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This paper considers the problem of optimizing robot navigation with respect to a time-varying objective encoded into a navigation density function. We are interested in designing state feedback control laws that lead to an almost everywhere stabilization of the closed-loop system to an equilibrium point while navigating a region optimally and safely (that is, the transient leading to the final equilibrium point is optimal and satisfies safety constraints). Though this problem has been studied in literature within many different communities, it still remains a challenging non-convex control problem. In our approach, under certain assumptions on the time-varying navigation density, we use Koopman and Perron-Frobenius Operator theoretic tools to transform the problem into a convex one in infinite dimensional decision variables. In particular, the cost function and the safety constraints in the transformed formulation become linear in these functional variables. Finally, we present some numerical examples to illustrate our approach, as well as discuss the current limitations and future extensions of our framework to accommodate a wider range of robotics applications., Part of ISBN 978-3-907144-08-4QC 20230911

This paper proposes a high-level path planning strategy under Time Petri net (TPN) formalism for a multi-agent system, which is subject to Metric Interval Temporal Logic (MITL) specifications. The work aims to design a scalable model with respect to the number of agents, as the MITL formula requires multiple agents to ensure similar tasks. The obtained model is denoted Composed Time Petri net and it couples two TPN representations assigned to the motion of the agents, respectively to the MITL specification. The planning approach is based on model-checking methods and the results are evaluated on a case study applied in robotics industry., Part of ISBN 978-3-907144-08-4QC 20230911

This paper proposes a method to navigate a mobile robot by estimating its state over a number of distributed sensor networks (DSNs) such that it can successively accomplish a sequence of tasks, i.e., its state enters each targeted set and stays inside no less than the desired time, under a resource-aware, time-efficient, and computation- and communication-constrained setting. We propose a new robot state estimation and navigation architecture, which integrates an event-triggered task-switching feedback controller for the robot and a two-time-scale distributed state estimator for each sensor. With the controller, the robot is able to accomplish a task by following a reference trajectory and switch to the next task when an event-triggered condition is fulfilled. With the estimator, each active sensor is able to estimate the robot state. We provide conditions to ensure that the state estimation error and the trajectory tracking deviation are upper bounded by two time-varying sequences, respectively. Furthermore, we find a sufficient condition for accomplishing a task and provide an upper bound of running time for the task. Numerical simulations of an indoor robot's localization and navigation are provided to validate the proposed architecture., Part of ISBN 978-3-907144-08-4QC 20230911

In this paper, we consider a planning problem for a hierarchical finite state machine (HFSM) and develop an algorithm for efficiently computing optimal plans between any two states. The algorithm consists of an offline and an online step. In the offline step, one computes exit costs for each machine in the HFSM. It needs to be done only once for a given HFSM, and it is shown to have time complexity scaling linearly with the number of machines in the HFSM. In the online step, one computes an optimal plan from an initial state to a goal state, by first reducing the HFSM (using the exit costs), computing an optimal trajectory for the reduced HFSM, and then expand this trajectory to an optimal plan for the original HFSM. The time complexity is near-linearly with the depth of the HFSM. It is argued that HFSMs arise naturally for large-scale control systems, exemplified by an application where a robot moves between houses to complete tasks. We compare our algorithm with Dijkstra's algorithm on HFSMs consisting of up to 2 million states, where our algorithm outperforms the latter, being several orders of magnitude faster., Part of ISBN 978-3-907144-08-4QC 20230911

This paper considers distributed nonconvex optimization for minimizing the average of local cost functions, by using local information exchange over undirected communication networks. Since the communication channels often have limited bandwidth or capacity, we first introduce a quantization rule and an encoder/decoder scheme to reduce the transmission bits. By integrating them with a distributed algorithm, we then propose a distributed quantized nonconvex optimization algorithm. Assuming the global cost function satisfies the Polyak-Lojasiewicz condition, which does not require the global cost function to be convex and the global minimizer is not necessarily unique, we show that the proposed algorithm linearly converges to a global optimal point. Moreover, a low data rate is shown to be sufficient to ensure linear convergence when the algorithm parameters are properly chosen. The theoretical results are illustrated by numerical simulation examples., QC 20230503

Control of multi-agent systems under temporal logical specifications has been popular due to its ability to tackle complex tasks that cannot be easily defined as classic control objectives. In this paper, a general class of leader-follower multi-agent systems subject to certain fragments of signal temporal logic (STL) specifications is considered. We first propose a funnel-based control strategy for the leader-follower multi-agent systems to enforce the satisfaction of the basic STL formulas by prescribing certain transient behavior on the funnels that constrain the closed-loop trajectories. A hybrid control strategy is then leveraged to satisfy the sequential STL formulas. Finally, a simulation example is given to illustrate the results., Part of proceeedings: ISBN 978-3-907144-07-7QC 20220621

