tu J (1998) State and input estimation for a class of uncertain systems. Automatica 34(6):757–764Dabros M, Schler M, Marison I (2010) Simple control of specific growth rate in biotechnological fed-batch processes based on enhanced online measurements of biomass. Bioprocess Biosyst Eng 33:1109–1118Davila A, Moreno J, Fridman L (2010) Variable gains super-twisting algorithm: a lyapunov based design. In: American control conference (ACC), 2010, pp 968–973Dávila J, Fridman L, Levant A (2005) Second-order sliding-mode observer for mechanical systems. IEEE Transact Automatic Control 50(11):1785–1789De Battista H, Picó J, Garelli F, Vignoni A (2011) Specific growth rate estimation in (fed-)batch bioreactors using second-order sliding observers. J Process Control 21:1049–1055Dochain D (2001) Bioprocess control. Wiley, HobokenDochain D (2003) State and parameter estimation in chemical and biochemical processes: a tutorial. J Process Control 13(8):801–818Edwards C, Spurgeon S, Patton R (2000) Sliding mode observers for fault detection and isolation. Automatica 36(2):541–553Evangelista C, Puleston P, Valenciaga F, Fridman L (2012) Lyapunov designed super-twisting sliding mode control for wind energy conversion optimization. Indus Electron IEEE Transact. doi: 10.1109/TIE.2012.2188256Farza M, Busawon K, Hammouri H (1998) Simple nonlinear observers for on-line estimation of kinetic rates in bioreactors. Automatica 34(3):301–318Fridman L, Davila J, Levant A (2008) High-order sliding modes observation. In: International workshop on variable structure systems, pp 203–208Fridman L, Levant A (2002) Sliding mode control in engineering, higher-order sliding modes. Marcel Dekker, Inc., New York, pp 53–101Fridman L, Shtessel Y, Edwards C, Yan X (2008) Higher-order sliding-mode observer for state estimation and input reconstruction in nonlinear systems. Int J Robust Nonlinear Control 18(3–4):399–412Gauthier J, Hammouri H, Othman S (1992) A simple observer for nonlinear systems: applications to bioreactors. IEEE Transact Automatic Control 37(6):875–880Gnoth S, Jenzsch M, Simutis R, Lubbert A (2008) Control of cultivation processes for recombinant protein production: a review. Bioprocess Biosyst Eng 31(1):21–39Hitzmann B, Broxtermann O, Cha Y, Sobieh O, Stärk E, Scheper T (2000) The control of glucose concentration during yeast fed-batch cultivation using a fast measurement complemented by an extended kalman filter. Bioprocess Eng 23(4):337–341Kiviharju K, Salonen K, Moilanen U, Eerikainen T (2008) Biomass measurement online: the performance of in situ measurements and software sensors. J Indus Microbiol Biotechnol 35(7):657–665Levant A (1998) Robust exact differentiation via sliding mode technique. Automatica 34(3):379–384Levant A (2003) Higher-order sliding modes, differentiation and output-feedback control. Int J Control 76(9/10):924–941Lubenova V, Rocha I, Ferreira E (2003) Estimation of multiple biomass growth rates and biomass concentration in a class of bioprocesses. Bioprocess Biosyst Eng 25:395–406Moreno J, Alvarez J, Rocha-Cozatl E, Diaz-Salgado J (2010) Super-twisting observer-based output feedback control of a class of continuous exothermic chemical reactors. In: Proceedings of the 9th IFAC international symposium on dynamics and control of process systems, pp 719–724. Leuven, BelgiumMoreno J, Osorio M (2008) A Lyapunov approach to second-order sliding mode controllers and observers. In: Proceedings of the 47th IEEE conference on decision and control. Cancún, México, pp 2856–2861Moreno J, Osorio M (2012) Strict Lyapunov functions for the super-twisting algorithm. IEEE Transact Automatic Control 57:1035–1040Navarro J, Picó J, Bruno J, Picó-Marco E, Vallés S (2001) On-line method and equipment for detecting, determining the evolution and quantifying a microbial biomass and other substances that absorb light along the spectrum during the development of biotechnological processes. Patent ES20010001757, EP20020751179Neeleman Boxtel (2001) Estimation of specific growth rate from cell density measurements. Bioprocess Biosyst Eng 24(3):179–185November E, van Impe J (2002) The tuning of a model-based estimator for the specific growth rate of Candidautilis. Bioprocess Biosyst Eng 25:1–12Park Y, Stein J (1988) Closed-loop, state and input observer for systems with unknown inputs. Int J Control 48(3):1121–1136Perrier M, de Azevedo SF, Ferreira E, Dochain D (2000) Tuning of observer-based estimators: theory and application to the on-line estimation of kinetic parameters. Control Eng Pract 8:377–388Picó J, De Battista H, Garelli F (2009) Smooth sliding-mode observers for specific growth rate and substrate from biomass measurement. J Process Control 19(8):1314–1323. Special section on hybrid systems: modeling, simulation and optimizationSchenk J, Balaszs K, Jungo C, Urfer J, Wegmann C, Zocchi A, Marison I, von Stockar U (2008) Influence of specific growth rate on specific productivity and glycosylation of a recombinant avidin produced by a Pichia pastoris Mut + strain. Biotecnol Bioeng 99(2):368–377Shtessel Y, Taleb M, Plestan F (2012) A novel adaptive-gain supertwisting sliding mode controller: Methodol Appl Automatica (in press)Soons Z, van Straten G, van der Pol L, van Boxtel A (2008) On line automatic tuning and control for fed-batch cultivation. Bioprocess Biosyst Eng 31(5):453–467Utkin V, Poznyak A, Ordaz P (2011) Adaptive super-twist control with minimal chattering effect. In: Proceedings of 50th IEEE conference on decision and control and European control conference. Orlando, pp 7009–7014Veloso A, Rocha I, Ferreira E (2009) Monitoring of fed-batch E. coli fermentations with software sensors. Bioprocess Biosyst Eng 32(3):381–388Venkateswarlu C (2004) Advances in monitoring and state estimation of bioreactors. J Sci Indus Res 63:491–498Zamboni N, Fendt S, Rühl M, Sauer U (2009) 13c-based metabolic flux analysis. Nat Protocols 4:878–892Zorzetto LFM, Wilson JA (1996) Monitoring bioprocesses using hybrid models and an extended kalman filter. Comput Chem Eng 20(Suppl 1):S689–S69

