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Model predictive controllers use dynamics models to solve constrained optimal control problems. However, computational requirements for real-time control have limited their use to systems with low-dimensional models. Nevertheless, high-dimensional models arise in many settings, for example, discretization methods for generating finite-dimensional approximations to partial differential equations can result in models with thousands to millions of dimensions. In such cases, reduced-order models (ROMs) can significantly reduce computational requirements, but model approximation error must be considered to guarantee controller performance. In this article, a reduced-order model predictive control (ROMPC) scheme is proposed to solve robust, output feedback, constrained optimal control problems for high-dimensional linear systems. Computational efficiency is obtained by using projection-based ROMs, and guarantees on robust constraint satisfaction and stability are provided. The performance of the approach is demonstrated in simulation for several examples, including an aircraft control problem leveraging an inviscid computational fluid dynamics model with dimension 998 930. [ABSTRACT FROM AUTHOR]

In this paper, we present a framework for risk-sensitive model predictive control (MPC) of linear systems affected by stochastic multiplicative uncertainty. Our key innovation is to consider a time-consistent, dynamic risk evaluation of the cumulative cost as the objective function to be minimized. This framework is axiomatically justified in terms of time-consistency of risk assessments, is amenable to dynamic optimization, and is unifying in the sense that it captures a full range of risk preferences from risk neutral (i.e., expectation) to worst case. Within this framework, we propose and analyze an online risk-sensitive MPC algorithm that is provably stabilizing. Furthermore, by exploiting the dual representation of time-consistent, dynamic risk measures, we cast the computation of the MPC control law as a convex optimization problem amenable to real-time implementation. Simulation results are presented and discussed. [ABSTRACT FROM AUTHOR]

Pickup and delivery problems (PDPs), in which objects or people have to be transported between specific locations, are among the most common combinatorial problems in real-world logistical operations. A widely-encountered type of PDP is the Stacker Crane Problem (SCP), where each commodity/customer is associated with a pickup location and a delivery location, and the objective is to find a minimum-length tour visiting all locations with the constraint that each pickup location and its associated delivery location are visited in immediate, consecutive order. The SCP is NP-Hard and the best known approximation algorithm only provides a 9/5 approximation ratio. In this paper, we examine an embedding of the SCP within a stochastic framework, and our objective is three-fold: First, we describe a large class of algorithms for the SCP, where every member is asymptotically optimal, i.e., it produces, almost surely, a solution approaching the optimal one as the number of pickups/deliveries goes to infinity; moreover, one can achieve computational complexity O(n^2+\varepsilon) within the class, where n is the number of pickup/delivery pairs and \varepsilon is an arbitrarily small positive constant. Second, we characterize the length of the optimal SCP tour asymptotically. Finally, we study a dynamic version of the SCP, whereby pickup and delivery requests arrive according to a Poisson process, and which serves as a model for large-scale demand-responsive transport (DRT) systems. For such a dynamic counterpart of the SCP, we derive a necessary and sufficient condition for the existence of stable vehicle routing policies, which depends only on the workspace geometry, the distributions of pickup and delivery points, the arrival rate of requests, and the number of vehicles. Our results leverage a novel connection between the Euclidean Bipartite Matching Problem and the theory of random permutations, and, for the dynamic setting, exhibit novel features that are absent in traditional spatially-distributed queueing systems. [ABSTRACT FROM AUTHOR]

A widely applied strategy for workload sharing is to equalize the workload assigned to each resource. In mobile multiagent systems, this principle directly leads to equitable partitioning policies whereby: 1) the environment is equitably divided into subregions of equal measure; 2) one agent is assigned to each subregion; and 3) each agent is responsible for service requests originating within its own subregion. The current lack of distributed algorithms for the computation of equitable partitions limits the applicability of equitable partitioning policies to limited-size multiagent systems operating in known, static environments. In this paper, first we design provably correct and spatially distributed algorithms that allow a team of agents to compute a convex and equitable partition of a convex environment. Second, we discuss how these algorithms can be extended so that a team of agents can compute, in a spatially distributed fashion, convex and equitable partitions with additional features, e.g., equitable and median Voronoi diagrams. Finally, we discuss two application domains for our algorithms, namely dynamic vehicle routing for mobile robotic networks and wireless ad hoc networks. Through these examples, we show how one can couple the algorithms presented in this paper with equitable partitioning policies to make these amenable to distributed implementation. More in general, we illustrate a systematic approach to devise spatially distributed control policies for a large variety of multiagent coordination problems. Our approach is related to the classic Lloyd algorithm and exploits the unique features of power diagrams. [ABSTRACT FROM AUTHOR]

In this paper, we present adaptive and distributed algorithms for motion coordination of a group of m vehicles. The vehicles must service demands whose time of arrival, spatial location, and service requirement are stochastic; the objective is to minimize the average time demands spend in the system. The general problem is known as the m-vehicle Dynamic Traveling Repairman Problem (m-DTRP). The best previously known control algorithms rely on centralized task assignment and are not robust against changes in the environment. In this paper, we first devise new control policies for the 1-DTRP that: i) are provably optimal both in light-load conditions (i.e., when the arrival rate for the demands is small) and in heavy-load conditions (i.e., when the arrival rate for the demands is large), and ii) are adaptive, in particular, they are robust against changes in load conditions. Then, we show that specific partitioning policies, whereby the environment is partitioned among the vehicles and each vehicle follows a certain set of rules within its own region, are optimal in heavy-load conditions. Building upon the previous results, we finally design control policies for the m-DTRP that i) are adaptive and distributed, and ii) have strong performance guarantees in heavy-load conditions and stabilize the system in any load condition. [ABSTRACT FROM AUTHOR]