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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…
In many resource-limited optimal control problems, multiple constraints may be enforced that are jointly infeasible due to external factors such as subsystem failures, unexpected disturbances, or fuel limitations. In this manuscript, we…
We systematically introduce an approach to the analysis and (numerical) solution of a broad class of nonlinear unconstrained optimal control problems, involving ordinary and distributed systems. Our approach relies on exact representations…
Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…
Quantum optimal control experiments and simulations have successfully manipulated the dynamics of systems ranging from atoms to biomolecules. Surprisingly, these collective works indicate that the effort (i.e., the number of algorithmic…
Deep neural networks are in the limelight of machine learning with their excellent performance in many data-driven applications. However, they can lead to inaccurate predictions when queried in out-of-distribution data points, which can…
Nonlinear receding horizon model predictive control is a powerful approach to controlling nonlinear dynamical systems. However, typical approaches that use the Jacobian, adjoint, and forward-backward passes may lose fidelity and efficacy…
The control landscape for various canonical quantum control problems is considered. For the class of pure-state transfer problems, analysis of the fidelity as a functional over the unitary group reveals no suboptimal attractive critical…
This article provides a review of recent developments in the formulation and execution of optimal control strategies for the dynamics of quantum systems. A brief introduction to the concept of optimal control, the dynamics of of open…
In this paper, stochastic optimal control problems in continuous time and space are considered. In recent years, such problems have received renewed attention from the lens of reinforcement learning (RL) which is also one of our motivation.…
We consider the problem of uncertainty quantification in high dimensional regression and classification for which deep ensemble have proven to be promising methods. Recent observations have shown that deep ensemble often return…
Autonomous driving depends on perception systems to understand the environment and to inform downstream decision-making. While advanced perception systems utilizing black-box Deep Neural Networks (DNNs) demonstrate human-like comprehension,…
In this paper, we address the problem of closed-loop control of nonlinear dynamical systems subjected to probabilistic uncertainties. More precisely, we design time-varying polynomial feedback controllers to follow the given nominal…
This article is aimed at extending the framework of optimal control techniques to the situation where the control field values are restricted to a finite set. We propose a generalization of the standard GRAPE algorithm suited to this…
In optimization problems, the quality of a candidate solution can be characterized by the optimality gap. For most stochastic optimization problems, this gap must be statistically estimated. We show that for risk-averse problems, standard…
Ensuring constraint satisfaction is a key requirement for safety-critical systems, which include most robotic platforms. For example, constraints can be used for modeling joint position/velocity/torque limits and collision avoidance.…
This paper presents an approach to deal with safety of dynamical systems in presence of multiple non-convex unsafe sets. While optimal control and model predictive control strategies can be employed in these scenarios, they suffer from high…
Optimal control problems with oscillations (chattering controls) and concentrations (impulsive controls) can have integral performance criteria such that concentration of the control signal occurs at a discontinuity of the state signal.…
This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization…
A non-equilibrium, generally time-dependent, environment whose form is deduced by optimal learning control is shown to provide a means for incoherent manipulation of quantum systems. Incoherent control by the environment (ICE) can serve to…