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Tytuł: Stochastic controllability of linear systems with delay in control

Autorzy:

Klamka, J.

Data:

2007

Typ:

Artykuły / Articles

Tytuł czasopisma:

Bulletin of the Polish Academy of Sciences Technical Sciences

Rocznik:

2007

Wolumin:

vol. 55

Numer:

No 1

Zakres:

23-29

Opis:

The Bulletin of the Polish Academy of Sciences Technical Sciences is published bimonthly by the Division IV Engineering Sciences of the Polish Academy of Sciences, since the beginning of the existence of the PAS in 1952. The journal is peer‐reviewed and is published both in printed and electronic form. It is established for the publication of original high quality papers from multidisciplinary Engineering sciences with the following topics preferred:

  • Artificial and Computational Intelligence,
  • Biomedical Engineering and Biotechnology,
  • Civil Engineering,
  • Control, Informatics and Robotics,
  • Electronics, Telecommunication and Optoelectronics,
  • Mechanical and Aeronautical Engineering, Thermodynamics,
  • Material Science and Nanotechnology,
  • Power Systems and Power Electronics.

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Journal Metrics:
JCR Impact Factor 2022: 1.2
5 Year Impact Factor 2020: 1.490
CiteScore 2022: 2.8
SCImago Journal Rank (SJR) 2022: 0.285
Source Normalized Impact per Paper (SNIP) 2022: 0.543
Ministry of Education and Science: 100 points

Abbreviated title: Bull. Pol. Acad. Sci. Tech. Sci.

Abstrakt:

In the paper finite-dimensional stationary dynamical control systems described by linear stochastic ordinary differential state equations with single point delay in the control are considered. Using notations, theorems and methods taken directly from deterministic controllability problems, necessary and sufficient conditions for different kinds of stochastic relative controllability are formulated and proved. It will be proved that under suitable assumptions relative controllability of a deterministic linear associated dynamical system is equivalent to stochastic relative exact controllability and stochastic relative approximate controllability of the original linear stochastic dynamical system. Some remarks and comments on the existing results for stochastic controllability of linear dynamical systems with delays are also presented. Finally, minimum energy control problem for stochastic dynamical system is formulated and solved.

Kontakt:

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Wydział IV Nauk Technicznych PAN

Pl. Defilad 1

PL 00-901 Warszawa

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Renata Podraza, e-mail: Renata.Podraza@pan.pl

Finance:

Katarzyna Łasak, e-mail: Katarzyna.Lasak@pan.pl

Redaktorzy:

Editorial Board 2023-2025

Editor-in-Chief:

A. Rogalski, Military University of Technology

Honorary (Past) Editor-in Chief:

T. Kaczorek, Warsaw University of Technology

M.P. Kaźmierkowski, Warsaw University of Technology

Deputy Editor-in-Chief:

B. Błachowski, Institute of Fundamental Technological Research PAN

M. Mrozowski, Gdansk University of Technology

Board of Topical Co-editors:

