Optimality Conditions For Singular Controls Research Articles

Necessary Optimality Conditions for Singular Controls in Stochastic Goursat–Darboux Systems

Necessary Optimality Conditions for Singular Controls in Stochastic Goursat–Darboux Systems

On Necessary Optimality Conditions for Singular Controls in Dynamical Systems with a Delay in Control

In this article, an optimal control problem with a delay in control is considered. The second-order necessary condition is obtained for the optimality of singular (in the sense of the maximum principle) control. Also, the notion of degenerate singular control of order k (k ≥ 1) is introduced and for optimality of this, the high-order necessary condition is obtained. Moreover, while studying the problem, one of the strengthened version of an analog of the maximum principle is shown. Finally, the rich content of the obtained results is illustrated by specific examples.

ОБ ОПТИМАЛЬНОСТИ ОСОБЫХ УПРАВЛЕНИЙ В ОДНОЙ ЗАДАЧЕ ОПТИМАЛЬНОГО УПРАВЛЕНИЯ

In this paper, a Moskalenko type optimal control problem is considered. We consider the optimal control problem of minimizing the terminal type functional x i S(u,v ) = ф(у (x,)) + J G (x, z (i, , x ))dx, x 0 under constraints u (,,x) e U с R r , (t,x) e D =[t 0 ,t,]x [x 0 ,x,], v(x) e V с R q , x e X - [x 0 ,x,], z t (I,x) - f (I,x,z (I,x),u (I,x)), (t,x) e D, z(t 0 ,x) - у (x), x e X, У ( x 0) - У0. Here, f (t,x,z,u) (g (x,y,v)) is an n-dimensional vector function which is continuous on the set of variables, together with partial derivatives with respect to z (у) up to second order, t 0 , t,, x 0 , x 1 (t 0 0 < x,) are given, ф(у) (G(x,z)) is a given twice continuously differentiable with respect to у (z) scalar function, U (V) is a given nonempty bounded set, and u (t, x) is an r-dimensional control vector function piecewise continuous with respect to t and continuous with respect to x , v(x) is a q-dimensional piecewise continuous vector of control actions. The necessary optimality conditions for singular controls in the sense of the Pontryagin maximum principle have been obtained.

Multipoint Necessary Optimality Conditions for Singular Controls in Processes Described by the System of Volterra Integral Equations

We consider the optimal control problem described by the system of Volterra nonlinear integral equations. The necessary optimality conditions for controls that are singular in the sense of the Pontryagin maximum principle are obtained.

Singular Controls in the Classical Sense for the Optimal Control Problem with Nonlocal Boundary Conditions

We consider an optimal control problem in which the states of the system are determined by the control systems of ordinary differential equations with two-point boundary conditions. Admissible controls are selected from the class of bounded measurable functions with values in an open set. We calculate the increment of the functional formula of the second order. We use variations of the control to derive the necessary optimality conditions for singular controls in the classical sense.

Singular controls in control problems for distributed-parameter systems

The paper gives an overview of necessary optimality conditions for singular controls and second-order necessary optimality conditions for certain classes of optimal control problems described by equations of mathematical physics, two-dimensional integral equations, and discrete two-parameter systems.

Necessary optimality conditions for singular controls

A definition of singular controls with respect to components is given that includes, in particular, the conventional definition. On the basis of this definition, new necessary optimiality conditions for singular controls with respect to components are derived for the processes governed by systems of ordinary differential equations.

On the Theory of Necessary Optimality Conditions in Control Systems

The report is devoted to necessary optimality conditions in terminal control systeme(1) . Terminal systems are widely used in practical probleme: they often appear in problems of control by moving objects, chemical and nuclear reactors, in economice etc. Many problems of optimization are reduced to the terminal control problems.In the report nonsmooth optimization problems, optimal control probleme in hereditary systems are investigated, neceesary optimality conditions for singular controls are given, the method of increment in the state space for getting neceseary optimality conditions is investigated.