Recent advances on recursive filtering and sliding mode design for networked nonlinear stochastic systems: A survey

Copyright © 2013 Jun Hu 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.Some recent advances on the recursive filtering and sliding mode design problems for nonlinear stochastic systems with network-induced phenomena are surveyed. The network-induced phenomena under consideration mainly include missing measurements, fading measurements, signal quantization, probabilistic sensor delays, sensor saturations, randomly occurring nonlinearities, and randomly occurring uncertainties. With respect to these network-induced phenomena, the developments on filtering and sliding mode design problems are systematically reviewed. In particular, concerning the network-induced phenomena, some recent results on the recursive filtering for time-varying nonlinear stochastic systems and sliding mode design for time-invariant nonlinear stochastic systems are given, respectively. Finally, conclusions are proposed and some potential future research works are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grant nos. 61134009, 61329301, 61333012, 61374127 and 11301118, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant no. GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

A Novel Fuzzy Logic Based Adaptive Supertwisting Sliding Mode Control Algorithm for Dynamic Uncertain Systems

This paper presents a novel fuzzy logic based Adaptive Super-twisting Sliding Mode Controller for the control of dynamic uncertain systems. The proposed controller combines the advantages of Second order Sliding Mode Control, Fuzzy Logic Control and Adaptive Control. The reaching conditions, stability and robustness of the system with the proposed controller are guaranteed. In addition, the proposed controller is well suited for simple design and implementation. The effectiveness of the proposed controller over the first order Sliding Mode Fuzzy Logic controller is illustrated by Matlab based simulations performed on a DC-DC Buck converter. Based on this comparison, the proposed controller is shown to obtain the desired transient response without causing chattering and error under steady-state conditions. The proposed controller is able to give robust performance in terms of rejection to input voltage variations and load variations.Comment: 14 page

Variance-constrained multiobjective control and filtering for nonlinear stochastic systems: A survey

The multiobjective control and filtering problems for nonlinear stochastic systems with variance constraints are surveyed. First, the concepts of nonlinear stochastic systems are recalled along with the introduction of some recent advances. Then, the covariance control theory, which serves as a practical method for multi-objective control design as well as a foundation for linear system theory, is reviewed comprehensively. The multiple design requirements frequently applied in engineering practice for the use of evaluating system performances are introduced, including robustness, reliability, and dissipativity. Several design techniques suitable for the multi-objective variance-constrained control and filtering problems for nonlinear stochastic systems are discussed. In particular, as a special case for the multi-objective design problems, the mixed H 2 / H ∞ control and filtering problems are reviewed in great detail. Subsequently, some latest results on the variance-constrained multi-objective control and filtering problems for the nonlinear stochastic systems are summarized. Finally, conclusions are drawn, and several possible future research directions are pointed out