Artificial and Computational Intelligence

S. Osowski, B. Sawicki and T. Leś, Warsaw University of Technology

Biomedical Engineering and Biotechnology

D. Pijanowska, Institute of Biocybernetics and Biomedical Engineering PAN

Civil Engineering

L. Czarnecki, Building Research Institute, ITB, Warsaw

Ł. Sadowski, Wroclaw University of Science and Technology

Control, Robotics and Informatics

J. Klamka and A. Babiarz, Silesian Technical University

J. Stefanowski, Poznan University of Technology

Electronics, Telecommunication and Optoelectronics

M. Mrozowski and A. Lamęcki, Gdansk University of Technology

Mechanical and Aeronautical Engineering, Thermodynamics

B. Błachowski, Institute of Fundamental Technological Research PAN

G. Zboiński, Institute of Fluid-Flow Machinery PAN and University of Warmia and Mazury in Olsztyn

Materials Science and Nanotechnology

B. Major and P. Czaja, Institute of Metallurgy and Materials Science PAN

Power Systems and Power Electronics

J. Rąbkowski and M. Jasiński, Warsaw University of Technology

International Editorial Advisory Board

R. Asthana, University of Wisconsin-Stout, Menomonie, USA

Xu Binshi, China Association of Plant Engineering, Beijing, P.R. China

F. Blaabjerg, Aalborg University, Denmark

C. Cecati, University of L’Aquila, Italy

A. Cichocki, RIKEN Institute, Tokyo, Japan

M. David, National Polytechnique de Toulouse, France

R. Ebner, Materials Centre Leoben, Leoben, Austria

E. Fornasini, University of Padova, Padova, Italy

L.G. Franquelo, University of Sevilla, Spain

M. Gad-el-Hak, Virginia Commonwealth University, Richmond, USA

M. Giersig, Free University of Berlin, Germany

D. van Gemert, Catholic University Leuven, KU Leuven, Belgium

L. Keviczky, Hungarian Academy of Sciences, Budapest, Hungary

V. Kučera, Czech Technical University in Prague, Prague, Czech Republic

R. Kennel, Technical University Munich, Germany

T.A. Kowalewski, Institute of Fundamental Technological Research PAN

E. Levi, Liverpool John Moore University, UK

G. Maier, Technical University of Milan, Milan, Italy

K.F. Man, City University of Hong Kong,

R. Maniewski, Institute of Biocybernetics and Biomedical Engineering PAN

H.A. Mang, Austrian Academy of Sciences, Vienna, Austria

H. Mihashi, Tohoku University, Aoba-ku, Sendai, Japan

S. Mindess, University of British Columbia, Vancouver, Canada

D.A. Mlynski, University of Karlsruhe, Karlsruhe, Germany

A.S. Nowak, University of Michigan, Ann Arbor, USA

K. Ohnishi, Keio University, Yokohama, Japan

A. Öberg, Linköping University, Linköping, Sweden

W. Pedrycz, University of Alberta, Canada

M. Razeghi, Northwestern University, Evanston, USA

J. Rodriguez, University of Andres Bello, Santiago, Chile

J.V. Sloten, Catholic University Leuven, Leuven, Belgium

B.M. Wilamowski, University of Auburn, Alabama, USA

A.L. Yarin, University of Illinois at Chicago, USA

Du Xiangwan, Chinese Academy of Engineering, China

J. Żurada, Department of Computer Engineering, University of Louisville, USA

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Open Access:

Bulletin of the Polish Academy of Sciences Technical Sciences jest czasopismem wydawanym w wolnym dostępie na licencji CC BY 4.0. </span></p> <p style="background: white;"><span style="font-size: 10pt;"> Bulletin of the Polish Academy of Sciences Technical Sciences is an open access journal with all content available with no charge in full text version. The journal content is available under the licencse CC BY 4.0.

Identyfikator:

oai:journals.pan.pl:111176 ; ISSN 2300-1917

Źródło:

Bulletin of the Polish Academy of Sciences: Technical Sciences; 2007; vol. 55; No 1; 23-29

Polityka Open Access:

The Bulletin of the Polish Academy of Sciences Technical Sciences is an open access journal with all content available with no charge in full text version.


The journal content is available under the licencse CC BY 4.0 https://creativecommons.org/licenses/by/4.0/.

Temat i słowa kluczowe:

controllability linear control systems stochastic control systems delayed controls minimum energy control Nauki Techniczne

Kolekcje, do których przypisany jest obiekt:

Data ostatniej modyfikacji:

24 sty 2024

Data dodania obiektu:

2 mar 2019

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Stochastic controllability of linear systems with delay in control 24 sty 2024

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Stochastic controllability of systems with variable delay in control

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Bulletin of the Polish Academy of Sciences Technical Sciences | 2008 | vol. 56 | No 3 | 279-284
Słowa kluczowe controllability linear control systems stochastic control systems delayed controls
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Abstrakt

In the paper finite-dimensional time-variable dynamical control systems described by linear stochastic ordinary differential state equations with single time-variable point delay in the control are considered. Using notations, theorems and methods taken directly from deterministic controllability problems necessary and sufficient conditions for different kinds of stochastic relative controllability in a given time interval are formulated and proved. It will be proved that under suitable assumptions relative controllability of a deterministic linear associated dynamical system is equivalent to stochastic relative exact controllability and stochastic relative approximate controllability of the original linear stochastic dynamical system. Some remarks and comments on the existing results for stochastic controllability of linear dynamical systems are also presented.
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Autorzy i Afiliacje

J. Klamka

Constrained controllability of semilinear systems with multiple delays in control

J. Klamka
Bulletin of the Polish Academy of Sciences Technical Sciences | 2004 | vol. 52 | No 1 | 25-30
Słowa kluczowe controllability nonlinear control systems semilinear control systems constrained controls delayed control systems
Pobierz PDF Pobierz RIS Pobierz Bibtex

