Related papers: Optimal Feedback Law Recovery by Gradient-Augmente…
Microgrids have more operational flexibilities as well as uncertainties than conventional power grids, especially when renewable energy resources are utilized. An energy storage based feedback controller can compensate undesired dynamics of…
Sparse regression models are increasingly prevalent due to their ease of interpretability and superior out-of-sample performance. However, the exact model of sparse regression with an $\ell_0$ constraint restricting the support of the…
This paper considers optimal control of dynamical systems which are represented by nonlinear stochastic differential equations. It is well-known that the optimal control policy for this problem can be obtained as a function of a value…
In this paper, we investigate an optimal control problem governed by parabolic equations with measure-valued controls over time. We establish the well-posedness of the optimal control problem and derive the first-order optimality condition…
This paper studies equality-constrained minimization problems through the lens of feedback control. We introduce a unified control-theoretic framework by showing that a PID feedback law acting on the dual variable induces the PID…
This paper considers the problem of closed-loop identification of linear scalar systems with Gaussian process noise, where the system input is determined by a deterministic state feedback policy. The regularized least-square estimate (LSE)…
Feedback control synthesis for nonlinear, parameter-dependent fluid flow control problems is considered. The optimal feedback law requires the solution of the Hamilton-Jacobi-Bellman (HJB) PDE suffering the curse of dimensionality. This is…
In high-dimensional sparse regression, would increasing the signal-to-noise ratio while fixing the sparsity level always lead to better model selection? For high-dimensional sparse regression problems, surprisingly, in this paper we answer…
The design of the performance index, also referred to as cost or reward shaping, is central to both optimal control and reinforcement learning, as it directly determines the behaviors, trade-offs, and objectives that the resulting control…
The naive application of Reinforcement Learning algorithms to continuous control problems -- such as locomotion and manipulation -- often results in policies which rely on high-amplitude, high-frequency control signals, known colloquially…
We develop and analyze stochastic optimization algorithms for problems in which the expected loss is strongly convex, and the optimum is (approximately) sparse. Previous approaches are able to exploit only one of these two structures,…
Model predictive control (MPC) is based on perpetually solving optimization problems. The solution of the optimization is usually interpreted as the optimal input for the current state. However, the solution of the optimization does not…
We establish a variety of results extending the well-known Pontryagin maximum principle of optimal control to discrete-time optimal control problems posed on smooth manifolds. These results are organized around a new theorem on critical and…
Sparse modeling has been widely and successfully used in many applications such as computer vision, machine learning, and pattern recognition. Accompanied with those applications, significant research has studied the theoretical limits and…
The recent work by Dong & Yang (2023) showed for misspecified sparse linear bandits, one can obtain an $O\left(\epsilon\right)$-optimal policy using a polynomial number of samples when the sparsity is a constant, where $\epsilon$ is the…
We consider the following signal recovery problem: given a measurement matrix $\Phi\in \mathbb{R}^{n\times p}$ and a noisy observation vector $c\in \mathbb{R}^{n}$ constructed from $c = \Phi\theta^* + \epsilon$ where $\epsilon\in…
This paper presents an inverse optimality method to solve the Hamilton-Jacobi-Bellman equation for a class of nonlinear problems for which the cost is quadratic and the dynamics are affine in the input. The method is inverse optimal because…
A new formulation of the particle filter for nonlinear filtering is presented, based on concepts from optimal control, and from the mean-field game theory. The optimal control is chosen so that the posterior distribution of a particle…
Infinite-time nonlinear optimal regulation control is widely utilized in aerospace engineering as a systematic method for synthesizing stable controllers. However, conventional methods often rely on linearization hypothesis, while recent…
In many real-world applications of reinforcement learning (RL), interactions with the environment are limited due to cost or feasibility. This presents a challenge to traditional RL algorithms since the max-return objective involves an…