Abstract
An algorithm was proposed to stabilize nonlinear systems with reduced level of impact of the measurement noise, parametric uncertainty, and external perturbation. Consideration was given to the noise of the measurements of dimensionality coinciding with that of the plant state vector. The parametric uncertainty and external perturbations can occur in any equation of the plant model. Conditions were obtained to calculate algorithm parameters in the form of solvability of the linear matrix inequality. Efficiency of the proposed scheme was illustrated by numerical examples.
Similar content being viewed by others
References
Polyak, B.T. and Topunov, M.V., Suppression of Bounded Exogenous Disturbances: Output Feedback, Autom. Remote Control, 2008, vol. 69, no. 5, pp. 801–818.
Nikiforov, V.O., Nonlinear Control System with Compensation of the External Deterministic Disturbances, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 1997, no. 4, pp. 69–73.
Fedele, G. and Ferrise, A., Biased Sinusoidal Disturbance Compensation with Unknown Frequency, IEEE Trans. Autom. Control, 2013, vol. 58, no. 12, pp. 3207–3212.
Bukov, V.N., Vlozhenie sistem. Analiticheskii podkhod k analizu i sintezu matrichnykh sistem (System Embedding. An Analytical Approach to Analysis and Design of the Matrix Systems), Kaluga: Izd. Nauch. Lit. Bochkarevoi, 2006.
Proskurnikov, A.V. and Yakubovich, V.A., Universal Controllers in Problens of Optimal Control with Reference Model under Unknown External Signals, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2012, no. 2, pp. 49–62.
Tsykunov, A.M., Robastnoe upravlenie s kompensatsiei vozmushchenii (Robust Control with Perturbation Compensation), Moscow: Fizmatlit, 2012.
Guo, G., Hill, D.J., and Wang, Y., Nonlinear Output Stabilization Control for Multimachine Power Systems, IEEE Trans. Circuit. Syst. 1, 2000, vol. 47, no. 1, pp. 46–53.
Chen, Y., Liu, F., Mei, S., and Ma, J., Toward Adaptive Robust State Estimation Based on MCC by Using the Generalized Gaussian Density as Kernel Functions, Electr. Power Energy Syst., 2015, vol. 71, pp. 297–304.
Belyaev, A.N., Smolovik, S.V., Fradkov, A.L., and Furtat, I.B., Robust Control of Electrical Generator under Nonstationary Mechanical Power, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2013, no. 5, pp. 78–86.
Metody robastnogo, neiro-nechetkogo i adaptivnogo upravleniya (Methods of Robust Neuro-Fuzzy and Adaptive Control), Egupov, N.D., Ed., Moscow: MTTU im. N.E. Baumana, 2002.
Baillieul, J., Feedback Coding for Information-Based Control: Operating Near the Data Rate Limit, in Proc. 41 IEEE Conf. Decision Control, ThP02-6, Las Vegas, Nevada, USA, 2002, pp. 3229–3236.
Delchamps, D.F., Extracting State Information from a Quantized Output Record, Syst. Control Lett., 1989, vol. 13, pp. 365–372.
Furtat, I.B., Fradkov, A.L., and Liberzon, D., Compensation of Disturbances for MIMO Systems with Quantized Output, Automatica, 2015, vol. 60, pp. 239–244.
Balandin, D.V. and Kogan, M.M., Sintez zakonov upravleniya na osnove lineinykh matrichnykh neravenstv (Design of Control Laws Based on Linear Matrix Inequalities), Moscow: Fizmatlit, 2007.
Polyak, B.T., Khlebnikov, M.V., and Shcherbakov, P.S., Upravlenie lineinymi sistemami pri vneshnikh vozmushcheniyakh. Tekhnika lineinykh matrichnykh neravenstv (Control of Linear Systems under External Perturbations. Technique of Linear Matrix Inequalities), Moscow: Lenand, 2014.
Furtat, I.B., Algorithm of Robust Control of Linear Plants with Vector Inputs-Outputs under Saturated Control Signal, Mekhatronika, Avtomatiz., Upravl., 2016, vol. 17, no. 9, pp. 579–587.
Fridman, E., A Refined Input Delay Approach to Sampled-data Control, Automatica, 2010, vol. 46, pp. 421–427.
Polyak, B.T. and Shcherbakov, P.S., Robastnaya ustoichivost’ i upravlenie (Robust Stability and Control), Moscow: Nauka, 2002.
Brammer, K. and Siffling, G., Kalman–Bucy-Filter: Deterministische Beobachtung und stochastische Filterung (Methoden der Regelungs-und Automatisierungstechnik), Wien: Oldenbourg, 1975. Translated under the title Determinirovannoe nablyudenie i stokhasticheskaya fil’tratsiya, Moscow: Nauka, 1982.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © I.B. Furtat, 2018, published in Avtomatika i Telemekhanika, 2018, No. 7, pp. 41–58.
Rights and permissions
About this article
Cite this article
Furtat, I.B. An Algorithm to Control Nonlinear Systems in Perturbations and Measurement Noise. Autom Remote Control 79, 1207–1221 (2018). https://doi.org/10.1134/S0005117918070032
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117918070032