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 -