Abstrakt

In the present paper .nite-dimensional, stationary dynamical control systems described by semilinear ordinary di.erential state equations with multiple point delays in control are considered. In.nite-dimensional semilinear stationary dynamical control systems with single point delay in the control are also discussed. Using a generalized open mapping theorem, su.cient conditions for constrained local relative controllability are formulated and proved. It is generally assumed, that the values of admissible controls are in a convex and closed cone with vertex at zero. Some remarks and comments on the existing results for controllability of nonlinear dynamical systems are also presented.
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Autorzy i Afiliacje

J. Klamka

Constrained controllability of semilinear systems with delayed controls

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Bulletin of the Polish Academy of Sciences Technical Sciences | 2008 | vol. 56 | No 4 | 333-337
Słowa kluczowe controllability nonlinear control systems semilinear control systems constrained controls delayed control systems
Pobierz PDF Pobierz RIS Pobierz Bibtex

Abstrakt

In the present paper finite-dimensional dynamical control systems described by semilinear ordinary differential state equations with multiple point delays in control are considered. It is generally assumed, that the values of admissible controls are in a convex and closed cone with vertex at zero. Using so-called generalized open mapping theorem, sufficient conditions for constrained local relative controllability near the origin are formulated and proved. Roughly speaking, it will be proved that under suitable assumptions constrained global relative controllability of a linear associated approximated dynamical system implies constrained local relative controllability near the origin of the original semilinear dynamical system. This is generalization to the constrained controllability case some previous results concerning controllability of linear dynamical systems with multiple point delays in the control and with unconstrained controls. Moreover, necessary and sufficient conditions for constrained global relative controllability of an associated linear dynamical system with multiple point delays in control are discussed. Simple numerical example, which illustrates theoretical considerations is also given. Finally, some remarks and comments on the existing results for controllability of nonlinear dynamical systems are also presented.
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J. Klamka

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Bulletin of the Polish Academy of Sciences Technical Sciences | 2022 | 70 | 5 | e143102 | DOI: 10.24425/bpasts.2022.143102
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In this paper the controllability properties of the convex linear combination of fractional, linear, discrete-time systems are characterized and investigated. The notions of linear convex combination and controllability in the context of fractional-order systems are recalled. Then, the controllability property of such a linear combination of discrete-time, linear fractional systems is proven. Further, the reduction of an infinite problem of transition matrix derivation is reduced to a finite one, which greatly simplifies the numerical burden of the controllability issue. Examples of controllable and uncontrollable, single-input, linear systems are presented. The possibility of extension of the considerations to multi-input systems is shown.
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Autorzy i Afiliacje

Tadeusz Kaczorek
1
ORCID: ORCID
Jerzy Klamka
2
ORCID: ORCID
Andrzej Dzieliński
3
ORCID: ORCID
  1. Bialystok University of Technology, Faculty of Electrical Engineering, ul. Wiejska 45D, Bialystok, Poland
  2. Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, ul. Bałtycka 5, Gliwice, Poland
  3. Warsaw University of Technology, Faculty of Electrical Engineering, ul. Koszykowa 75, Warsaw, Poland

Assignability of numerical characteristics of time-varying systems

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Bulletin of the Polish Academy of Sciences Technical Sciences | 2019 | 67 | No. 6 | 107-1022 | DOI: 10.24425/bpasts.2019.130890
Słowa kluczowe assignability controllability Lyapunov spectrum linear time-varying systems
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Abstrakt

The main aim of this article is to survey and discuss the existing state of art concerning the assignability by a feedback of numerical characteristics of linear continuous and discrete time-varying systems. Most of the results present necessary or sufficient conditions for different formulation of the Lyapunov spectrum assignability problem. These conditions are expressed in terms of various controllability types and optimalizability of the controlled systems and certain properties of the free system such as: regularity, diagonalizability, boundness away, integral separation and reducibility.
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Autorzy i Afiliacje

A. Babiarz
A. Czornik
J. Klamka

Optimal control problems with a fixed terminal time in linear fractional-order systems

Mikhail I. Gomoyunov
Archives of Control Sciences | 2020 | vol. 30 | No 4 | 721-744 | DOI: 10.24425/acs.2020.135849
Słowa kluczowe optimal control fractional derivatives linear systems open-loop control feed-back control reduction
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Abstrakt

