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The paper focuses on mean-field type multi-agent control problems with finite state and action spaces where the dynamics and cost structures are symmetric and homogeneous, and are affected by the distribution of the agents. A standard…
The aim of this work is to make a survey on recent sufficient optimality conditions for optimal control problems with time delays in both state and control variables. The results are obtained by transforming delayed optimal control problems…
This paper develops a unified methodology for probabilistic analysis and optimal control design for jump diffusion processes defined by polynomials. For such systems, the evolution of the moments of the state can be described via a system…
This paper considers an optimal impulse control problem of dynamical systems generated by a flow. The performance criteria are total costs over the infinite time horizon. Apart from the main performance to be minimized, there are multiple…
Large-scale networked systems typically operate under resource constraints, and it is also difficult to exactly obtain the network structure between nodes. To address these issues, this paper investigates a sparse optimal control for…
Existing methods for nonlinear robust control often use scenario-based approaches to formulate the control problem as nonlinear optimization problems. Increasing the number of scenarios improves robustness, while increasing the size of the…
This paper studies the finite-horizon robust optimal control of constrained linear systems subject to model mismatch and additive stochastic disturbances. Utilizing the system level synthesis (SLS) parameterization, we propose a novel SLS…
This paper is concerned with the design of optimal control for finite-dimensional control-affine nonlinear dynamical systems. We introduce an optimal control problem that specifically optimizes nonlinear observability in addition to…
Optimal control of the singular nonlinear parabolic PDE which is a distributional formulation of multidimensional and multiphase Stefan-type free boundary problem is analyzed. Approximating sequence of finite-dimensional optimal control…
In this paper we study the problem of synthesizing optimal control policies for uncertain continuous-time nonlinear systems from syntactically co-safe linear temporal logic (scLTL) formulas. We formulate this problem as a sequence of…
We present a methodology for bounding the error term of an asymptotic solution to a singularly perturbed optimal control (SPOC) problem whose exact solution is known to be computationally intractable. In previous works, reduced or…
Infinite-dimensional linear conic formulations are described for nonlinear optimal control problems. The primal linear problem consists of finding occupation measures supported on optimal relaxed controlled trajectories, whereas the dual…
We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite…
An optimal control problem for the continuity equation is considered. The aim of a "controller" is to maximize the total mass within a target set at a given time moment. The existence of optimal controls is established. For a particular…
This paper introduces a novel approach to the optimal control of linear discrete-time systems subject to bounded disturbances. Our approach is based on the newly established duality between ellipsoidal approximations of reachable and hardly…
It has been recently established that a deterministic infinite horizon discounted optimal control problem in discrete time is closely related to a certain infinite dimensional linear programming problem and its dual. In the present paper,…
The present work deals with quantitative two-phase reach-avoid problems on nonlinear control systems. This class of optimal control problem requires the plant's state to visit two (rather than one) target sets in succession while minimizing…
We consider the problem of robotic planning under uncertainty in this paper. This problem may be posed as a stochastic optimal control problem, a solution to which is fundamentally intractable owing to the infamous "curse of…
This paper discusses the problem of assembly line control and introduces an optimal control formulation that can be used to improve the performance of the assembly line, in terms of cycle time minimization, resources' utilization, etc. A…
This survey is focused on certain sequential decision-making problems that involve optimizing over probability functions. We discuss the relevance of these problems for learning and control. The survey is organized around a framework that…