最优化与控制

Optimal maintenance policies play an important role in the reliability analysis of repairable systems. This paper examines a two-unit priority standby system with a repair facility, where the priority unit is subject to preventive…

This paper proposes a stabilizing state-feedback control law for vector-valued state systems with a scalar control input, governed by a general class of integral difference equations that incorporate both pointwise and distributed input…

We consider nonlinear model predictive control (MPC) schemes without stabilizing terminal conditions, where the model used in the optimization step is generated based on input-output data only. We establish exponential stability for…

This letter presents an optimal-transport (OT)-driven, distributionally robust attack detection algorithm, OT-DETECT, for cyber-physical systems (CPS) modeled as partially observed linear stochastic systems. The underlying detection problem…

We consider continuous-time heterogeneous agent models with recursive utility (Epstein-Zin utility) cast as mean field games, in which agents prefer late resolution of uncertainty. The model leads to a system coupling a pair of…

High intermittent renewable penetration in the energy mix presents challenges in robustness for the management of power systems' operation. If a tail realization of the distribution of weather yields a prolonged period of time during which…

We present a theoretical analysis of stochastic optimization methods in terms of their sensitivity with respect to the step size. We identify a key quantity that, for each method, describes how the performance degrades as the step size…

For first-order optimization of non-convex functions with Lipschitz continuous gradient and Hessian, the best known complexity for reaching an $\varepsilon$-approximation of a stationary point is $\mathcal{O}(\varepsilon^{-7/4})$. Existing…

Time-optimal control for triple integrator under full box constraints is a fundamental problem in the field of optimal control, which has been widely applied in the industry. However, scenarios involving asymmetric constraints,…

This paper introduces specular differentiation, which generalizes G\^ateaux and Fr\'echet differentiation in normed vector spaces. We investigate its fundamental theoretical properties and establish weak forms of the Mean Value Theorem and…

We present a functional calculus treatment of Entropic Optimal Transport (EOT) between Gaussian measures on separable Hilbert spaces, providing a unified framework that handles infinite-dimensional degeneracy. By leveraging the notion of…

We propose a mathematically principled PDE gradient flow framework for distributionally robust optimization (DRO). Exploiting the recent advances in the intersection of Markov Chain Monte Carlo sampling and gradient flow theory, we show…

We introduce and study a new class of generalized convex functions termed star quasiconvex functions. This class includes convex, star-convex, quasiconvex, quasar-convex, and positively homogeneous functions of any degree $p>0$ as special…

A variant of consensus based distributed gradient descent (\textbf{DGD}) is studied for finite sums of smooth but possibly non-convex functions. In particular, the local gradient term in the fixed step-size iteration of each agent is…

We study a class of constrained nonconvex-nonconcave minimax optimization problems in which the inner maximization involves potentially complex constraints. Under the assumption that the inner problem of a novel lifted minimax reformulation…

We use classical tools from calculus of variations to formally derive necessary conditions for a Markov control to be optimal in a standard finite time horizon stochastic control problem. As an example, we solve the well-known Merton…

We address the stabilization of linear, time-varying parabolic PDEs using finite-dimensional receding horizon controls (RHCs) derived from reduced-order models (ROMs). We first prove exponential stability and suboptimality of the…

In this paper, we investigate the problem of decentralized online resource allocation in the presence of Byzantine attacks. In this problem setting, some agents may be compromised due to external manipulations or internal failures, causing…

Reliability-based design optimization (RBDO) is a methodology for designing systems and components under the consideration of probabilistic uncertainty. In practical engineering, the number of input data is often limited, which can damage…

We introduce a new algorithm to solve constrained nonlinear optimal control problem, with an emphasis on low-thrust trajectory in highly nonlinear dynamics. The algorithm, dubbed Pontryagin-Bellman Differential Dynamic Programming (PDDP),…