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Minimum-time navigation within constrained and dynamic environments is of special relevance in robotics. Seeking time-optimality, while guaranteeing the integrity of time-varying spatial bounds, is an appealing trade-off for agile vehicles,…
In this paper we estimate the minimal controllability time for a class of non-linear control systems with a bounded convex state constraint. An explicit expression is given for the controllability time if the image of the control matrix is…
Recently, a theory for stochastic optimal control in non-linear dynamical systems in continuous space-time has been developed (Kappen, 2005). We apply this theory to collaborative multi-agent systems. The agents evolve according to a given…
In this paper we consider the minimum time population transfer problem for a two level quantum system driven by {\em two} external fields with bounded amplitude. The controls are modeled as real functions and we do not use the Rotating Wave…
When an optimal control problem is solved for all possible initial conditions at once, the initial-state space splits into critical regions, each carrying a closed-form control law that can be evaluated online without solving any…
We consider a nonlinear system, affine with respect to an unbounded control $u$ which is allowed to range in a closed cone. To this system we associate a Bolza type minimum problem, with a Lagrangian having sublinear growth with respect to…
We present an algebraic framework to study the time-optimal synthesis of arbitrary unitaries in SU(2), when the control set is restricted to rotations around two non-parallel axes in the Bloch sphere. Our method bypasses commonly used…
We present a branch-and-bound algorithm for globally solving parabolic optimal control problems with binary switches that have bounded variation and possibly need to satisfy further combinatorial constraints. More precisely, for a given…
A major challenge in autonomous driving is designing control architectures that guarantee safety in all relevant driving scenarios. Given a safe desired reference trajectory for the vehicle, a trajectory following controller has to ensure…
We consider a vibrating string that is fixed at one end with Neumann control action at the other end. We investigate the optimal control problem of steering this system from given initial data to rest, in time T , by minimizing an objective…
This paper focuses on optimal control problem for a class of discrete-time nonlinear systems. In practical applications, computation time is a crucial consideration when solving nonlinear optimal control problems, especially under real-time…
In this paper, we propose a trajectory optimization for computing smooth collision free trajectories for nonholonomic curvature bounded vehicles among static and dynamic obstacles. One of the key novelties of our formulation is a hierarchal…
We find the attainable set for a control system on the free Carnot group of rank $3$ and step $2$ with positive controls. This kind of control systems is connected with the theory of free Lie semigroups; with some estimates for…
This article concerns a class of time-optimal state constrained control problems with dynamics defined by an ordinary differential equation involving a three-dimensional steady flow vector field. The problem is solved via an indirect method…
We present a Pontryagin maximum principle for discrete time optimal control problems with (a) pointwise constraints on the control actions and the states, (b) frequency constraints on the control and the state trajectories, and (c)…
In this article, we are interested in optimal aircraft trajectories in climbing phase. We consider the cost index criterion which is a convex combination of the time-to-climb and the fuel consumption. We assume that the thrust is constant…
We consider stochastic control with discretionary stopping for the drift of a diffusion process over an infinite time horizon. The objective is to choose a control process and a stopping time to minimize the expectation of a convex terminal…
Time-optimal control of a multi-rotor remains an open problem due to the under-actuation and nonlinearity of its dynamics, which make it difficult to solve this problem directly. In this paper, the time-optimal control problem of the…
This paper completely solves the controllability problems of two-dimensional multi-input discrete-time bilinear systems with and without drift. Necessary and sufficient conditions for controllability, which cover the existing results, are…
We establish three tractable, jointly sufficient conditions for the control landscapes of non-linear control systems to be trap free comparable to those now well known in quantum control. In particular, our results encompass end-point…