Related papers: Second-order analysis for the time crisis problem
This paper studies a kind of minimal time control problems related to the exact synchronization for a controlled linear system of parabolic equations. Each problem depends on two parameters: the bound of controls and the initial state. The…
Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second-…
Time crystals are many-body systems that spontaneously break time-translation symmetry, and thus exhibit long-range spatiotemporal order and robust periodic motion. Recent results have demonstrated how to build time-crystal phases in driven…
Motivated by the applications, a class of optimal control problems is investigated, where the goal is to influence the behavior of a given population through another controlled one interacting with the first. Diffusive terms accounting for…
Nonlinear contraction theory is a comparatively recent dynamic control system design tool based on an exact differential analysis of convergence, in essence converting a nonlinear stability problem into a linear time-varying stability…
In this paper, we consider a time-optimal control problem with uncertainties. Dynamics of controlled object is expressed by crisp linear system of differential equations with fuzzy initial and final states. We introduce a notion of fuzzy…
We study a system of nonlinear partial differential equations resulting from the traditional modelling of oil engineering within the framework of the mechanics of a continuous medium. Recent results on the problem provide existence,…
This paper is the second part of our series of work to establish pointwise second-order necessary conditions for stochastic optimal controls. In this part, we consider the general cases, i.e., the control region is allowed to be nonconvex,…
This paper introduces a novel approach to the optimal control of linear discrete-time systems subject to bounded disturbances. Our approach is based on the newly established duality between ellipsoidal approximations of reachable and hardly…
In this paper, we propose a new control design scheme for solving the obstacle avoidance problem for nonlinear driftless control-affine systems. The class of systems under consideration satisfies controllability conditions with iterated Lie…
Recently, there has been a growing interest in developing inventory control policies which are robust to model misspecification. One approach is to posit that nature selects a worst-case distribution for any stochastic primitives from some…
Many physical phenomena, governed by partial differential equations (PDEs), are second order in nature. This makes sense to pose the control on the second order derivatives of the field solution, in addition to zero and first order ones, to…
We consider a bilinear optimal control for an evolution equation involving the fractional Laplace operator of order $0<s<1$. We first give some existence and uniqueness results for the considered evolution equation. Next, we establish some…
This paper provides necessary and sufficient conditions of optimality for variational problems that deal with a fractional derivative with respect to another function. Fractional Euler--Lagrange equations are established for the fundamental…
We consider a singular stochastic control problem, which is called the Monotone Follower Stochastic Control Problem and give sufficient conditions for the existence and uniqueness of a local-time type optimal control. To establish this…
In this work, optimality conditions and classical results from duality theory are derived for continuous-time linear optimization problems with inequality constraints. The optimality conditions are given in the Karush-Kuhn-Tucker form. Weak…
The paper presents results about strong metric subregularity of the optimality mapping associated with the system of first-order necessary optimality conditions for a problem of optimal control of a semilinear parabolic equation. The…
In this study, we consider an optimal control problem driven by a stochastic differential system with a stopping time terminal cost functional. We establish the stochastic maximum principle for this new kind of an optimal control problem by…
Second-order optimality conditions are essential for nonsmooth optimization, where both the objective and constraint functions are Lipschitz continuous and second-order directionally differentiable. This paper provides no-gap second-order…
For optimal stopping problems with time-inconsistent preference, we measure the inherent level of time-inconsistency by taking the time needed to turn the naive strategies into the sophisticated ones. In particular, when in a repeated…