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1
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Forward invariant sets, homogeneity and small-time local controllability

100%
Krastanov M.
Banach Center Publications
|
1995
|
tom 32
|
nr 1
287-300
EN
The property of forward invariance of a subset of $R^n$ with respect to a differential inclusion is characterized by using the notion of a perpendicular to a set. The obtained results are applied for investigating the dependence of the small-time local controllability of a homogeneous control system on parameters.
2
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Feedback Nash equilibria in optimal taxation problems

63%
Krastanov M., Rozenov R.
Open Mathematics
|
2009
|
tom 7
|
nr 4
757-774
EN
A well-known result in public economics is that capital income should not be taxed in the long run. This result has been derived using necessary optimality conditions for an appropriate dynamic Stackelberg game. In this paper we consider three models of dynamic taxation in continuous time and suggest a method for calculating their feedback Nash equilibria based on a sufficient condition for optimality. We show that the optimal tax on capital income is generally different from zero.
3
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Nonlinear stabilizing control of an uncertain bioprocess model

63%
Dimitrova N., Krastanov M.
International Journal of Applied Mathematics and Computer Science
|
2009
|
tom 19
|
nr 3
441-454
EN
In this paper we consider a nonlinear model of a biological wastewater treatment process, based on two microbial populations and two substrates. The model, described by a four-dimensional dynamic system, is known to be practically verified and reliable. First we study the equilibrium points of the open-loop system, their stability and local bifurcations with respect to the control variable. Further we propose a feedback control law for asymptotic stabilization of the closed-loop system towards a previously chosen operating point. A numerical extremum seeking algorithm is designed to stabilize the dynamics towards the maximum methane output flow rate in the presence of coefficient uncertainties. Computer simulations in Maple are reported to illustrate the theoretical results.
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