We consider a type of routing problems common in defence and security, in which we control a fleet of unmanned aerial vehicles (UAVs) that have to reach one or more target locations without being detected by an adversary. Detection can be carried out by a variety of sensors (radio receivers, cameras, personnel, etc) placed by … Read more
Quantum optimal control is a technique for controlling the evolution of a quantum system and has been applied to a wide range of problems in quantum physics. We study a binary quantum control optimization problem, where control decisions are binary-valued and the problem is solved in diverse quantum algorithms. In this paper, we utilize classical … Read more
Linear-Quadratic-Gaussian (LQG) control is a fundamental control paradigm that is studied in various fields such as engineering, computer science, economics, and neuroscience. It involves controlling a system with linear dynamics and imperfect observations, subject to additive noise, with the goal of minimizing a quadratic cost function for the state and control variables. In this work, … Read more
\(\) A fundamental challenge in learning an unknown dynamical system is to reduce model uncertainty by making measurements while maintaining safety. In this work, we formulate a mathematical definition of what it means to safely learn a dynamical system by sequentially deciding where to initialize the next trajectory. In our framework, the state of the … Read more
We present a new algorithm for addressing nonconvex Mixed-Integer Nonlinear Programs (MINLPs) where the cost function is of nonlinear least squares form. We exploit this structure by leveraging a Gauss-Newton quadratic approximation of the original MINLP, leading to the formulation of a Mixed-Integer Quadratic Program (MIQP), which can be solved efficiently. The integer solution of the … Read more
This paper studies duality and optimality conditions for general convex stochastic optimization problems. The main result gives sufficient conditions for the absence of a duality gap and the existence of dual solutions in a locally convex space of random variables. It implies, in particular, the necessity of scenario-wise optimality conditions that are behind many fundamental … Read more
Robust controllers that stabilize dynamical systems even under disturbances and noise are often formulated as solutions of nonsmooth, nonconvex optimization problems. While methods such as gradient sampling can handle the nonconvexity and nonsmoothness, the costs of evaluating the objective function may be substantial, making robust control challenging for dynamical systems with high-dimensional state spaces. In … Read more
For the fast approximate solution of Mixed-Integer Non-Linear Programs (MINLPs) arising in the context of Mixed-Integer Optimal Control Problems (MIOCPs) a decomposition algorithm exists that solves a sequence of three comparatively less hard subproblems to determine an approximate MINLP solution. In this work, we propose a problem formulation for the second algorithm stage that is … Read more
The aim of this paper is to formulate several questions related to distributionally robust Stochastic Optimal Control modeling. As an example, the distributionally robust counterpart of the classical inventory model is discussed in details. Finite and infinite horizon stationary settings are considered. Article Download View Distributionally Robust Modeling of Optimal Control
We consider nonlinear optimization problems that involve surrogate models represented by neural net-works. We demonstrate first how to directly embed neural network evaluation into optimization models, highlight a difficulty with this approach that can prevent convergence, and then characterize stationarity of such models. We then present two alternative formulations of these problems in the specific … Read more