Related papers: Efficient Reachable Sets on Lie Groups Using Lie A…
We consider the decidability of state-to-state reachability in linear time-invariant control systems over continuous time. We analyse this problem with respect to the allowable control sets, which are assumed to be the image under a linear…
We present variational theory for optimal control over a finite time interval in quantum systems with relaxation. The corresponding Euler-Lagrange equations determining the optimal control field are derived. In our theory the optimal…
Anytime sampling-based methods are an attractive technique for solving kino-dynamic motion planning problems. These algorithms scale well to higher dimensions and can efficiently handle state and control constraints. However, an intelligent…
The usefulness in control theory of the geometric theory of motion on Lie groups and homogeneous spaces will be shown. We quickly review some recent results concerning two methods to deal with these systems, namely, a generalization of the…
In this paper we study reachability verification problems of stochastic discrete-time dynamical systems over the infinite time horizon. The reachability verification of interest in this paper is to certify specified lower and upper bounds…
In this paper, we introduce the group version of a Lie-Leibniz triple, which we call a Lie group-rack triple. We define a Lie group-rack triple whose tangent structure is a Lie-Leibniz triple, which is a generalization of an augmented Lie…
We consider the decidability of state-to-state reachability in linear time-invariant control systems over discrete time. We analyse this problem with respect to the allowable control sets, which in general are assumed to be defined by…
We present an operator-algebraic approach to the quantization and reduction of lattice field theories. Our approach uses groupoid C*-algebras to describe the observables and exploits Rieffel induction to implement the quantum gauge…
This paper considers discrete-time linear systems with bounded additive disturbances, and studies the convergence properties of the backward reachable sets of robust controlled invariant sets (RCIS). Under a simple condition, we prove that…
Neural Networks (NNs) can provide major empirical performance improvements for closed-loop systems, but they also introduce challenges in formally analyzing those systems' safety properties. In particular, this work focuses on estimating…
While a natural fit for modeling and understanding mobile networks, time-varying graphs remain poorly understood. Indeed, many of the usual concepts of static graphs have no obvious counterpart in time-varying ones. In this paper, we…
We establish the exponential law for suitably topologies on spaces of vector-valued smooth functions on topological groups, where smoothness is defined by using differentiability along continuous one-parameter subgroups. As an application,…
This paper presents an optimization-based solution to task and motion planning (TAMP) on mobile manipulators. Logic-geometric programming (LGP) has shown promising capabilities for optimally dealing with hybrid TAMP problems that involve…
Problems involving control of large ensmebles of structurally identical dynamical systems, called \emph{ensemble control}, arise in numerous scientific areas from quantum control and robotics to brain medicine. In many of such applications,…
We investigate the theory of affine group schemes over a symmetric tensor category, with particular attention to the tangent space at the identity. We show that this carries the structure of a restricted Lie algebra, and can be viewed as…
Reachable sets for a dynamical system describe collections of system states that can be reached in finite time, subject to system dynamics. They can be used to guarantee goal satisfaction in controller design or to verify that unsafe…
In the first part of this paper we introduced an algorithm that uses reachable set approximation to approximate the minimum time function of linear control problems. To illustrate the error estimates and to demonstrate differences to other…
Neural networks (NNs) have been shown to learn complex control laws successfully, often with performance advantages or decreased computational cost compared to alternative methods. Neural network controllers (NNCs) are, however, highly…
A tautological system, introduced in [16][17], arises as a regular holonomic system of partial differential equations that govern the period integrals of a family of complete intersections in a complex manifold $X$, equipped with a suitable…
This paper deals with some reachability issues for piecewise linear switched systems with time-dependent coefficients and multiplicative noise. Namely, it aims at characterizing data that are almost reachable at some fixed time T > 0…