Related papers: A Linear Test for Global Nonlinear Controllability
We consider affine control systems with two scalar controls, such that one control vector field vanishes at an equilibrium state. We state two necessary conditions of local controllability around this equilibrium, involving the iterated Lie…
In this work, we investigate the approximate controllability of a class of one-dimensional degenerate parabolic equations with Robin boundary conditions. The degeneracy occurs at one endpoint of the spatial domain, and we apply an impulsive…
This work studies the design of safe control policies for large-scale non-linear systems operating in uncertain environments. In such a case, the robust control framework is a principled approach to safety that aims to maximize the…
Reliable controllers with high flexibility and performance are necessary for the control of intricate, advanced, and expensive systems such as aircraft, marine vessels, automotive vehicles, and satellites. Meanwhile, control allocation has…
In this paper we investigate the controllability and observability properties of a family of linear dynamical systems, whose structure is induced by the Laplacian of a grid graph. This analysis is motivated by several applications in…
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…
This paper studies controllability properties of recurrent neural networks. The new contributions are: (1) an extension of the result in the previous paper "Complete controllability of continuous-time recurrent neural networks" (Sontag and…
In this work we provide a computationally tractable procedure for designing affine control policies, applied to constrained, discrete-time, partially observable, linear systems subject to set bounded disturbances, stochastic noise and…
We investigate the universality of multi-spin systems in architectures of various symmetries of coupling type and topology. Explicit reachability sets under symmetry constraints are provided. Thus for a given (possibly symmetric)…
This paper is concerned with the controllability problem of a connected threshold graph following the Laplacian dynamics. An algorithm is proposed to generate a spanning set of orthogonal Laplacian eigenvectors of the graph from a…
An optimal control problem on finite-dimensional positive cones is stated. Under a critical assumption on the cone, the corresponding Bellman equation is satisfied by a linear function, which can be computed by convex optimization. A…
This paper is devoted to the study of the null and approximate controllability for some classes of linear coupled parabolic systems with less controls than equations. More precisely, for a given bounded domain in R^N, we consider a system…
In the comparison of nonholonomic mechanics and constrained variational mechanics, invariant affine subbundles arise in the determination of the initial conditions where the two methods yield the same trajectories. Motivated by this,…
Positive systems describing networks with inherently non-negative states and inputs arise naturally in routing, logistics, and compartmental modelling. We consider problems modelled as positive linear systems in incidence form with linear…
We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time domains. The approach here is based on…
This paper is devoted to the controllability of a general linear hyperbolic system in one space dimension using boundary controls on one side. Under precise and generic assumptions on the boundary conditions on the other side, we previously…
Contraction theory is a recently developed dynamic analysis and nonlinear control system design tool based on an exact differential analysis of convergence. This paper extends contraction theory to local and global stability analysis of…
This paper presents a constraint-lifting control framework for designing stabilizing controllers that guarantee the forward invariance of a prescribed safe set. State-of-the-art safety-enforcing methods, such as control barrier functions…
This paper tackles the problem of nonlinear systems, with sublinear growth but unbounded control, under perturbation of some time-varying state constraints. It is shown that, given a trajectory to be approximated, one can find a neighboring…
This paper is concerned with data-driven optimal control of nonlinear systems. We present a convex formulation to the optimal control problem (OCP) with a discounted cost function. We consider OCP with both positive and negative discount…