This paper proposes a data-driven set-based estimation algorithm for a class of nonlinear systems with polynomial nonlinearities. Using the system's input-output data, the proposed method computes a set that guarantees the inclusion of the system's state in real-time. Although the system is assumed to be a polynomial type, the exact polynomial functions, and their coefficients are assumed to be unknown. To this end, the estimator relies on offline and online phases. The offline phase utilizes past input-output data to estimate a set of possible coefficients of the polynomial system. Then, using this estimated set of coefficients and the side information about the system, the online phase provides a set estimate of the state. Finally, the proposed methodology is evaluated through its application on SIR (Susceptible, Infected, Recovered) epidemic model., Part of proceedings: ISBN 978-3-907144-07-7, QC 20221101

In this paper, we develop and analyze a gossip-based average consensus algorithm that enables all of the components of a distributed system, each with some initial value, to reach (approximate) average consensus on their initial values after executing a finite number of iterations, and without having to reveal to other curious components the specific value they contribute to the average calculation. We consider a fully-connected (undirected) network in which curious components do not interfere in the computation in any other way, but can collaborate arbitrarily and are aware of the privacy-preserving strategy. We characterize precisely conditions on the information exchange that guarantee privacy preservation for a specific node. The protocol also provides a criterion that allows the nodes to determine, in a distributed manner (while running the proposed gossip protocol), when to terminate their operation because approximate average consensus has been reached., Part of proceedings: ISBN 978-3-907144-07-7, QC 20221101

Control of multi-agent systems under temporal logical specifications has been popular due to its ability to tackle complex tasks that cannot be easily defined as classic control objectives. In this paper, a general class of leader-follower multi-agent systems subject to certain fragments of signal temporal logic (STL) specifications is considered. We first propose a funnel-based control strategy for the leader-follower multi-agent systems to enforce the satisfaction of the basic STL formulas by prescribing certain transient behavior on the funnels that constrain the closed-loop trajectories. A hybrid control strategy is then leveraged to satisfy the sequential STL formulas. Finally, a simulation example is given to illustrate the results., Part of proceeedings: ISBN 978-3-907144-07-7QC 20220621

The paper studies the spread of a virus over a (possibly) time-varying graph, with the spread being (possibly) worsened by the presence of a shared resource. We propose a time-varying susceptible-infected-water-susceptible (SIWS) model, with the water compartment representing the contamination level in the shared resource. We say that the system is in the disease-free equilibrium (DFE) if none of the nodes (representative of sub-populations, such as cities, districts, etc.) are infected, and the shared resource is contaminant-free. We identify multiple sufficient conditions for exponential convergence to the DFE. Based on one of the aforementioned sufficient conditions, an on/off lockdown strategy that eradicates the infection spread is proposed. More specifically, we design a switching rule between lockdown and free (i.e., no lockdown) modes to guarantee exponential convergence to the DFE., Part of proceedings: ISBN 978-3-907144-07-7Not duplicate with DiVA 1622798QC 20221031

Control of multi-agent systems under temporal logical specifications has been popular due to its ability to tackle complex tasks that cannot be easily defined as classic control objectives. In this paper, a general class of leader-follower multi-agent systems subject to certain fragments of signal temporal logic (STL) specifications is considered. We first propose a funnel-based control strategy for the leader-follower multi-agent systems to enforce the satisfaction of the basic STL formulas by prescribing certain transient behavior on the funnels that constrain the closed-loop trajectories. A hybrid control strategy is then leveraged to satisfy the sequential STL formulas. Finally, a simulation example is given to illustrate the results., Part of proceeedings: ISBN 978-3-907144-07-7QC 20220621

Control of multi-agent systems under temporal logical specifications has been popular due to its ability to tackle complex tasks that cannot be easily defined as classic control objectives. In this paper, a general class of leader-follower multi-agent systems subject to certain fragments of signal temporal logic (STL) specifications is considered. We first propose a funnel-based control strategy for the leader-follower multi-agent systems to enforce the satisfaction of the basic STL formulas by prescribing certain transient behavior on the funnels that constrain the closed-loop trajectories. A hybrid control strategy is then leveraged to satisfy the sequential STL formulas. Finally, a simulation example is given to illustrate the results., Part of proceeedings: ISBN 978-3-907144-07-7QC 20220621

Control of multi-agent systems under temporal logical specifications has been popular due to its ability to tackle complex tasks that cannot be easily defined as classic control objectives. In this paper, a general class of leader-follower multi-agent systems subject to certain fragments of signal temporal logic (STL) specifications is considered. We first propose a funnel-based control strategy for the leader-follower multi-agent systems to enforce the satisfaction of the basic STL formulas by prescribing certain transient behavior on the funnels that constrain the closed-loop trajectories. A hybrid control strategy is then leveraged to satisfy the sequential STL formulas. Finally, a simulation example is given to illustrate the results., Part of proceeedings: ISBN 978-3-907144-07-7QC 20220621

