最优化与控制

This paper addresses the challenge of ensuring safety in stochastic control systems with high-relative-degree constraints, while maintaining feasibility and mitigating conservatism in risk evaluation. Control Barrier Functions (CBFs)…

In this paper, we analyze the convergence rate of the Jacobi-Proximal Alternating Direction Method of Multipliers (ADMM) initially introduced by Deng et al. for the block-structured optimization problem with linear constraint. The algorithm…

In almost all algorithms for Model Predictive Control (MPC), the most time-consuming step is to solve some form of Linear Quadratic (LQ) Optimal Control Problem (OCP) repeatedly. The commonly recognized best option for this is a Riccati…

We study the problem of finding curves of minimum pointwise-maximum arc-length derivative of curvature, here simply called curves of minimax spirality, among planar curves of fixed length with prescribed endpoints and tangents at the…

We develop a parallel-in-time multigrid preconditioner for augmented systems. These saddle-point systems are foundational to numerical optimization. Our preconditioner, when paired with a suitable optimization method, accelerates the…

In this paper, we consider non-smooth convex optimization with a zeroth-order oracle corrupted by symmetric stochastic noise. Unlike the existing high-probability results requiring the noise to have bounded $\kappa$-th moment with $\kappa…

In this paper we propose a novel adaptive online optimization algorithm tailored to the management of microgrids with high renewable energy penetration, which can be formulated as a constrained, online optimization problem. The proposed…

We develop a robust linear-quadratic mean-field control framework for systemic risk under model uncertainty, in which a central bank jointly optimizes interest rate policy and supervisory monitoring intensity against adversarial…

This paper establishes a unified framework connecting local controllability, necessary conditions for optimality, and attainability in free-time optimal control problems. The central object of our investigation is the $\Lambda$-set, which…

The increasing penetration of renewable energy requires greater use of storage resources to manage system intermittency. As a result, there is growing interest in evaluating the opportunity cost of stored energy, or usage values, which can…

Prediction-correction algorithms are a highly effective class of methods for solving pseudo-convex optimization problems. The descent direction of these algorithms can be viewed as an adjustment to the gradient direction based on the…

This paper proposes a dual Riemannian alternating direction method of multipliers (ADMM) for solving low-rank semidefinite programs with unit diagonal constraints. We recast the ADMM subproblem as a Riemannian optimization problem over the…

An absorbing game is a stochastic game with a single nonabsorbing state. Such a game is called recursive if all players receive a payoff of 0 in the nonabsorbing state, and positive if all payoffs in absorbing states are positive. An action…

We propose a simple safety filter design for stochastic discrete-time systems based on piecewise affine probabilistic control barrier functions, providing an appealing balance between modeling flexibility and computational complexity. Exact…

This paper studies distributed convex optimization with both affine equality and nonlinear inequality couplings through the duality analysis. We first formulate the dual of the coupling-constraint problem and reformulate it as a consensus…

In a mean field game of controls, a large population of identical players seek to minimize a cost that depends on the joint distribution of the states of the players and their controls. We first consider the classes of mean field games of…

We present a novel method to synthesize a terminal cost function for a nonlinear model predictive controller (MPC) through value function approximation using supervised learning. Existing methods enforce a descent property on the terminal…

This paper studies the discrete-time linear-quadratic-Gaussian mean field (MF) social control problem in an infinite horizon, where the dynamics of all agents are unknown. The objective is to design a reinforcement learning (RL) algorithm…

We investigate a dynamic inverse problem using a regularization which implements the so-called Wasserstein-$1$ distance. It naturally extends well-known static problems such as lasso or total variation regularized problems to a (temporally)…

In this paper, we introduce the notion of boundary delay equations, establishing a unified framework for analyzing linear time-invariant systems with pure time-delayed boundary conditions. We establish mild sufficient conditions for the…