Related papers: The turnpike property in finite-dimensional nonlin…
We establish structural properties of optimal stopping problems under time-consistent dynamic (coherent) risk measures, focusing on value function monotonicity and the existence of control limit (threshold) optimal policies. While such…
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…
We study global optimization of non-convex functions through optimal control theory. Our main result establishes that (quasi-)optimal trajectories of a discounted control problem converge globally and practically asymptotically to the set…
At the core of optimal control theory is the Pontryagin maximum principle - the celebrated first order necessary optimality condition - whose solutions are called extremals and which are obtained through a function called Hamiltonian, akin…
We investigate different turnpike phenomena of generalized discrete-time stochastic linear-quadratic optimal control problems. Our analysis is based on a novel strict dissipativity notion for such problems, in which a stationary stochastic…
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…
This paper is dedicated to the elementary proof of Pontryagin's maximum principle for problems with free right end point. The proof for the standard problem is taken from the monography of Ioffe and Tichomirov. We assume piecewise…
We consider optimal control problems, where the control appears in the main part of the operator. We derive the Pontryagin maximum principle as a necessary optimality condition. The proof uses the concept of topological derivatives. In…
This note discusses properties of parametric discrete-time Mixed-Integer Optimal Control Problems (MIOCPs) as they often arise in mixed-integer NMPC. We argue that in want for a handle on similarity properties of parametric MIOCPs the…
In this paper, we investigate system theoretic properties of transient average constrained economic model predictive control (MPC) without terminal constraints. We show that the optimal open-loop solution passes by the optimal steady-state…
This paper presents a simulation study on turnpike phenomena in stochastic optimal control problems. We employ the framework of Polynomial Chaos Expansions (PCE) to investigate the presence of turnpikes in stochastic LQ problems. Our…
Transferring a physical system from an initial to a final state while minimizing energetic losses is an interdisciplinary control problem that bridges stochastic thermodynamics and optimal transport theory. Recent research typically…
The fundamental theorem of the theory of optimal control, the Pontryagin maximum principle (PMP), is extended to the setting of almost Lie (AL) algebroids, geometrical objects generalizing Lie algebroids. This formulation of the PMP yields,…
Considering a general nonlinear dissipative finite dimensional optimal control problem in fixed time horizon T , we establish a two-term asymptotic expansion of the value function as $T\rightarrow+\infty$. The dominating term is T times the…
The first-order optimality conditions for a generic nonlinear optimization problem are generated as part of the terminal transversality conditions of an optimal control problem. It is shown that the Lagrangian of the optimization problem is…
We analyze the sensitivity of the extremal equations that arise from the first order necessary optimality conditions of nonlinear optimal control problems with respect to perturbations of the dynamics and of the initial data. To this end,…
In this paper we introduce a new procedure to solve nonlinear optimal control problems with delays which exploits indirect methods combined with numerical homotopy procedures. It is known that solving this kind of problems via indirect…
We extend the Pontryagin Maximum Principle (PMP) to the geometric setting of almost-Lie (AL) algebroids -- objects which generalize Lie algebroids. The result may be understood as a very general reduction scheme for optimal control problems…
We obtain turnpike results for optimal control problems with lack of stabilizability in the state equation and/or detectability in the state term in the cost functional. We show how, under weakened stabilizability/detectability conditions,…
We establish a variety of results extending the well-known Pontryagin maximum principle of optimal control to discrete-time optimal control problems posed on smooth manifolds. These results are organized around a new theorem on critical and…