Related papers: A note on first-order and transversality condition…
In this paper we derive a necessary optimality condition for a local optimal solution of some control problems. These optimal control problems are governed by a semi-linear Vettsel boundary value problem of a linear elliptic equation. The…
We derive existence results and first order necessary optimality conditions for optimal control problems governed by quasilinear parabolic PDEs with a class of first order nonlinearities that include for instance quadratic gradient terms.…
We study the time optimal control problem with a general target $\mathcal S$ for a class of differential inclusions that satisfy mild smoothness and controllability assumptions. In particular, we do not require Petrov's condition at the…
In this paper, we consider the application of optimal periodic control sequences to switched dynamical systems. The control sequence is obtained using a finite-horizon optimal method based on dynamic programming. We then consider Euler…
This work considers infinite-horizon optimal control of positive linear systems applied to the case of network routing problems. We demonstrate the equivalence between Stochastic Shortest Path (SSP) problems and optimal control of a certain…
In this paper we summarize our results in infinite horizon optimal control. We present optimality conditions for weak local minimizer in the framework of weighted functions. Moreover we formulate the Pontryagin Maximum Principle for strong…
This survey collects, within a unified framework, various results (primarily by the authors themselves) on the use of Deterministic Infinite-Dimensional Optimal Control Theory to address applied economic models. The main aim is to…
For an infinite-horizon continuous-time optimal stopping problem under non-exponential discounting, we look for an optimal equilibrium, which generates larger values than any other equilibrium does on the entire state space. When the…
This paper is concerned with a discounted stochastic optimal control problem for regime switching diffusion in an infinite horizon. First, as a preliminary with particular interests in its own right, the global well-posedness of infinite…
Existential rules have been proposed for representing ontological knowledge, specifically in the context of Ontology-Based Query Answering. Entailment with existential rules is undecidable. We focus in this paper on conditions that ensure…
We study the optimal control problem for a control-affine system, where we want to minimize the $L^1$ norm of the control. First, we show how Pontryagin Maximum Principle (PMP) applies to this problem and we divide the extremal trajectories…
In this article we derive a strong version of the Pontryagin Maximum Principle for general nonlinear optimal control problems on time scales in finite dimension. The final time can be fixed or not, and in the case of general boundary…
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…
This paper considers an optimal impulse control problem of dynamical systems generated by a flow. The performance criteria are total costs over the infinite time horizon. Apart from the main performance to be minimized, there are multiple…
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 the determination of the optimal stationary singular stochastic control of a linear diffusion for a class of average cumulative cost minimization problems arising in various financial and economic applications of stochastic…
According to recent results, convergence in a prespecified or prescribed finite time can be achieved under extreme model uncertainty if control is applied continuously over time. This paper shows that this extreme amount of uncertainty…
We consider optimal control problems governed by systems describing the unsteady flows of an incompressible second grade fluid with Navier-slip boundary conditions. We prove the existence of an optimal solution and derive the corresponding…
This paper is devoted to establishing an enhanced Fritz John type first-order necessary condition for a general constrained nonlinear infinite-dimensional optimization problem. Unlike traditional constraint qualifications in optimization…
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,…