相关论文: Turnpike in optimal control and beyond: a survey
Traffic dynamics is universally crucial in analyzing and designing almost any network. This article introduces a novel theoretical approach to analyzing network traffic dynamics. This theory's machinery is based on the notion of traffic…
Model predictive control (MPC) is a popular strategy for urban traffic management that is able to incorporate physical and user defined constraints. However, the current MPC methods rely on finite horizon predictions that are unable to…
Standard optimal control methods perform optimization in the time domain. However, many experimental settings demand the expression of the control signal as a superposition of given waveforms, a case that cannot easily be accommodated using…
A common goal of quantum control is to maximize a physical observable through the application of a tailored field. The observable value as a function of the field constitutes a quantum control landscape. Previous works have shown, under…
Empirical observations and theoretical studies indicate that the overall travel-time of vehicles in a traffic network can be optimized by means of ramp metering control systems. Here, we present an analysis of traffic data of the highway…
A counterexample to uniqueness of global minimizers of semilinear optimal control problems is given. The lack of uniqueness occurs for a special choice of the state-target in the cost functional. Our arguments show also that, for some…
Controllability, a basic property of various networked systems, has gained profound theoretical applications in complex social, technological, biological, and brain networks. Yet, little attention has been given to the control trajectory…
We present a general holistic theory for the organization of complex networks, both human-engineered and naturally-evolved. Introducing concepts of value of interactions and satisfaction as generic network performance measures, we show that…
The broad success of optimally controlling quantum systems with external fields has been attributed to the favorable topology of the underlying control landscape, where the landscape is the physical observable as a function of the controls.…
We present an information theoretic approach to stochastic optimal control problems that can be used to derive general sampling based optimization schemes. This new mathematical method is used to develop a sampling based model predictive…
We consider the control problem with \textit{exit time}. Unlike the Bolza and Mayer problems, in this problem the terminal time of the trajectories is not fixed, but it is the first time at which they reach a given closed subset -…
At the core of optimal control theory is the Pontryagin maximum principle - the celebrated first order necessary optimality condition - whose solutions are called extremals and which are obtained through a function called Hamiltonian, akin…
Let $\Phi$ be a correspondence from a normed vector space $X$ into itself, let $u: X\to \mathbf{R}$ be a function, and $\mathcal{I}$ be an ideal on $\mathbf{N}$. Also, assume that the restriction of $u$ on the fixed points of $\Phi$ has a…
This note outlines a mean-field approach to dynamic optimal transport problems based on the recently proposed McKean-Pontryagin maximum principle. Key aspects of the proposed methodology include i) avoidance of sampling over stochastic…
We establish structural properties of optimal stopping problems under time-consistent dynamic (coherent) risk measures, focusing on value function monotonicity and the existence of control limit (threshold) optimal policies. While such…
In this paper we revise the theory of turnpikes in discounted Markov decision processes, prove the turnpike theorem for the undiscounted model and apply the results to the specific random walk.
The theory of optimal transportation has developed into a powerful and elegant framework for comparing probability distributions, with wide-ranging applications in all areas of science. The fundamental idea of analyzing probabilities by…
Optimal control is a central problem in quantum thermodynamics. When minimizing dissipated work and work fluctuations defined via the two-point measurement scheme in open quantum systems, existing approaches largely focus on the rapid- and…
In this paper, we investigate system theoretic properties of transient average constrained economic model predictive control (MPC) without terminal constraints. We show that the optimal open-loop solution passes by the optimal steady-state…
The first-order optimality conditions for a generic nonlinear optimization problem are generated as part of the terminal transversality conditions of an optimal control problem. It is shown that the Lagrangian of the optimization problem is…