Related papers: Fast Approximate Dynamic Programming for Input-Aff…
We propose a method of approximating multivariate Gaussian probabilities using dynamic programming. We show that solving the optimization problem associated with a class of discrete-time finite horizon Markov decision processes with…
We propose a dual dynamic integer programming (DDIP) framework for solving multi-scale mixed-integer model predictive control (MPC) problems. Such problems arise in applications that involve long horizons and/or fine temporal…
Differential Dynamic Programming (DDP) is one of the indirect methods for solving an optimal control problem. Several extensions to DDP have been proposed to add stagewise state and control constraints, which can mainly be classified as…
Differential Dynamic Programming (DDP) is an efficient trajectory optimization algorithm relying on second-order approximations of a system's dynamics and cost function, and has recently been applied to optimize systems with time-invariant…
In this paper, we develop deterministic fully dynamic algorithms for computing approximate distances in a graph with worst-case update time guarantees. In particular, we obtain improved dynamic algorithms that, given an unweighted and…
We present a method of exploiting symmetries of discrete-time optimal control problems to reduce the dimensionality of dynamic programming iterations. The results are derived for systems with continuous state variables, and can be applied…
Recent advances in symbolic dynamic programming (SDP) combined with the extended algebraic decision diagram (XADD) data structure have provided exact solutions for mixed discrete and continuous (hybrid) MDPs with piecewise linear dynamics…
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…
We consider an inertial primal-dual fixed point algorithm (IPDFP) to compute the minimizations of the following Problem (1.1). This is a full splitting approach, in the sense that the nonsmooth functions are processed individually via their…
A robust-to-dynamics optimization (RDO) problem is an optimization problem specified by two pieces of input: (i) a mathematical program (an objective function $f:\mathbb{R}^n\rightarrow\mathbb{R}$ and a feasible set…
The idea of dynamic programming (DP), proposed by Bellman in the 1950s, is one of the most important algorithmic techniques. However, in parallel, many fundamental and sequentially simple problems become more challenging, and open to a…
Let $P=(P_1, P_2, \ldots, P_n)$, $P_i \in \field{R}$ for all $i$, be a signal and let $C$ be a constant. In this work our goal is to find a function $F:[n]\rightarrow \field{R}$ which optimizes the following objective function: $$ \min_{F}…
We consider a nonlinear ordinary differential equation and want to control its behavior so that it reaches a target by minimizing a cost function. Our approach is to use hybrid systems to solve this problem: the complex dynamic is replaced…
Though switched dynamical systems have shown great utility in modeling a variety of physical phenomena, the construction of an optimal control of such systems has proven difficult since it demands some type of optimal mode scheduling. In…
In this paper, we present a discretization algorithm for finite horizon risk constrained dynamic programming algorithm in [Chow_Pavone_13]. Although in a theoretical standpoint, Bellman's recursion provides a systematic way to find optimal…
Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use…
We study discrete-time finite-horizon optimal control problems in probability spaces, whereby the state of the system is a probability measure. We show that, in many instances, the solution of dynamic programming in probability spaces…
Highway vehicular traffic is an inherently multi-agent problem. Traffic jams can appear and disappear mysteriously. We develop a method for traffic flow control that is applied at the vehicular level via mean-field games. We begin this work…
Soft robots can execute tasks with safer interactions. However, control techniques that can effectively exploit the systems' capabilities are still missing. Differential dynamic programming (DDP) has emerged as a promising tool for…
Markov Decision Processes (MDP) is an useful framework to cast optimal sequential decision making problems. Given any MDP the aim is to find the optimal action selection mechanism i.e., the optimal policy. Typically, the optimal policy…