The paper deals with an optimal control problem in a dynamical system described by a linear differential equation with the Caputo fractional derivative. The goal of control is to minimize a Bolza-type cost functional, which consists of two terms: the first one evaluates the state of the system at a fixed terminal time, and the second one is an integral evaluation of the control on the whole time interval. In order to solve this problem, we propose to reduce it to some auxiliary optimal control problem in a dynamical system described by a first-order ordinary differential equation. The reduction is based on the representation formula for solutions to linear fractional differential equations and is performed by some linear transformation, which is called the informational image of a position of the original system and can be treated as a special prediction of a motion of this system at the terminal time. A connection between the original and auxiliary problems is established for both open-loop and feedback (closed-loop) controls. The results obtained in the paper are illustrated by examples.
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Autorzy i Afiliacje

Mikhail I. Gomoyunov

Unified design method of time delayed PI controller for first order plus dead-time process models with different dead-time to time constant ratio

Arun R. Pathiran R. Muniraj M. Willjuice Iruthayarajan S.R. Boselin Prabhu T. Jarin
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Słowa kluczowe PI controller time delayed PI controller dead-time compensation
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Abstrakt

The time delay element present in the PI controller brings dead-time compensation capability and shows improved performance for dead-time processes. However, design of robust time delayed PI controller needs much responsiveness for uncertainty in dead-time processes. Hence in this paper, robustness of time delayed PI controller has been analyzed for First Order plus Dead-Time (FOPDT) process model. The process having dead-time greater than three times of time constant is very sensitive to dead-time variation. A first order filter is introduced to ensure robustness. Furthermore, integral time constant of time delayed PI controller is modified to attain better regulatory performance for the lag-dominant processes. The FOPDT process models are classified into dead-time/lag dominated on the basis of dead-time to time constant ratio. A unified tuning method is developed for processes with a number of dead-time to time constant ratio. Several simulation examples and experimental evaluation are exhibited to show the efficiency of the proposed unified tuning technique. The applicability to the process models other than FOPDT such as high-order, integrating, right half plane zero systems are also demonstrated via simulation examples.
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Bibliografia

