TY - JOUR
AB - In this work, we consider optimal control problems for mechanical systems with fixed initial and free final state and a quadratic Lagrange term. Specifically, the dynamics is described by a second order ODE containing an affine control term. Classically, Pontryagin's maximum principle gives necessary optimality conditions for the optimal control problem. For smooth problems, alternatively, a variational approach based on an augmented objective can be followed. Here, we propose a new Lagrangian approach leading to equivalent necessary optimality conditions in the form of Euler-Lagrange equations. Thus, the differential geometric structure (similar to classical Lagrangian dynamics) can be exploited in the framework of optimal control problems. In particular, the formulation enables the symplectic discretisation of the optimal control problem via variational integrators in a straightforward way.
AU - Leyendecker, Sigrid
AU - Maslovskaya, Sofya
AU - Ober-Blöbaum, Sina
AU - Almagro, Rodrigo T. Sato Martín de
AU - Szemenyei, Flóra Orsolya
ID - 53101
JF - Journal of Computational Dynamics
KW - Optimal control problem
KW - Lagrangian system
KW - Hamiltonian system
KW - Variations
KW - Pontryagin's maximum principle.
SN - 2158-2491
TI - A new Lagrangian approach to control affine systems with a quadratic Lagrange term
ER -
TY - JOUR
AB - AbstractWe consider the problem of maximization of metabolite production in bacterial cells formulated as a dynamical optimal control problem (DOCP). According to Pontryagin’s maximum principle, optimal solutions are concatenations of singular and bang arcs and exhibit the chattering or Fuller phenomenon, which is problematic for applications. To avoid chattering, we introduce a reduced model which is still biologically relevant and retains the important structural features of the original problem. Using a combination of analytical and numerical methods, we show that the singular arc is dominant in the studied DOCPs and exhibits the turnpike property. This property is further used in order to design simple and realistic suboptimal control strategies.
AU - Caillau, Jean-Baptiste
AU - Djema, Walid
AU - Gouzé, Jean-Luc
AU - Maslovskaya, Sofya
AU - Pomet, Jean-Baptiste
ID - 30861
JF - Journal of Optimization Theory and Applications
KW - Applied Mathematics
KW - Management Science and Operations Research
KW - Control and Optimization
SN - 0022-3239
TI - Turnpike Property in Optimal Microbial Metabolite Production
ER -
TY - JOUR
AU - Djema, Walid
AU - Giraldi, Laetitia
AU - Maslovskaya, Sofya
AU - Bernard, Olivier
ID - 29543
JF - Automatica
KW - Electrical and Electronic Engineering
KW - Control and Systems Engineering
SN - 0005-1098
TI - Turnpike features in optimal selection of species represented by quota models
VL - 132
ER -
TY - CONF
AU - Jean, Frederic
AU - Maslovskaya, Sofya
ID - 20812
SN - 9781728113982
T2 - 2019 IEEE 58th Conference on Decision and Control (CDC)
TI - Injectivity of the inverse optimal control problem for control-affine systems
ER -
TY - JOUR
AU - Jean, Frédéric
AU - Maslovskaya, Sofya
AU - Zelenko, Igor
ID - 29545
IS - 1
JF - Geometriae Dedicata
KW - Geometry and Topology
SN - 0046-5755
TI - On Weyl’s type theorems and genericity of projective rigidity in sub-Riemannian geometry
VL - 213
ER -
TY - GEN
AU - Maslovskaya, Sofya
AU - Caillau, Jean-Baptiste
AU - Djema, Walid
AU - Giraldi, Laetitia
AU - Jean-Luc, Jean-Luc
AU - Pomet, Jean-Baptiste
ID - 29546
TI - The turnpike property in maximization of microbial metabolite production
ER -
TY - CONF
AU - Caillau, Jean-Baptiste
AU - Maslovskaya, Sofya
AU - Mensch, Thomas
AU - Moulinier, Timothee
AU - Pomet, Jean-Baptiste
ID - 20813
SN - 9781728113982
T2 - 2019 IEEE 58th Conference on Decision and Control (CDC)
TI - Zermelo-Markov-Dubins problem and extensions in marine navigation
ER -
TY - CONF
AU - Jean, Frederic
AU - Maslovskaya, Sofya
ID - 20810
SN - 9781538613955
T2 - 2018 IEEE Conference on Decision and Control (CDC)
TI - Inverse optimal control problem: the linear-quadratic case
ER -
TY - JOUR
AU - Jean, Frédéric
AU - Maslovskaya, Sofya
AU - Zelenko, Igor
ID - 20811
JF - Geometriae Dedicata
SN - 0046-5755
TI - On projective and affine equivalence of sub-Riemannian metrics
ER -
TY - THES
AU - Maslovskaya, Sofya
ID - 20815
TI - Inverse Optimal Control : theoretical study
ER -
TY - JOUR
AU - Jean, Frédéric
AU - Maslovskaya, Sofya
AU - Zelenko, Igor
ID - 20809
JF - IFAC-PapersOnLine
SN - 2405-8963
TI - Inverse Optimal Control Problem: the Sub-Riemannian Case
ER -