相关论文: Optimal control of ODEs with state suprema
Optimal Control (OC) is the process of determining control and state trajectories for a dynamic system, over a period of time, in order to optimize a given performance index. With the increasing of variables and complexity, OC problems can…
We give answer to an open question by proving a sufficient optimality condition for state-linear optimal control problems with time delays in state and control variables. In the proof of our main result, we transform a delayed state-linear…
The paper is concerned with an optimal control problem governed by the rate-independent system of quasi-static perfect elasto-plasticity. The objective is optimize the displacement field in the domain occupied by the body by means of…
The paper is devoted to deriving necessary optimality conditions in a general optimal control problem for dynamical systems governed by controlled sweeping processes with hard-constrained control actions entering both polyhedral moving sets…
We consider the design of smoothings of the (coordinate-wise) max function in $\mathbb{R}^d$ in the infinity norm. The LogSumExp function $f(x)=\ln(\sum^d_i\exp(x_i))$ provides a classical smoothing, differing from the max function in value…
Optimal control of stochastic nonlinear dynamical systems is a major challenge in the domain of robot learning. Given the intractability of the global control problem, state-of-the-art algorithms focus on approximate sequential optimization…
Here an original idea is suggested to prove the existence of optimal control for some types of non- linear problems. The obtained results can be considered as individual existence theorems (in some sense).
The paper presents an approach to studying optimal control problems in the space of nonnegative measures with dynamics given by a nonlocal balance law. This approach relies on transforming the balance law into a continuity equation in the…
We make some remarks on a variant of the classical Tikhonov regularization in optimal control under PDEs which allows for a certain flexibility in dealing with non-linearities and state restrictions, in the sense that differential…
A general maximum principle (necessary and sufficient conditions) for an optimal control problem governed by a stochastic differential equation driven by an infinite dimensional martingale is established. The solution of this equation takes…
This paper considers the problem of regulating a dynamical system to equilibria that are defined as solutions of an input- and state-constrained optimization problem. To solve this regulation task, we design a state feedback controller…
In this paper, we discuss optimality conditions for optimization problems involving random state constraints, which are modeled in probabilistic or almost sure form. While the latter can be understood as the limiting case of the former, the…
We establish the existence of an optimal control for a general class of singular control problems with state constraints. The proof uses weak convergence arguments and a time rescaling technique. The existence of optimal controls for…
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…
In ergodic singular stochastic control problems, a decision-maker can instantaneously adjust the evolution of a state variable using a control of bounded variation, with the goal of minimizing a long-term average cost functional. The cost…
In this paper, we consider a state constrained optimal control problem governed by the transient Stokes equations. The state constraint is given by an L2 functional in space, which is required to fulfill a pointwise bound in time. The…
We consider the problem of stochastic optimal control in the presence of an unknown disturbance. We characterize the disturbance via empirical characteristic functions, and employ a chance constrained approach. By exploiting properties of…
In this paper we study an optimal control problem with nonsmooth mixed state and control constraints. In most of the existing results, the necessary optimality condition for optimal control problems with mixed state and control constraints…
Optimal sampled-data control of a nonlinear system is considered with the stable-manifold approach and extensive use of numerical techniques. The idea is to notice the Hamiltonian system associated with the considered optimal control…
We present a novel reformulation of nonsmooth differential equations with state jumps which enables their easier simulation and use in optimal control problems without the need of using integer variables. The main idea is to introduce an…