相关论文: Non-linear Symmetry-preserving Observer on Lie Gro…
This paper presents the equivariant systems theory and observer design for second order kinematic systems on matrix Lie groups. The state of a second order kinematic system on a matrix Lie group is naturally posed on the tangent bundle of…
Trajectory tracking for the kinematic unicycle has been heavily studied for several decades. The unicycle admits a natural $\SE(2)$ symmetry, a key structure exploited in many of the most successful nonlinear controllers in the literature.…
In this paper we derive structure theorems that characterize the spaces of linear and non-linear differential operators that preserve finite dimensional subspaces generated by polynomials in one or several variables. By means of the useful…
This paper extends the application of a recently proposed nonlinear observer (cubic observer) for state estimation of linear systems with unknown inputs and delays. The generalized structure proposed here, makes it possible to establish a…
Lie group analysis of differential equations is a generally recognized method, which provides invariant solutions, integrability, conservation laws etc. In this paper we present three characteristic examples of the construction of invariant…
Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal…
In this paper, we consider several geometric inverse problems for linear elliptic systems. We prove uniqueness and stability results. In particular, we show the way that the observation depends on the perturbations of the domain. In some…
This paper considers the observability of nonlinear systems from a Koopman operator theoretic perspective--and in particular--the effect of symmetry on observability. We first examine an infinite-dimensional linear system (constructed using…
In various applications in the field of control engineering the estimation of the state variables of dynamic systems in the presence of unknown inputs plays an important role. Existing methods require the so-called observer matching…
We compute the full isometry group of any left invariant metric on a simply connected, non-unimodular Lie group of dimension three. As an application, we determine the index of symmetry of such metrics and prove that the singularities of…
The aim of this note is to present a unified approach to the results given in \cite{bb99} and \cite{bs04} which also covers examples of models not presented in these two papers (e.g. $d$-dimensional Minkowski space-time for $d\geq 3$).…
The design of a nonlinear Luenberger observer for a parametrized linear SISO (single-input single-output) system is studied. From an observability assumption of the system, the existence of such an observer is concluded. In a second step, a…
A fixed-order set-valued observer is presented for linear parameter-varying systems with bounded-norm noise and under completely unknown attack signals, which simultaneously finds bounded sets of states and unknown inputs that include the…
State estimation for linear time-invariant systems with unknown inputs is a fundamental problem in various research domains. In this article, we establish conditions for the design of unknown input observers (UIOs) from a geometric approach…
This manuscript focuses on the $\mathcal{H}_\infty$ observer design for a class of nonlinear discrete systems under the presence of measurement noise or external disturbances. Two new Linear Matrix Inequality (LMI) conditions are developed…
Lie symmetry analysis is one of the powerful tools to analyze nonlinear ordinary differential equations. We review the effectiveness of this method in terms of various symmetries. We present the method of deriving Lie point symmetries,…
Let M be an analytic manifold modelled on an ultrametric Banach space over a complete ultrametric field. Let f be an analytic diffeomorphism from M onto itself and p be a fixed point of f. We discuss invariant manifolds around p, like…
A fifth-order KdV equation with time dependent coefficients and linear damping has been studied. Symmetry groups have several different applications in the context of nonlinear differential equations. For instance, they can be used to…
For a system of partial differential equations admitting point, contact, or higher symmetries, the framework of invariant reduction systematically computes how invariant geometric structures, such as conservation laws, presymplectic…
We present a new scheme of defining invariant observables for general relativistic systems. The scheme is based on the introduction of an observer which endowes the construction with a straightforward physical interpretation. The…