We address control synthesis of stochastic discrete-time linear multi-agent systems under jointly chance-constrained collaborative signal temporal logic specifications in a distribution-free manner using available disturbance samples, which are partitioned into training and calibration sets. Leveraging linearity, we decompose each agent’s system into deterministic nominal and stochastic error parts, and design disturbance feedback controllers to bound the stochastic errors by solving a tractable optimization problem over the training data. We then quantify prediction regions (PRs) for the aggregate error trajectories corresponding to agent \textit{cliques}, involved in collaborative tasks, using conformal prediction and calibration data. This enables us to address the specified joint chance constraint via Lipschitz tightening and the computed PRs, and relax the centralized stochastic optimal control problem to a deterministic one, whose solution represents feedforward inputs. To enhance scalability, we decompose the deterministic problem into agent-level subproblems solved in an MPC fashion, yielding a distributed control policy. Finally, we present an illustrative example and a comparison with [1].

We consider multi-robot systems under recurring tasks formalized as linear temporal logic (LTL) specifications. To solve the planning problem efficiently, we propose a bottomup approach combining offline plan synthesis with online coordination, dynamically adjusting plans via real-time communication. To address action delays, we introduce a synchronization mechanism ensuring coordinated task execution, leading to a multi-agent coordination and synchronization framework that is adaptable to a wide range of multi-robot applications. The software package is developed in Python and ROS2 for broad deployment. We validate our findings through lab experiments involving nine robots showing enhanced adaptability compared to previous methods. Additionally, we conduct simulations with up to ninety agents to demonstrate the reduced computational complexity and the scalability features of our work.

We consider linear systems with additive exogenous signals, whose range is state-dependent and is constrained in a polytope in the state-disturbance space. We observe that these systems are equivalent (i) to a linear inclusion defined as projection of a polytopic set on the state space, and (ii) to piecewise polytopic affine dynamics, which is convex on the support of the disturbance set. We use these descriptions to characterise the reachable sets and consequently characterise the minimal Robust Positively Invariant (mRPI) set. Our results can be used in a variety of applications.

We consider the scheduling problem of requests entering a distributed computing network consisting of a set of noncooperative nodes, where a node is represented by a queue combined with a computing unit. Our interaction-free setup between nodes renders decentralized scheduling challenging, with most existing results focusing on centralized or static solutions. Inspired by congestion control, we propose a new average-based additive increase multiplicative decrease (AIMD) admission control policy, which requires minimal communication between individual nodes and an aggregator. The proposed admission policy infers a discrete-event model expressed as a positive, constrained switching system that is triggered whenever the queue of the aggregation point of requests vanishes. We show convergence of the proposed AIMD system under unknown, peak-bounded workload profiles by analyzing the spectrum of rank-one perturbations of symmetric matrices and the boundedness of the joint spectral radius of sets of symmetric matrices. Contrary to methods that address scheduling and resource allocation asynchronously or via a two-step approach, our AIMD-based scheme can tackle both tasks simultaneously. This is illustrated by proposing a decentralized resource allocation controller coupled with the scheduling scheme leading to a stable closed-loop control system that is guaranteed to avoid underutilization of resources and is tunable via the sets of AIMD parameters.

We address an optimal control problem for linear stochastic systems with unknown noise distributions and joint chance constraints using conformal prediction. Our approach involves designing a feedback controller to maintain an error system within a prediction region (PR). We define PRs as sublevel sets of a nonconformity score over error trajectories, enabling the handling of joint chance constraints. We propose two methods to design feedback control and PRs: one through direct optimization over error trajectory samples, and the other indirectly using the S-procedure with a disturbance ellipsoid obtained from data. By tightening constraints with PRs, we solve a relaxed problem to synthesize a feedback policy. Our method ensures reliable probabilistic guarantees based on marginal coverage, independent of data size.

We consider the synthesis problem of a multi-agent system under signal temporal logic (STL) specifications representing bounded-time tasks that need to be satisfied recurrently over an infinite horizon. Motivated by the limited approaches to handling recurring STL systematically, we tackle the infinite-horizon control problem with a receding horizon scheme equipped with additional STL constraints that introduce minimal complexity and a backward-reachability-based terminal condition that is straightforward to construct and ensures recursive feasibility. Subsequently, we decompose the global receding horizon optimization problem into agent-level programs the objectives of which are to minimize local cost functions subject to local and joint STL constraints. We propose a scheduling policy that allows individual agents to sequentially optimize their control actions while maintaining recursive feasibility. This results in a distributed strategy that can operate online as a model predictive controller. Last, we illustrate the effectiveness of our method via a multi-agent system example assigned a surveillance task.

We consider distributionally robust optimal control of stochastic linear systems under signal temporal logic (STL) chance constraints when the disturbance distribution is unknown. By assuming that the underlying predicate functions are Lipschitz continuous and the noise realizations are drawn from a distribution having a concentration of measure property, we first formulate the underlying chance-constrained control problem as stochastic programming with constraints on expectations and propose a solution using a distributionally robust approach based on the Wasserstein metric. We show that by choosing a proper Wasserstein radius, the original chance-constrained optimization can be satisfied with a user-defined confidence level. A numerical example illustrates the efficacy of the method.

We consider the control design of stochastic discrete-time linear multi-agent systems (MASs) under a global signal temporal logic (STL) specification to be satisfied at a predefined probability. By decomposing the dynamics into deterministic and error components, we construct a probabilistic reachable tube (PRT) as the Cartesian product of reachable sets of the individual error systems driven by disturbances lying in confidence regions (CRs) with a fixed probability. By bounding the PRT probability with the specification probability, we tighten all state constraints induced by the STL specification by solving tractable optimization problems over segments of the PRT, and relax the underlying stochastic problem with a deterministic one. This approach reduces conservatism compared to tightening guided by the STL structure. Additionally, we propose a recursively feasible algorithm to attack the resulting problem by decomposing it into agent-level subproblems, which are solved iteratively according to a scheduling policy. We demonstrate our method on a ten-agent system, where existing approaches are impractical.

This paper addresses the control synthesis of heterogeneous stochastic linear multi-agent systems with realtime allocation of signal temporal logic (STL) specifications. Based on previous work, we decompose specifications into subspecifications on the individual agent level. To leverage the efficiency of task allocation, a heuristic filter evaluates potential task allocation based on STL robustness, and subsequently, an auctioning algorithm determines the definitive allocation of specifications. Finally, a control strategy is synthesized for each agent-specification pair using tube-based model predictive control (MPC), ensuring provable probabilistic satisfaction. We demonstrate the efficacy of the proposed methods using a multi-shuttle scenario that highlights a promising extension to automated driving applications like vehicle routing.