16 research outputs found
High-Order Control Variations and Small-Time Local Controllability
The importance of âcontrol variationsâ 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 a new sufficient
STLC condition is proved.* This work is partly supported by the Bulgarian Ministry of Science and Higher Education
â National Fund for Science Research under contract DO 02â359/2008
On the Strong Invariance Property for Non-Lipschitz Dynamics
We provide a new sufficient condition for strong invariance for differential
inclusions, under very general conditions on the dynamics, in terms of a
Hamiltonian inequality. In lieu of the usual Lipschitzness assumption on the
multifunction, we assume a feedback realization condition that can in
particular be satisfied for measurable dynamics that are neither upper nor
lower semicontinuous.Comment: 15 pages, 0 figures. For this revision, the authors added a remark
about an alternative nonconstructive proof of the main resul
Deformation Lemma, Ljusternik-Schnirellmann Theory and Mountain Pass Theorem on C1-Finsler Manifolds
âPartially supported by Grant MM409/94 Of the Ministy of Science and Education, Bulgaria.
ââPartially supported by Grant MM442/94 of the Ministy of Science and Education, Bulgaria.Let M be a complete C1âFinsler manifold without boundary and
f : M â 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 result. This allows us to prove some known results in a more general
setting (minimax theorem, a theorem of Ljusternik-Schnirelmann type, mountain
pass theorem). This approach enables us to drop the compactness assumptions
characteristic for recent papers in the field using the Ekelandâs variational principle
as the main tool
Global Asymptotic Stability of a Functional Differential Model with Time Delay of an Anaerobic Biodegradation Process
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 for maximizing the biogas flow rate in real time.
Numerical simulation results are also included.
ACM Computing Classification System (1998): D.2.6, G.1.10, J.2
Forward invariant sets, homogeneity and small-time local controllability
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
Local small time controllability and attainability of a set for nonlinear control system
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
Stabilization of a Nonlinear Anaerobic Wastewater Treatment Model â
Abstract. A nonlinear anaerobic digester model of wastewater treatment plants is considered. The stabilizability of the dynamic system is studied and a continuous stabilizing feedback, depending only on an online measurable variable, is proposed. Computer simulations are carried out in Maple to illustrate the theoretical results.