scholarly journals On controllability for Sturm-Liouville type differential inclusions

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1321-1327
Author(s):  
Aurelian Cernea
Keyword(s):  
Differential Inclusion ◽  
Differential Inclusions ◽  
Sufficient Conditions ◽  
Second Order ◽  
Local Controllability ◽  
Reference Trajectory ◽  
Liouville Type ◽  
Sturm Liouville

We consider a second-order differential inclusion and we obtain sufficient conditions for h-local controllability along a reference trajectory.

scholarly journals On controllability for a class of second-order differential inclusions

2011 ◽  
Vol 27 (1) ◽  
pp. 34-40
Author(s):  
AURELIAN CERNEA ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Inclusion ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Second Order ◽  
Sufficient Condition ◽  
Liouville Type ◽  
Sturm Liouville ◽  
The Right

By using a suitable fixed point theorem a sufficient condition for controllability is obtained for a Sturm-Liouville type differential inclusion in the case when the right hand side has convex values.

Optimal control of higher order differential inclusions with functional constraints

2020 ◽  
Vol 26 ◽  
pp. 37 ◽  
Author(s):  
Elimhan N. Mahmudov
Keyword(s):  
Optimal Control ◽  
Optimality Conditions ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Higher Order ◽  
Second Order ◽  
Sufficient Optimality Conditions ◽  
Functional Constraints ◽  
Complementary Slackness ◽  
Complementary Slackness Conditions

The present paper studies the Mayer problem with higher order evolution differential inclusions and functional constraints of optimal control theory (PFC); to this end first we use an interesting auxiliary problem with second order discrete-time and discrete approximate inclusions (PFD). Are proved necessary and sufficient conditions incorporating the Euler–Lagrange inclusion, the Hamiltonian inclusion, the transversality and complementary slackness conditions. The basic concept of obtaining optimal conditions is locally adjoint mappings and equivalence results. Then combining these results and passing to the limit in the discrete approximations we establish new sufficient optimality conditions for second order continuous-time evolution inclusions. This approach and results make a bridge between optimal control problem with higher order differential inclusion (PFC) and constrained mathematical programming problems in finite-dimensional spaces. Formulation of the transversality and complementary slackness conditions for second order differential inclusions play a substantial role in the next investigations without which it is hardly ever possible to get any optimality conditions; consequently, these results are generalized to the problem with an arbitrary higher order differential inclusion. Furthermore, application of these results is demonstrated by solving some semilinear problem with second and third order differential inclusions.

scholarly journals Distributed Consensus Tracking for Second-Order Nonlinear Multiagent Systems with a Specified Reference State

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Guoguang Wen ◽  
Yongguang Yu ◽  
Zhaoxia Peng ◽  
Ahmed Rahmani
Keyword(s):  
Multiagent Systems ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Second Order ◽  
Lyapunov Theory ◽  
Reference Trajectory ◽  
Distributed Consensus ◽  
Consensus Tracking ◽  
Velocity Information ◽  
Virtual Leader

This paper mainly addresses the distributed consensus tracking problem for second-order nonlinear multiagent systems with a specified reference trajectory. The dynamics of each follower consists of two terms: nonlinear inherent dynamics and a simple communication protocol relying only on the position and velocity information of its neighbors. The consensus reference is taken as a virtual leader, whose output is only its position and velocity information that is available to only a subset of a group of followers. To achieve consensus tracking, a class of nonsmooth control protocols is proposed which reply on the relative information among the neighboring agents. Then some corresponding sufficient conditions are derived. It is shown that if the communication graph associated with the virtual leader and followers is connected at each time instant, the consensus can be achieved at least globally exponentially with the proposed protocol. Rigorous proofs are given by using graph theory, matrix theory, and Lyapunov theory. Finally, numerical examples are presented to illustrate the theoretical analysis.

scholarly journals Global Bifurcation for Second-Order Neumann Problem with a Set-Valued Term

2009 ◽  
Vol 2009 ◽  
pp. 1-16
Author(s):  
Ruyun Ma ◽  
Jiemei Li
Keyword(s):  
Neumann Problem ◽  
Differential Inclusion ◽  
Line Segment ◽  
Global Bifurcation ◽  
Second Order ◽  
Approximation Procedure ◽  
Bifurcation Theorem ◽  
Jump Discontinuities ◽  
Sturm Liouville

We study the global bifurcation of the differential inclusion of the form−(ku′)′+g(⋅,u)∈μF(⋅,u),  u′(0)=0=u′(1), whereFis a “set-valued representation” of a function with jump discontinuities along the line segment[0,1]×{0}. The proof relies on a Sturm-Liouville version of Rabinowitz's bifurcation theorem and an approximation procedure.

Impulsive differential inclusions via variational method

2017 ◽  
Vol 24 (3) ◽  
pp. 313-323 ◽  
Author(s):  
Mouffak Benchohra ◽  
Juan J. Nieto ◽  
Abdelghani Ouahab
Keyword(s):  
Variational Method ◽  
Critical Point ◽  
Differential Inclusion ◽  
Critical Point Theory ◽  
Differential Inclusions ◽  
Point Theory ◽  
Existence Results ◽  
Second Order ◽  
Impulsive Differential Inclusions

AbstractIn this paper, we establish several results about the existence of second-order impulsive differential inclusion with periodic conditions. By using critical point theory, several new existence results are obtained. We also provide an example in order to illustrate the main abstract results of this paper.

scholarly journals Minimum principle and controllability for multiparameter discrete inclusions via derived cones

2006 ◽  
Vol 2006 ◽  
pp. 1-12
Author(s):  
Aurelian Cernea
Keyword(s):  
Optimization Problem ◽  
Minimum Principle ◽  
Sufficient Conditions ◽  
Reachable Set ◽  
Local Controllability ◽  
Reference Trajectory ◽  
Endpoint Constraints ◽  
Discrete Inclusion

We consider a multiparameter discrete inclusion and we prove that the reachable set of a certain variational multiparameter discrete inclusion is a derived cone in the sense of Hestenes to the reachable set of the discrete inclusion. This result allows to obtain sufficient conditions for local controllability along a reference trajectory and a new proof of the minimum principle for an optimization problem given by a multiparameter discrete inclusion with endpoint constraints.

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