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Attempts from different disciplines to provide a fundamental understanding of deep learning have advanced rapidly in recent years, yet a unified framework remains relatively limited. In this article, we provide one possible way to align…
In this paper, we consider the problem of multi-objective optimal control of a dynamical system with additive and multiplicative noises with given second moments and arbitrary probability distributions. The objectives are given by quadratic…
MPC (Model predictive control)-based motion planning and trajectory generation are essential in applications such as unmanned aerial vehicles, robotic manipulators, and rocket control. However, the real-time implementation of such…
The problem of constrained Markov decision process is considered. An agent aims to maximize the expected accumulated discounted reward subject to multiple constraints on its costs (the number of constraints is relatively small). A new dual…
A large-scale complex system comprising many, often spatially distributed, dynamical subsystems with partial autonomy and complex interactions are called system of systems. This paper describes an efficient algorithm for model predictive…
Safety is one of the fundamental challenges in control theory. Recently, multi-step optimal control problems for discrete-time dynamical systems were formulated to enforce stability, while subject to input constraints as well as…
The paper concerns the study of new classes of nonlinear and nonconvex optimization problems of the so-called infinite programming that are generally defined on infinite-dimensional spaces of decision variables and contain infinitely many…
We propose a Model Predictive Control (MPC) with a single-step prediction horizon to approximate the solution of infinite horizon optimal control problems with the expected sum of convex stage costs for constrained linear uncertain systems.…
In this article, we survey the primary research on polyhedral computing methods for constrained linear control systems. Our focus is on the modeling power of convex optimization, featured to design set-based robust and optimal controllers.…
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,…
We are interested in risk constraints for infinite horizon discrete time Markov decision processes (MDPs). Starting with average reward MDPs, we show that increasing concave stochastic dominance constraints on the empirical distribution of…
We consider the problem of estimating a probability distribution that maximizes the entropy while satisfying a finite number of moment constraints, possibly corrupted by noise. Based on duality of convex programming, we present a novel…
We consider a broad class of dynamic programming (DP) problems that involve a partially linear structure and some positivity properties in their system equation and cost function. We address deterministic and stochastic problems, possibly…
This material provides thorough tutorials on some optimization techniques frequently used in various engineering disciplines, including convex optimization, linearization techniques and mixed-integer linear programming, robust optimization,…
This paper studies the problem of mapping optimization in decentralized control problems. A global optimization algorithm is proposed based on the ideas of ``deterministic annealing" - a powerful non-convex optimization framework derived…
Traditional maximum entropy and sparsity-based algorithms for analytic continuation often suffer from the ill-posed kernel matrix or demand tremendous computation time for parameter tuning. Here we propose a neural network method by convex…
Control theory plays a pivotal role in understanding and optimizing the behavior of complex dynamical systems across various scientific and engineering disciplines. Two key frameworks that have emerged for modeling and solving control…
In this paper we introduce the notion of optimization under control and communication constraint in a robotic network. Starting from a general setup, we focus our attention on the problem of achieving rendezvous in minimum time for a…
A class of infinite horizon optimal control problems involving $L^p$-type cost functionals with $0<p\leq 1$ is discussed. The existence of optimal controls is studied for both the convex case with $p=1$ and the nonconvex case with $0<p<1$,…
Markov Decision Processes (MDPs) have been used to formulate many decision-making problems in science and engineering. The objective is to synthesize the best decision (action selection) policies to maximize expected rewards (minimize…