Related papers: Constructing Feedback Linearizable Discretizations…
Dynamic feedback linearization-based methods allow us to design control algorithms for a fairly large class of nonlinear systems in continuous time. However, this feature does not extend to their sampled counterparts, i.e., for a given…
Mechanical systems are most often described by a set of continuous-time, nonlinear, second-order differential equations (SODEs) of a particular structure governed by the covariant derivative. The digital implementation of controllers for…
Retraction maps have been generalized to discretization maps in (Barbero Li\~n\'an and and Mart\'{\i}n de Diego, 2022). Discretization maps are used to systematically derive numerical integrators that preserve the symplectic structure, as…
This paper proposes a feedback linearizing law for single-track dynamic models, allowing the design of a trajectory tracking controller exploiting linear control theory. The main characteristics of this algorithm are its simplicity, its…
Differential flatness serves as a powerful tool for controlling continuous time nonlinear systems in problems such as motion planning and trajectory tracking. A similar notion, called difference flatness, exists for discrete-time systems.…
Discretizing continuous-time linear systems typically requires numerical integration. This document presents a convenient method for discretizing the dynamics, input, and process noise state-space matrices of a continuous-time linear system…
We present a new type of feedback linearization that is tailored for mechanical control systems. We call it a mechanical feedback linearization. Its basic feature is preservation of the mechanical structure of the system. For mechanical…
The stabilization of unstable nonlinear systems and tracking control are challenging engineering problems due to the encompassed nonlinearities in dynamic systems and their scale. In the past decades, numerous observer-based control designs…
The problem under consideration is the synthesis of a distributed controller for a nonlinear network composed of input affine systems. The objective is to achieve exponential convergence of the solutions. To design such a feedback law,…
This paper proposes a framework for adaptively learning a feedback linearization-based tracking controller for an unknown system using discrete-time model-free policy-gradient parameter update rules. The primary advantage of the scheme over…
In this article, we present data-driven feedback linearization for nonlinear systems with periodic orbits in the zero-dynamics. This scenario is challenging for data-driven control design because the higher order terms of the internal…
Control systems of interest are often invariant under Lie groups of transformations. For such control systems, a geometric framework based on Lie symmetry is formulated, and from this a sufficient condition for dynamic feedback…
A new geometric procedure to construct symplectic methods for constrained mechanical systems is developed in this paper. The definition of a map coming from the notion of retraction maps allows to adapt the continuous problem to the…
This work studies the design problem of feedback stabilizers for discrete-time systems with input delays. A backstepping procedure is proposed for disturbance-free discrete-time systems. The feedback law designed by using backstepping…
Data-driven control offers a powerful alternative to traditional model-based methods, particularly when accurate system models are unavailable or prohibitively complex. While existing data-driven control methods primarily aim to construct…
The paper proposes an algorithm for a discretization (sampled-time implementation) of a homogeneous control preserving the finite-time and nearly fixed-time stability property of the original (sampling-free) system. The sampling period is…
Linearising the dynamics of nonlinear mechanical systems is an important and open research area. A common approach is feedback linearisation, which is a nonlinear control method that transforms the input-output response of a nonlinear…
The paper addresses the exact linearization of flat nonlinear discrete-time systems by generalized static or dynamic feedbacks which may also depend on forward-shifts of the new input. We first investigate the question which forward-shifts…
This letter presents a data-driven framework for the design of stabilizing controllers from input-output data in the continuous-time, linear, and time-invariant domain. Rather than relying on measurements or reliable estimates of input and…
In this paper, we propose a constructive algorithm to dynamically linearize two-input control systems via successive one-fold prolongations of a control that has to be suitably chosen at each step of the algorithm. Linearization via…