Related papers: Backward Linear Control Systems on Time Scales
A notion of $L^p$-exact controllability is introduced for linear controlled (forward) stochastic differential equations, for which several sufficient conditions are established. Further, it is proved that the $L^p$-exact controllability,…
This work focuses on developing a data-driven framework using Koopman operator theory for system identification and linearization of nonlinear systems for control. Our proposed method presents a deep learning framework with recursive…
Koopman operator theory yields powerful tools for modeling, analysis, and control of nonlinear dynamical systems. Prominently, linear time-invariant (LTI) Koopman representations have been proposed to enable the application of linear…
We study the time-inconsistent linear quadratic optimal control problem for forward-backward stochastic differential equations with potentially indefinite cost weighting matrices for both the state and the control variables. Our research…
In this paper we will generalize the Kalman rank condition for the null controllability to $n$-coupled linear degenerate parabolic systems with constant coefficients, diagonalizable diffusion matrix, and $m$-controls. For that we prove a…
This paper studies the Kalman decomposition for linear quantum systems. Contrary to the classical case, the coordinate transformation used for the decomposition must belong to a specific class of transformations as a consequence of the laws…
Duality between estimation and control is a foundational concept in Control Theory. Most students learn about the elementary duality -- between observability and controllability -- in their first graduate course in linear systems theory.…
Online optimal control of quadruped robots would enable them to adapt to varying inputs and changing conditions in real time. A common way of achieving this is linear model predictive control (LMPC), where a quadratic programming (QP)…
Given a linear control system in a Hilbert space with a bounded control operator, we establish a characterization of exponential stabilizability in terms of an observability inequality. Such dual characterizations are well known for exact…
The duality between controllability and observability enables methods developed for full-state control to be applied to full-state estimation, and vice versa. In applications in which control or estimation of all state variables is…
The Koopman operator allows for handling nonlinear systems through a (globally) linear representation. In general, the operator is infinite-dimensional - necessitating finite approximations - for which there is no overarching framework.…
This paper focuses on the discrete-time backward stochastic linear quadratic (BSLQ) optimal control problem with nonhomogeneous system terms and cost function cross terms. The terminal constraint of such systems distinguishes it from…
This review surveys previous and recent results on null controllability and inverse problems for parabolic systems with dynamic boundary conditions. We aim to demonstrate how classical methods such as Carleman estimates can be extended to…
Time-fractional parabolic equations with a Caputo time derivative are considered. For such equations, we explore and further develop the new methodology of the a-posteriori error estimation and adaptive time stepping proposed in [7]. We…
In this paper, we study the null controllability of forward and backward stochastic semilinear complex Ginzburg-Landau equations with global Lipschitz nonlinear terms. For this purpose, by deriving an improved global Carleman estimates for…
The problem of existence of solutions to nabla differential equations and nabla differential inclusions on time scales is considered. Under a special form of the set-valued constraint map, sufficient conditions for the existence of at least…
Given a finite-dimensional time continuous control system and $\varepsilon>0$, we address the question of the existence of controls that maintain the corresponding state trajectories in the $\varepsilon$-neighborhood of any prescribed path…
This paper explores the decentralized control of linear deterministic systems in which different controllers operate based on distinct state information, and extends the findings to the output feedback scenario. Assuming the controllers…
The goal of the present article is to study controllability properties of mixed systems of linear parabolic-transport equations, with possibly non-diagonalizable diffusion matrix, on the one-dimensional torus. The equations are coupled by…
In the context of the linear programming (LP) approach to data-driven control, one assumes that the dynamical system is unknown but can be observed indirectly through data on its evolution. Both theoretical and empirical evidence suggest…