The property of forward invariance of a subset of 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.
In the present paper, we study the problem of small-time local attainability (STLA) of a closed set. For doing this, we introduce a new concept of variations of the reachable set well adapted to a given closed set and prove a new attainability result for a general dynamical system. This provide our main result for nonlinear control systems. Some applications to linear and polynomial systems are discussed and STLA necessary and sufficient conditions are obtained when the considered set is a hyperplane....
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...
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.
In the present paper, we study the problem of small-time local attainability (STLA) of a closed set. For doing this, we introduce a new concept of variations of the reachable set well adapted to a given closed set and prove a new attainability result for a general dynamical system. This provide our main result for nonlinear control systems. Some applications to linear and polynomial systems are discussed and STLA necessary and sufficient conditions are obtained when the considered set...
The importance of “control variations” for obtaining local approximations of the reachable set of nonlinear control systems is well known. Heuristically, if one can construct control variations in all possible directions, then the considered control system is small-time locally controllable (STLC). Two concepts of control variations of higher order are introduced for the case of smooth control systems. The relation between these variations and the small-time local controllability is studied and...
∗Partially supported by Grant MM409/94 Of the Ministy of Science and Education, Bulgaria. ∗∗Partially supported by Grant MM442/94 of the Ministy of Science and Education, Bulgaria. Let M be a complete C1−Finsler manifold without boundary and f : M → R be a locally Lipschitz function. The classical proof of the well known deformation lemma can not be extended in this case because integral lines may not exist. In this paper we establish existence of deformations generalizing the classical...
We study a nonlinear functional differential model of an anaerobic digestion process of wastewater treatment with biogas production. The model equations of biomass include two different discrete time delays. A mathematical analysis of the model is completed including existence and local stability of nontrivial equilibrium points, existence and boundedness of the model solutions as well as global stabilizability towards an admissible equilibrium point. We propose and apply a numerical extremum seeking algorithm...
[Donchev Tzanko; Дончев Цанко]; [Krastanov Mikhail; Кръстанов Михаил]; [Ribarska Nadezhda; Рибарска Надежда]; [Tsachev Tsvetomir; Цачев Цветомир]; [Zlateva Nadia; Златева Надя]
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