Positive 1D and 2D Systems
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Beschreibung
In the last decade a dynamic development in positive systems has been observed. Roughly speaking, positive systems are systems whose inputs, state variables and outputs take only nonnegative values. Examples of positive systems are industrial processes involving chemical reactors, heat exchangers and distillation columns, storage systems, compartmental systems, water and atmospheric pollution models. A variety of models having positive linear system behaviour can be found in engineering, management science, economics, social sciences, biology and medicine, etc. The basic mathematical tools for analysis and synthesis of linear systems are linear spaces and the theory of linear operators. Positive linear systems are defined on cones and not on linear spaces. This is why the theory of positive systems is more complicated and less advanced. The theory of positive systems has some elements in common with theories of linear and non-linear systems. Schematically the relationship between the theories of linear, non-linear and positive systems is shown in the following figure Figure 1.
Will give the reader tools for dealing with uncertainty in control systems which are more advanced and flexible than either traditional optimal control or robust control. Reduces the computational cost of high-quality control and the complexity of the algorithms involved making similar results achievable with less effort by the user.
Demand for Randomized Algorithms for Analysis and Control of Uncertain Systems will come from theoretical control engineers who wish to apply more workable methods to a wide variety of uncertainties (a high proportion of control systems) and from practicing engineers who need a middle path between the restrictive demands of robust control and the unnecessary complications of optimal control.
Autor*in
Tadeusz Kaczorek
Themen in »Positive 1D and 2D Systems«
1D Linear Systems 2D Linear Systems Applied Mathematics Control Systems Theory Discrete-time systems Monte Carlo Method Positive Continuous-time systems algorithms calculus complexity