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We address optimal control problems on the space of measures for an objective containing a smooth functional and an optimal transport regularization. That is, the quadratic Monge-Kantorovich distance between a given prior measure and the…
The optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion…
We consider the minimum-energy control of a car, which is modelled as a point mass sliding on the ground in a fixed direction, and so it can be mathematically described as the double integrator. The control variable, representing the…
Collisions are common in many dynamical systems with real applications. They can be formulated as hybrid dynamical systems with discontinuities automatically triggered when states transverse certain manifolds. We present an algorithm for…
We consider a discrete-time linear-quadratic Gaussian control problem in which we minimize a weighted sum of the directed information from the state of the system to the control input and the control cost. The optimal control and sensing…
Optimal control problems with symmetries often admit a non stationary turnpike property called trim turnpike, which characterizes the convergence of optimal solutions to certain symmetry induced trajectories called trim primitives. In this…
This paper considers the relaxed version of the transport problem for general nonlinear control systems, where the objective is to design time-varying feedback laws that transport a given initial probability measure to a target probability…
In this paper, problems of optimal control are considered where in the objective function, in addition to the control cost there is a tracking term that measures the distance to a desired stationary state. The tracking term is given by some…
We consider the problem of controlling in minimum time a two-level quantum system which can be subject to a drift. The control is assumed to be bounded in magnitude, and to affect two or three independent generators of the dynamics. We…
In addition to the theoretical value of challenging optimal control problmes, recent progress in autonomous vehicles mandates further research in optimal motion planning for wheeled vehicles. Since current numerical optimal control…
This paper focusses on the optimal control problems governed by fourth-order linear elliptic equations with clamped boundary conditions in the framework of the Hessian discretisation method (HDM). The HDM is an abstract framework that…
The trajectory optimization of the atmospheric entry of a reusable launch vehicle is studied. The objective is to maximize the crossrange of the vehicle subject to two control-inequality path constraints, two state-inequality path…
In this paper we discuss the numerical solution of elliptic distributed optimal control problems with state or control constraints when the control is considered in the energy norm. As in the unconstrained case we can relate the…
This paper devotes to the development of an optimal acceleration/speed profile for autonomous vehicles approaching a traffic light. The design objective is to achieve both short travel time and low energy consumption as well as avoid idling…
A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed…
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…
Modern optimal control theory involves adjoining the already known equations of motion of a dynamic system to the objective function using dynamic costates; this is done in order to constrain the optimal control solutions to satisfy the…
In this paper, we first design a time optimal control problem for the heat equation with sampled-data controls, and then use it to approximate a time optimal control problem for the heat equation with distributed controls. Our design is…
This paper studies an optimal control problem for continuous-time stochastic systems subject to reachability objectives specified in a subclass of metric interval temporal logic specifications, a temporal logic with real-time constraints.…
This paper presents, using dynamical system theory, a framework for investigating the turnpike property in nonlinear optimal control. First, it is shown that a turnpike-like property appears in general dynamical systems with hyperbolic…