最优化与控制
Electric power infrastructure faces increasing risk of damage and disruption due to wildfire. Operators of power grids in wildfire-prone regions must consider the potential impacts of unpredictable fires. However, traditional wildfire…
We present a novel relaxation framework for general mixed-integer nonlinear programming (MINLP) grounded in computational geometry. Our approach constructs polyhedral relaxations by convexifying finite sets of strategically chosen points,…
In this paper, we will investigate the moment exponential stabilization of highly nonlinear hybrid stochastic differential delay equations. A periodically intermittent controller based on discrete time state observations with asynchronous…
This paper presents novel theoretical results to guarantee multi-agent set invariance using Matrix Control Barrier Functions in sampled-data systems. More specifically, the paper presents conditions under which heterogeneous control-affine…
We formulate and study a class of two-player zero-sum stochastic dynamic games with partial and asymmetric information. Information asymmetry introduces fundamental challenges involving \emph{belief representation} and \emph{theory of mind}…
Sparsity is a fundamental modeling principle in statistics, signal processing, and data science. However, optimization with sparsity constraints is notoriously difficult. We introduce a new convex relaxation framework for {sparse…
The U.S. power grid is undergoing a major paradigm shift with the increased development of renewable generators, electric vehicles, and data centers. In response to this growing need, the U.S. has ramped up the construction of…
To explore the feasibility of avoiding the confident error (or hallucination) of generation models (GMs), we formalise the system of GMs as a class of stochastic dynamical systems through the lens of control theory. Numerous factors can be…
In this paper, we propose a descent method for composite optimization problems with linear operators. Specifically, we first design a structure-exploiting preconditioner tailored to the linear operator so that the resulting preconditioned…
Complex engineered systems require coordinated design choices across heterogeneous components under multiple conflicting objectives and uncertain specifications. Monotone co-design provides a compositional framework for such problems by…
The leader-following consensus problem for general linear multi-agent systems over jointly connected switching networks has been a challenging problem and the solvability of the problem has been limited to the class of linear multi-agent…
The optimal controller design problem for a linear, first-order spatially-invariant distributed parameter system is considered. Through a case study of the Linear Quadratic Regulator (LQR) problem for the diffusion equation over the torus,…
Finding the state feedback control in an $% H^{\infty }$-optimal control problem involves a challenging approach of the associated algebraic Riccati equation of the generic form $A^{\ast }P+PA+P\Gamma P=F$. In view of this objective, we…
It was recently established that for convex optimization problems with sparse optimal solutions (be it entry-wise sparsity or matrix rank-wise sparsity) it is possible to design first-order methods with linear convergence rates that depend…
The set of real matrices of upper-bounded rank is a real algebraic variety called the real generic determinantal variety. An explicit description of the tangent cone to that variety is given in Theorem 3.2 of Schneider and Uschmajew [SIAM…
The Fr\'{e}chet mean is a fundamental notion of central tendency defined as a minimizer of a sum of squared distances in a general metric space. In this paper, we study Fr\'{e}chet means in tropical geometry -- a piecewise linear,…
We investigate the well-posedness in the Hadamard sense and the absence of price manipulation in the optimal execution problem within the Almgren-Chriss framework, where the temporary and permanent impact parameters vary deterministically…
Overconservatism has long been recognized as a major issue with robust optimization, despite its key advantages of tractability, performance guarantee, and limited information. To address this issue, a new criterion is proposed that can…
We consider a multi-commodity Dynamic Traffic Assignment (DTA) problem formulated as a network flow control problem on the Cell Transmission Model (CTM). The objective is to design optimal control policies using variable speed limits, ramp…
In this letter, we derive minimum-energy controls for a broad class of control-affine systems using a Lagrange multiplier fixed-point equation and a generally non-symmetric Gramian-like matrix. In feasible coercivity classes, this fixed…