On the solution of the variational problem of the arc length in 4-dimensinal affine space.
On transformations of singular quadratic functionals corresponding to equation
Optimal control of an inventory system with ameliorating and deteriorating items.
Optimal control of combined therapy in a single strain HIV-1 model.
Optimal control of nonlinear delay systems with implicit derivative and quadratic performance
The existence of optimal control for nonlinear delay systems having an implicit derivative with quadratic performance criteria is proved. The results are established by an iterative technique and using the Darbo fixed point theorem.
Optimal control problem and maximum principle for fractional order cooperative systems
In this paper, by using the classical control theory, the optimal control problem for fractional order cooperative system governed by Schrödinger operator is considered. The fractional time derivative is considered in a Riemann-Liouville and Caputo senses. The maximum principle for this system is discussed. We first study by using the Lax-Milgram Theorem, the existence and the uniqueness of the solution of the fractional differential system in a Hilbert space. Then we show that the considered optimal...
Optimal control processes associated with a class of discontinuous control systems: Applications to sliding mode dynamics
This paper presents a theoretical approach to optimal control problems (OCPs) governed by a class of control systems with discontinuous right-hand sides. A possible application of the framework developed in this paper is constituted by the conventional sliding mode dynamic processes. The general theory of constrained OCPs is used as an analytic background for designing numerically tractable schemes and computational methods for their solutions. The proposed analytic method guarantees consistency...
Optimal controllability of impulsive control systems.
Optimal design of an elastic beam with a unilateral elastic foundation: semicoercive state problem
A design optimization problem for an elastic beam with a unilateral elastic foundation is analyzed. Euler-Bernoulli's model for the beam and Winkler's model for the foundation are considered. The state problem is represented by a nonlinear semicoercive problem of 4th order with mixed boundary conditions. The thickness of the beam and the stiffness of the foundation are optimized with respect to a cost functional. We establish solvability conditions for the state problem and study the existence of...
Optimal impulsive harvest policy for time-dependent logistic equation with periodic coefficients.
Optimal solutions for a model of tumor anti-angiogenesis with a penalty on the cost of treatment
The scheduling of angiogenic inhibitors to control a vascularized tumor is analyzed as an optimal control problem for a mathematical model that was developed and biologically validated by Hahnfeldt et al. [Cancer Res. 59 (1999)]. Two formulations of the problem are considered. In the first one the primary tumor volume is minimized for a given amount of angiogenic inhibitors to be administered, while a balance between tumor reduction and the total amount of angiogenic inhibitors given is minimized...
Optimale Steuerungen. Eine Einführung.
Optimality and sensitivity for semilinear bang-bang type optimal control problems
In optimal control problems with quadratic terminal cost functionals and systems dynamics linear with respect to control, the solution often has a bang-bang character. Our aim is to investigate structural solution stability when the problem data are subject to perturbations. Throughout the paper, we assume that the problem has a (possibly local) optimum such that the control is piecewise constant and almost everywhere takes extremal values. The points of discontinuity are the switching points. In...
Optimality Conditions for a Nonlinear Boundary Value Problem Using Nonsmooth Analysis
We study in this paper a Lipschitz control problem associated to a semilinear second order ordinary differential equation with pointwise state constraints. The control acts as a coefficient of the state equation. The nonlinear part of the equation is governed by a Nemytskij operator defined by a Lipschitzian but possibly nonsmooth function. We prove the existence of optimal controls and obtain a necessary optimality conditions looking somehow to the Pontryagin’s maximum principle. These conditions...
Optimální regulace
Optimization of dynamical systems
Pareto optimality for nonlinear infinite dimensional control systems.
Pointwise minimization of supplemented variational problems
We describe an approach to variational problems, where the solutions appear as pointwise (finite-dimensional) minima for fixed t of the supplemented Lagrangian. The minimization is performed simultaneously with respect to the state variable x and ẋ, as opposed to Pontryagin's maximum principle, where optimization is done only with respect to the ẋ-variable. We use the idea of the equivalent problems of Carathéodory employing suitable (and simple) supplements to the original minimization problem....
Problems of economic system optimization with quadratic criteria and monotone controls. Some algorithms for its numerical solution
Projective Reeds-Shepp car on S2 with quadratic cost
Fix two points and two directions (without orientation) of the velocities in these points. In this paper we are interested to the problem of minimizing the cost along all smooth curves starting from x with direction η and ending in with direction . Here g is the standard Riemannian metric on S2 and is the corresponding geodesic curvature. The interest of this problem comes from mechanics and geometry of vision. It can be formulated as a sub-Riemannian problem on the lens space L(4,1). We...