Related papers: On Absolute Equivalence and Linearization I
In this paper, we consider the problems of approximating uncertainties and feedback control for a class of nonlinear systems without full-known states, and two approximation methods are proposed: universal approximation using integral-chain…
In this manuscript, we investigate symbolic abstractions that capture the behavior of piecewise-affine systems under input constraints and bounded external noise. This is accomplished by considering local affine feedback controllers that…
This paper deals with optimal control problems for systems affine in the control variable. We consider nonnegativity constraints on the control, and finitely many equality and inequality constraints on the final state. First, we obtain…
In this paper we consider $(x,u)$-flat nonlinear control systems with two inputs, and show that every such system can be rendered static feedback linearizable by prolongations of a suitably chosen control. This result is not only of…
This paper introduces a simulation preorder among lifted systems, a generalization of finite-dimensional Koopman approximations (also known as approximate immersions) to systems with inputs. It is proved that this simulation relation…
Controlling nonlinear systems, especially when data are being used to offset uncertainties in the model, is hard. A natural approach when dealing with the challenges of nonlinear control is to reduce the system to a linear one via change of…
The paper studies the output-feedback synchronization problem for a network of identical, linear time-invariant systems. A criterion to test network synchronization is derived and the class of output-feedback synchronizable systems is…
A careful reexamination of the quantization of systems with first- and second-class constraints from the point of view of coherent-state phase-space path integration reveals several significant distinctions from more conventional…
This paper is concerned with the stabilization problem of singular fractional order systems with order $\alpha\in(0,2)$. In addition to the sufficient and necessary condition for observer based control, a sufficient and necessary condition…
Determining whether a nonlinear multi-input system is differentially flat remains challenging. One way to obtain computationally tractable sufficient conditions is to give complete characterizations of flat normal forms. We introduce a…
We present sufficient conditions under which a given linear nonautonomous system and its nonlinear perturbation are topologically conjugated. Our conditions are of a very general form and provided that the nonlinear perturbations are…
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 known Pfaffian structure of the boundary spin correlations, and more generally order-disorder correlation functions, is given a new explanation through simple topological considerations within the model's random current representation.…
We focus on a chaotic differential system in 3-dimension, including an absolute term and a line of equilibrium points. Which describes in the following This system has an implementation in electronic components. The first purpose of this…
This paper deals with the stabilization problem for nonlinear control-affine systems with the use of oscillating feedback controls. We assume that the local controllability around the origin is guaranteed by the rank condition with Lie…
An equivalence between the $\mathrm{Schr\ddot{o}dinger}$ dynamics of a quantum system with a finite number of basis states and a classical dynamics is presented. The equivalence is an isomorphism that connects in univocal way both dynamical…
For periodic linear control systems with bounded control range, an autonomized system is introduced by adding the phase to the state of the system. Here a unique control set (i.e., a maximal set of approximate controllability) with nonvoid…
Coalescing particles on a line merge when they meet. As they do, their basins of attraction merge and the walls between basins disappear. If every site is initially occupied, these walls at any positive time form a Pfaffian point process:…
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…
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…