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Necessary optimality conditions for quasi-singular controls for systems with Caputo fractional derivatives

Yusubov Shakir Sh., Mahmudov Elimhan N.

Archives of Control Sciences

2023

Vol. 33, No. 3

463--496

In this paper, we consider an optimal control problem in which a dynamical system is controlled by a nonlinear Caputo fractional state equation. First we get the linearized maximum principle. Further, the concept of a quasi-singular control is introduced and, on this basis, an analogue of the Legendre-Clebsch conditions is obtained. When the analogue of Legendre-Clebsch condition degenerates, a necessary high-order optimality condition is derived. An illustrative example is considered.

Extremals in the problem of minimum time obstacle avoidance for a 2D double integrator system

Osmolovskii N. P., Figura A., Koska M., Wojtowicz M.

Control and Cybernetics

2015

Vol. 44, no. 2

185--209

This paper provides an analysis of time optimal control problem of motion of a material point in the plane outside the given circle, without friction. The point is controlled by a force whose absolute value is limited by one. The closure of exterior of the circle plays the role of the state constraint. The analysis of the problem is based on the minimum principle.

On necessary conditions in variable end-time optimal control problems

Ioffe A.

Control and Cybernetics

2005

Vol. 34, no 3

805-817

The paper contains a new necessary optimality condition for optimal control problems with free terminal time and discontinuous time dependence, which, actually is a family of conditions, each corresponding to a continuation of optimal trajectory beyond the optimal time for an arbitrary small interval.

Shape optimization of thermoviscoelastic contact problems

Myśliński A.

Control and Cybernetics

2003

Vol. 32, no 3

611-627

This paper is concerned with a shape optimization problem of a viscoelastic body in unilateral dynamic contact with a rigid foundation. The contact with Coulomb friction is assumed to occur at a portion of the boundary of the body. The nonpenetration condition is described in terms of velocities. The thermal deformation is taken into account. Using the material derivative method as well as the results concerning the regularity of solutions to dynamic variational thermoviscoelastic problem the directional derivative of the cost functional is calculated. A necessary optimality condition is formulated.