相关论文: Arrow of Time in Estimation and Control: Duality T…

This paper is concerned with the development and use of duality theory for a hidden Markov model (HMM) with white noise observations. The main contribution of this work is to introduce a backward stochastic differential equation (BSDE) as a…

This thesis is concerned with the stochastic filtering problem for a hidden Markov model (HMM) with the white noise observation model. For this filtering problem, we make three types of original contributions: (1) dual controllability…

This paper is concerned with a characterization of the observability for a continuous-time hidden Markov model where the state evolves as a general continuous-time Markov process and the observation process is modeled as nonlinear function…

Control of non-episodic, finite-horizon dynamical systems with uncertain dynamics poses a tough and elementary case of the exploration-exploitation trade-off. Bayesian reinforcement learning, reasoning about the effect of actions and future…

Duality between estimation and optimal control is a problem of rich historical significance. The first duality principle appears in the seminal paper of Kalman-Bucy, where the problem of minimum variance estimation is shown to be dual to a…

Reversal of the time direction in stochastic systems driven by white noise has been central throughout the development of stochastic realization theory, filtering and smoothing. Similar ideas were developed in connection with certain…

Output controllability and functional observability are properties that enable, respectively, the control and estimation of part of the state vector. These notions are of utmost importance in applications to high-dimensional systems, such…

This paper presents a mathematical framework for causal nonlinear prediction in settings where observations are generated from an underlying hidden Markov model (HMM). Both the problem formulation and the proposed solution are motivated by…

A dual control problem is presented for the optimal stochastic control of a system governed by partial differential equations. Relationships between the optimal values of the original and the dual problems are investigated and two duality…

We study a class of systems whose parameters are driven by a Markov chain in reverse time. A recursive characterization for the second moment matrix, a spectral radius test for mean square stability and the formulas for optimal control are…

This paper is concerned with the development and use of duality theory for a nonlinear filtering model with white noise observations. The main contribution of this paper is to introduce a stochastic optimal control problem as a dual to the…

TWe establish regret lower bounds for adaptively controlling an unknown linear Gaussian system with quadratic costs. We combine ideas from experiment design, estimation theory and a perturbation bound of certain information matrices to…

While the microscopic laws of physics are often symmetric under time reversal, most natural processes that we observe are not. The emergent asymmetry between typical and time-reversed processes is referred to as the arrow of time. In…

A new interpretation of quantum mechanics, similar to the Copenhagen interpretation, is developed from time-symmetry arguments and commonly held principles concerning time and causality. These principles, which are grounded in ideas outside…

We present an extension of Willems' Fundamental Lemma to the class of multi-input multi-output discrete-time feedback linearizable nonlinear systems, thus providing a data-based representation of their input-output trajectories. Two sources…

We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Under a qualification condition, we show that the problem is…

This paper addresses the problems of stabilization, robust control, and observer design for nonlinear systems. We build upon recently a proposed method based on contraction theory and convex optimization, extending the class of systems to…

Dual control addresses the trade-off between exploitation and exploration, where control inputs both regulate the system and generate informative data for estimation and identification. For certain problem classes, control and estimation…

The purpose of this paper is to highlight the central role that the time asymmetry of stability plays in feedback control. We show that this provides a new perspective on the use of doubly-infinite or semi-infinite time axes for signal…

Bases, mappings, projections and metrics, natural for Neural network training, are introduced. Graph-theoretical interpretation is offered. Non-Gaussianity naturally emerges, even in relatively simple datasets. Training statistics,…