Related papers: Infinite horizon control and minimax observer desi…
In this note we construct minimax observers for linear stationary DAEs with bounded uncertain inputs, given noisy measurements. We prove a new duality principle and show that a finite (infinite) horizon minimax observer exists if and only…
This paper describes a minimax state estimation approach for linear Differential-Algebraic Equations (DAE) with uncertain parameters. The approach addresses continuous-time DAE with non-stationary rectangular matrices and uncertain bounded…
Author's Summary of the dissertation for the degree of the Candidate of Science (physics and mathematics). The aim of the dissertation is to develop a generalized Kalman Duality concept applicable for linear unbounded non-invertible…
This paper presents a state estimation approach for an uncertain linear equation with a non-invertible operator in Hilbert space. The approach addresses linear equations with uncertain deterministic input and noise in the measurements,…
In this report we address the linear state estimation problem: to estimate a linear transformation $\ell(\varphi)$ of the state $\varphi$ through an algorithm $\widehat{\ell(\varphi)}$ operating on measurements $y$, where…
A finite-horizon optimal estimation problem for discrete-time linear systems is formulated and solved. The formulation is a natural extension of that which yields a deadbeat observer. The resultant observer is the dual of the controller…
This paper is concerned with the problem of state estimation for discrete-time linear systems in the presence of additional (equality or inequality) constraints on the state (or estimate). By use of the minimum variance duality, the…
A linear-quadratic (LQ, for short) optimal control problem is considered for mean-field stochastic differential equations with constant coefficients in an infinite horizon. The stabilizability of the control system is studied followed by…
We study a non standard infinite horizon, infinite dimensional linear-quadratic control problem arising in the physics of non-stationary states (see e.g. \cite{BDGJL4,BertiniGabrielliLebowitz05}): finding the minimum energy to drive a given…
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…
We provide a solution to the problem of receding horizon control for stochastic discrete-time systems with bounded control inputs and imperfect state measurements. For a suitable choice of control policies, we show that the finite-horizon…
This paper is concerned with stochastic linear quadratic (LQ, for short) optimal control problems in an infinite horizon with constant coefficients. It is proved that the non-emptiness of the admissible control set for all initial state is…
This paper investigates an infinite horizon discounted linear-quadratic (LQ) optimal control problem for stochastic differential equations (SDEs) incorporating regime switching and mean-field interactions. The regime switching is modeled by…
Explicit solutions to optimal control problems are rarely obtainable. Of particular interest are the explicit solutions derived for minimax problems, providing a framework to address adversarial conditions and uncertainty. This work…
Finite-time linear-quadratic control of partial differential-algebraic equations (PDAEs) is considered. The discussion is restricted to those that are radial with index $0$; this corresponds to a nilpotency degree of 1. We establish the…
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…
We investigate a state estimation problem for the dynamical system described by uncertain linear operator equation in Hilbert space. The uncertainty is supposed to admit a set-membership description. We present explicit expressions for…
These notes present preliminary results regarding two different approximations of linear infinite-horizon optimal control problems arising in model predictive control. Input and state trajectories are parametrized with basis functions and a…
We revisit the linear programming approach to deterministic, continuous time, infinite horizon discounted optimal control problems. In the first part, we relax the original problem to an infinite-dimensional linear program over a measure…
In this work, we address the output--feedback control problem for nonlinear systems under bounded disturbances using a moving horizon approach. The controller is posed as an optimization-based problem that simultaneously estimates the state…