Systems theory (engineering): Difference between revisions
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In [[engineering]] and [[mathematics]], '''systems theory''' or '''mathematical systems theory''' refers broadly to the mathematical study of complex systems in engineering and interconnections among such systems. Systems in this context refers to [[dynamical system|dynamical systems]]. | In [[engineering]] and [[mathematics]], '''systems theory''' or '''mathematical systems theory''' refers broadly to the mathematical study of (complex) systems in engineering and interconnections among such systems. Systems in this context refers to [[dynamical system|dynamical systems]]. | ||
The fundamental principle in systems theory is ''mathematical modelling'' of systems. This means that the dynamics of the system or systems under study should be describable or representable by a | The fundamental principle in systems theory is ''mathematical modelling'' of systems. This means that the dynamics of the system or systems under study should be describable or representable by a set of mathematical equations. For example, it may be that the appropriate equations can be derived from first principles by using the laws of [[physics]] or empirically derived by [[system identification]]. A mathematical model is considered essential for a quantitative study of systems and may be used for purposes such as: | ||
*Analysis of the behaviour of systems to make quantitative predictions about | *Analysis of the behaviour of systems to make quantitative predictions about a system's long term behavior. This can be seen for example in the use of mathematical models in the study of population dynamics <ref>F. Bauer and C. Castillo-Chavez, ''Mathematical models in Population Biology and Epidemiology'', ser. Text in Applied Mathematics 40, New York: Springer-Verlag, 2001</ref>. | ||
*Design of another system which can be interconnected with an existing system so that the interconnected system | *Design of another system which can be interconnected with an existing system so that the resulting interconnected system has certain desired properties. This is typically the type of problem studied in [[control engineering]]. | ||
Although systems theory was originally developed in the context of engineering and technological systems, its general principles and tools can in principle be adapted and applied to other types of systems, such as economic and biological systems, as long as mathematical models are available or can be developed. For example, the theory of electrical networks can also be applied to mechanical networks by analogy if the equations representing the latter network are analogous to the equations for the former. More recently, there has been significant activity | Although systems theory was originally developed in the context of engineering and technological systems, its general principles and tools can in principle be adapted and applied to other types of systems, such as economic and biological systems, as long as mathematical models are available or can be developed. For example, the theory of electrical networks can also be applied to mechanical networks by analogy if the equations representing the latter network are analogous to the equations for the former. More recently, there has been significant interest and activity in extending the tools of systems theory for application to complex biological systems within the rapidly expanding field known as [[systems biology]] (see, for example, [http://www.hamilton.ie/systemsbiology/ The Hamilton Institute Systems Biology Group's homepage (retrieved on 2007-09-19)] and the paper <ref>P. Wellstead, "The role of control and system theory in systems biology," edited text of a Plenary Lecture presented at the 10th International Federation of Automatic Control (IFAC) International Symposium on Computer Applications in Biotechnology and the 8th IFAC Symposium on Dynamics and the Control of Process Systems, The Hamilton Institute, 2007, Online: http://www.hamilton.ie/systemsbiology/files/2007/ControlAndSystemsBiology.pdf (retrieved on 2007-9-18).</ref>), bringing biologists, control engineers and applied mathematicians together to study some important and difficult problems in the life sciences. | ||
Systems theory in the above sense is also recognized as a branch of mathematics and is currently assigned the [[American mathematical society|American Mathematical Society's]] [[mathematical subject classification|mathematical subject classification (MSC)]] of 93-xx (Systems theory; control) <ref>2000 Mathematical Subject Classification, American Mathematical Society, Online: http://www.ams.org/msc/ (retrieved on 2007-08-21).</ref><ref>D. Rusin, The Mathematical Atlas (93: Systems Theory;Control), Online: http://www.math.niu.edu/~rusin/known-math/index/93-XX.html (retrieved on 2007-09-19).</ref>. | Systems theory in the above sense is also recognized as a branch of mathematics and is currently assigned the [[American mathematical society|American Mathematical Society's]] [[mathematical subject classification|mathematical subject classification (MSC)]] of 93-xx (Systems theory; control) <ref>2000 Mathematical Subject Classification, American Mathematical Society, Online: http://www.ams.org/msc/ (retrieved on 2007-08-21).</ref><ref>D. Rusin, The Mathematical Atlas (93: Systems Theory;Control), Online: http://www.math.niu.edu/~rusin/known-math/index/93-XX.html (retrieved on 2007-09-19).</ref>. | ||
Revision as of 06:08, 19 September 2007
In engineering and mathematics, systems theory or mathematical systems theory refers broadly to the mathematical study of (complex) systems in engineering and interconnections among such systems. Systems in this context refers to dynamical systems.
The fundamental principle in systems theory is mathematical modelling of systems. This means that the dynamics of the system or systems under study should be describable or representable by a set of mathematical equations. For example, it may be that the appropriate equations can be derived from first principles by using the laws of physics or empirically derived by system identification. A mathematical model is considered essential for a quantitative study of systems and may be used for purposes such as:
- Analysis of the behaviour of systems to make quantitative predictions about a system's long term behavior. This can be seen for example in the use of mathematical models in the study of population dynamics [1].
- Design of another system which can be interconnected with an existing system so that the resulting interconnected system has certain desired properties. This is typically the type of problem studied in control engineering.
Although systems theory was originally developed in the context of engineering and technological systems, its general principles and tools can in principle be adapted and applied to other types of systems, such as economic and biological systems, as long as mathematical models are available or can be developed. For example, the theory of electrical networks can also be applied to mechanical networks by analogy if the equations representing the latter network are analogous to the equations for the former. More recently, there has been significant interest and activity in extending the tools of systems theory for application to complex biological systems within the rapidly expanding field known as systems biology (see, for example, The Hamilton Institute Systems Biology Group's homepage (retrieved on 2007-09-19) and the paper [2]), bringing biologists, control engineers and applied mathematicians together to study some important and difficult problems in the life sciences.
Systems theory in the above sense is also recognized as a branch of mathematics and is currently assigned the American Mathematical Society's mathematical subject classification (MSC) of 93-xx (Systems theory; control) [3][4].
References
- ↑ F. Bauer and C. Castillo-Chavez, Mathematical models in Population Biology and Epidemiology, ser. Text in Applied Mathematics 40, New York: Springer-Verlag, 2001
- ↑ P. Wellstead, "The role of control and system theory in systems biology," edited text of a Plenary Lecture presented at the 10th International Federation of Automatic Control (IFAC) International Symposium on Computer Applications in Biotechnology and the 8th IFAC Symposium on Dynamics and the Control of Process Systems, The Hamilton Institute, 2007, Online: http://www.hamilton.ie/systemsbiology/files/2007/ControlAndSystemsBiology.pdf (retrieved on 2007-9-18).
- ↑ 2000 Mathematical Subject Classification, American Mathematical Society, Online: http://www.ams.org/msc/ (retrieved on 2007-08-21).
- ↑ D. Rusin, The Mathematical Atlas (93: Systems Theory;Control), Online: http://www.math.niu.edu/~rusin/known-math/index/93-XX.html (retrieved on 2007-09-19).