· Journal of Convex Analysis· 0 citations· 10 references
Abstract
In non-autonomous time-optimal control problems the question of the sufficiency of the maximum principle is considered. We also briefly discuss the question of uniqueness of optimal control. New conditions are obtained that guarantee the sufficiency of the maximum principle in terms of convex analysis, properties of matrices in the linear system, the geometry of the control set and the nonempty interior of some set-valued integrals. Examples that demonstrate the unimprovability of the obtained results are considered
This paper presents a finite-time stabilization method for the integrator chain via optimal control techniques by introducing a tailored cost function. We analyze key properties of the resulting value function to derive the corresponding Hamilton-Jacobi-Bellman equation. Numerical simulations illustrate the effectivene...
Parametric optimal control problems for semilinear parabolic equations are considered. Using recent Lipschitz stability results for solutions of such problems, it is shown that, under standard coercivity conditions, the solutions are Bouligand differentiable (in
L^p
L
p
, p finite) functions o...
K. Malanowski· Journal of Convex Analysis· 5 citations· ⚡1
This paper studies a dynamical system approach for solving indefinite quadratic programming problems subject to linear constraints. We investigate the convergence of the trajectory generated by the system to a Karush-Kuhn-Tucker point of the quadratic programs. In addition, we derive an estimate for the distance betwee...
This paper uses the commutant lifting theorem for representations of
the nest algebra to deal with the optimal control of infinite dimensional linear time-varying systems. We solve the model matching problem and a certain optimal feedback control problem, each of which corresponds with one type of four-block problem.
W...
Liu Liu, Yu-Feng Lu· Communications in Mathematic...· 0 citations
We consider control-affine optimal control problems on the torus, where the dynamics and cost functions are only accessed through samples. Starting from a weak formulation of such problems, we derive a dual, a primal, and a primal-dual formulation, compatible with stochastic optimization. We show convergence of stochas...
Eloıse Berthier, Z. Kobeissi, F. Bach· 0 citations
We consider a dynamic system with a perturbation in the right side. The perturbation is given by some geometrical restriction. We consider the question: find a feedback control that stabilizes a solution of the system required to be viable in a given compact convex subset? We construct minimal, in a certain sense, cont...
M. V. Balashov· Journal of Convex Analysis· 0 citations
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