[1] A. Ingimundarson and T. Hagglund: Robust tuning procedures of deadtime compensating controllers. Control Engineering Practice, 9(11), (2001), 1195–1208, DOI: 10.1016/s0967-0661(01)00065-x. [2] A. O’Dwyer: Handbook of PI and PID Controller Tuning Rules. Imperial College Press, London. 2006. [3] A.R. Pathiran and J. Prakash: Design and implementation of a modelbased PI-like control scheme in a reset configuration for stable single-loop systems. The Canadian Journal of Chemical Engineering, 92(9), (2014), 1651–1660, DOI: 10.1002/cjce.22014. [4] B.D. Tyreus and W.L. Luyben: Tuning PI controllers for integrator/dead time processes. Industrial & Engineering Chemistry Research, 31(11), (1992), 2625–2628, DOI: 10.1021/ie00011a029. [5] D. Efimov, A. Polyakov, L. Fridman,W. Perruquetti, and J.P. Richard: Delayed sliding mode control. Automatica, 64 (2016), 37–43, DOI: 10.1016/j.automatica.2015.10.055. [6] D.E. Rivera, M. Morari, and S. Skogestad: Internal model control: PID controller design. Industrial & Engineering Chemistry Process Design and Development, 25(1), (1986), 252–265, DOI: 10.1021/i200032a041. [7] F. Gao, M. Wu, J. She, and Y. He: Delay-dependent guaranteedcost control based on combination of Smith predictor and equivalentinput- disturbance approach. ISA Transactions, 62, (2016), 215–221, DOI: 10.1016/j.isatra.2016.02.008. [8] F.G. Shinskey: PID-deadtime control of distributed processes. Control Engineering Practice, 9(11), (2001), 1177–1183. DOI: 10.1016/s0967- 0661(01)00063-6. [9] F.G. Shinskey: Process Control Systems – Application, Design, and Tuning. McGraw-Hill, New York. 1998. [10] I.L. Chien: IMC-PID controller design-an extension. IFAC Proceedings, 21(7), (1988), 147–152, DOI: 10.1016/s1474-6670(17)53816-1. [11] J. Lee and T.F. Edgar: Improved PI controller with delayed or filtered integral mode. AIChE Journal, 48(12), (2002), 2844–2850, DOI: 10.1002/aic.690481212. [12] J. Na, X. Ren, R. Costa-Castello, and Y. Guo: Repetitive control of servo systems with time delays. Robotics and Autonomous Systems, 62(3), (2014), 319–329, DOI: 10.1016/j.robot.2013.09.010. [13] J.E. Normey-Rico, C. Bordons and E.F. Camacho: Improving the robustness of dead-time compensating PI controllers. Control Engineering Practice, 5(6), (1997), 801–810, DOI: 10.1016/s0967-0661(97)00064-6. [14] J.E.Normey-Rico, R. Sartori, M. Veronesi, and A. Visioli: An automatic tuning methodology for a unified dead-time compensator. Control Engineering Practice, 27, (2014), 11–22, DOI: 10.1016/j.conengprac.2014.02.001. [15] J.E. Normey-Rico, R.C.C. Flesch, T.L.M. Santos and E.F. Camacho: Comments on A novel dead time compensator for stable processes with long dead times. Journal of Process Control, 22(7), (2012), 1404–1407, DOI: 10.1016/j.jprocont.2012.05.009. [16] K. Kirtania and M.A.A.S. Choudhury: A novel dead time compensator for stable processes with long dead times. Journal of Process Control, 22(3), (2012), 612–625, DOI: 10.1016/j.jprocont.2012.01.003. [17] K.J. Astrom and T. Hagglund: Advanced PID Control. Instrument Society of America, Research Triangle Park, N.C. 2006. [18] K.J. Åstrom and T. Hagglund: The future of PID control. Control Engineering Practice, 9(11), (2001), 1163–1175, DOI: 10.1016/s0967- 0661(01)00062-4. [19] R. Arun, R. Muniraj, and M.S. Willjuice Iruthayarajan: A new controller design method for single loop internal model control systems. Studies in Informatics and Control, 29(2), (2020), 219–229, DOI: 10.24846/v29i2y202007. [20] R. Gudin and L. Mirkin: On the delay margin of dead-time compensators. International Journal of Control, 80(8), (2007), 1316–1332, DOI: 10.1080/00207170701316616. [21] T. Hagglund: An industrial dead-time compensating PI controller. Control Engineering Practice, 4(6), (1996), 749–756, DOI: 10.1016/0967- 0661(96)00065-2. [22] W.K. Ho, C.C. Hang, and L.S. Cao: Tuning of PID controllers based on gain and phase margin specifications. Automatica, 31(3), (1995), 497–502, DOI: 10.1016/0005-1098(94)00130-b. [23] X. Sun, J. Xu, and J. Fu: The effect and design of time delay in feedback control for a nonlinear isolation system, Mechanical Systems and Signal Processing, 87, (2017), 206–217, DOI: 10.1016/j.ymssp.2016.10.022. [24] Y. Wang, F. Yan, S. Jiang, and B. Chen: Time delay control of cabledriven manipulators with adaptive fractional-order nonsingular terminal sliding mode. Advances in Engineering Software, 121, (2018), 13–25, DOI: 10.1016/j.advengsoft.2018.03.004.
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Autorzy i Afiliacje

Arun R. Pathiran
1
R. Muniraj
2
ORCID: ORCID
M. Willjuice Iruthayarajan
3
ORCID: ORCID
S.R. Boselin Prabhu
4
T. Jarin
5
ORCID: ORCID
  1. Department of Electrical and Electronics Technology, Ethiopian Technical University, Addis Ababa, Ethiopia
  2. Department of Electrical and Electronics Engineering, P.S.R. Engineering College, Sivakasi, Virudhunagar District, Tamilnadu, India
  3. Department of Electrical and Electronics Engineering, National Engineering College, Kovilpatti, India
  4. Department of Electronics and Communication Engineering, Surya Engineering College, Mettukadai, India
  5. Department of Electrical and Electronics Engineering, Jyothi Engineering College, Thrissur, India

Explicit commutativity conditions for second-order linear time-varying systems with non-zero initial conditions

Mehmet Emir Koksal
Archives of Control Sciences | 2019 | vol. 29 | No 3 | 529–548 | DOI: 10.24425/acs.2019.130204
Słowa kluczowe commutativity linear systems analogue control robust control differential equations non-zero initial conditions
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Abstrakt

Although the explicit commutativitiy conditions for second-order linear time-varying systems have been appeared in some literature, these are all for initially relaxed systems. This paper presents explicit necessary and sufficient commutativity conditions for commutativity of second-order linear time-varying systems with non-zero initial conditions. It has appeared interesting that the second requirement for the commutativity of non-relaxed systems plays an important role on the commutativity conditions when non-zero initial conditions exist. Another highlight is that the commutativity of switched systems is considered and spoiling of commutativity at the switching instants is illustrated for the first time. The simulation results support the theory developed in the paper.
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Autorzy i Afiliacje

Mehmet Emir Koksal
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