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We investigate the existence of the solution to the following problem
min φ(x) subject to G(x)=0,
where φ: X → ℝ, G: X → Y and X,Y are Banach spaces. The question of existence is considered in a neighborhood of such point x₀ that the Hessian of the Lagrange function is degenerate. There was obtained an approximation for the distance of solution x* to the initial point x₀.
In this paper we study Lavrentiev-type regularization concepts for linear-quadratic parabolic control problems with pointwise state constraints. In the first part, we apply classical Lavrentiev regularization to a problem with distributed control, whereas in the second part, a Lavrentiev-type regularization method based on the adjoint operator is applied to boundary control problems with state constraints in the whole domain. The analysis for both classes of control problems is investigated and...
In this paper we study Lavrentiev-type regularization concepts for
linear-quadratic parabolic control problems with pointwise state constraints. In
the first part, we apply classical Lavrentiev regularization to a problem with
distributed control, whereas in the second part, a Lavrentiev-type
regularization method based on the adjoint operator is applied to boundary
control problems with state constraints in the whole domain. The analysis for
both classes of control problems is investigated and...
The motivation for this work is the real-time solution of a standard optimal control problem arising in robotics and aerospace applications. For example, the trajectory planning problem for air vehicles is naturally cast as an optimal control problem on the tangent bundle of the Lie Group which is also a parallelizable riemannian manifold. For an optimal control problem on the tangent bundle of such a manifold, we use frame co-ordinates and obtain first-order necessary conditions employing calculus...
The motivation for this work is the real-time solution of a
standard optimal control problem arising in robotics and aerospace
applications. For example, the trajectory planning problem for air
vehicles is naturally cast as an optimal control problem on the
tangent bundle of the Lie Group SE(3), which is also a
parallelizable Riemannian manifold. For an optimal control problem
on the tangent bundle of such a manifold, we use frame
co-ordinates and obtain first-order necessary conditions...
In this paper, we solve an optimal control problem using the
calculus of variation. The system under consideration is a
switched autonomous delay system that undergoes jumps at the
switching times. The control variables are the instants when the
switches occur, and a set of scalars which determine the jump
amplitudes. Optimality conditions involving analytic expressions
for the partial derivatives of a given cost function with respect
to the control variables are derived using the calculus of
variation....
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