In this paper we consider the complexity of verifying the property of AA-diagnosability in probabilistic finite automata and establish that AA-diagnosability is, in general, a PSPACE-hard problem. In deterministic and non-deterministic finite automata, the property of diagnosability captures our ability to determine, based on our observation of the activity in a given finite automaton, the occurrence of any fault event, at least if we wait for at most a finite number of events (following the occurrence of the unobservable fault event). In stochastic settings where the underlying system is a probabilistic finite automaton under partial observation, there is not a prevalent notion of diagnosability and many variations have been proposed, including A-diagnosability and AA-diagnosability. Earlier work has shown that the verification of A-diagnosability (also referred to as strong stochastic diagnosability) for a given probabilistic finite automaton is a PSPACE-hard problem. In this paper, we establish that the verification of AA-diagnosability (also referred to as stochastic diagnosability) is a PSPACE-hard problem., QC 20201007

In this and a companion paper a dynamic programming (DP) approach to solve a smart home appliances scheduling problem is considered. The challenge with solving the scheduling problem is the coupling of decision variables due to some time precedence constraints. In general, the system of precedence constraints may contain redundant constraints that offer opportunities for simplification. This simplification is desirable for reducing the computation effort of the nonserial DP procedure presented in the companion paper (i.e., Part II). The current paper establishes the uniqueness of the maximum set of redundant constraints and its polynomial-time solvability with optimality guarantee, under the sufficient and necessary condition that the precedence graph (a graph representation of the precedence constraints system) does not contain any cycle with nonnegative weight. A numerical case study indicates the efficiency of the proposed simplification algorithm versus the brute-force enumerative search. Besides helping to reduce the computation effort in the DP procedure described in the companion paper, the algorithm in the current paper solves a generalization of a precedence graph simplification problem arising from application areas such as parallel computing., QC 20150408

This paper focuses on the problem of distributed consensus control of multi-agent systems while considering two main practical concerns (i) stochastic noise in the agent dynamics and (ii) predefined performance constraints over evolutions of multi-agent systems. In particular, we consider that each agent is driven by a stochastic differential equation with state-dependent noise which makes the considered problem more challenging compare to non-stochastic agents. The work provides sufficient conditions under which the proposed time-varying distributed control laws ensure consensus in expectation and almost sure consensus of stochastic multi-agent systems while satisfying prescribed performance constraints over evolutions of the systems in the sense of the qth moment. Finally, we demonstrate the effectiveness of the proposed results with a numerical example., Part of proceedings: ISBN 978-1-6654-3659-5QC 20220530

This paper considers the use of homomorphic encryption for the realisation of distributed formation control of multi-agent systems via edge computer. In our proposed framework, the distributed control computation in the edge computer uses only the encrypted data without the need for a reset mechanism that is commonly required to avoid error accumulation. Simulation results show that, despite the use of encrypted data on the controller and errors introduced by the quantization process prior to the encryption, the formation is able to converge to the desired shape. The proposed architecture offers insight on the mechanism for realising distributed control computation in an edge/cloud computer while preserving the privacy of local information coming from each agent., Part of proceedings: ISBN 978-1-6654-3659-5QC 20220530

Control policies, trained using Deep Reinforcement Learning, have been recently shown to be vulnerable to adversarial attacks introducing even minimal perturbations to the policy input. The attacks proposed so far have been designed using heuristics, based on existing adversarial example crafting techniques used to dupe classifiers in supervised learning. In contrast, this paper investigates the problem of devising optimal attacks, depending on a well-defined attacker's objective, e.g., to minimize the main agent average reward. When the policy and the system dynamics, as well as the rewards, are known to the attacker, a scenario referred to as a white-box attack, designing optimal attacks amounts to solving a Markov Decision Process. For what we call black-box attacks, where neither the policy nor the system is known, optimal attacks can be trained using Reinforcement Learning. We present numerical experiments demonstrating the efficiency of our attacks compared to existing attacks. We further quantify the potential impact of attacks and establish its connection to the smoothness of the policy under attack. Smooth policies are naturally less prone to attacks (e.g. Lipschitz policies, with respect to the state, are more resilient). Finally, we show that from the main agent perspective, the system uncertainties induced by the attack can be modelled using a Partially Observable Markov Decision Process (POMDP) framework. We demonstrate that using Reinforcement Learning methods tailored to POMDP (e.g. using Recurrent Neural Networks) leads to more resilient policies., Part of proceedings: ISBN 978-1-6654-4197-1, QC 20230117

The problem of estimating the largest gain of an unknown linear and time-invariant filter is studied, known as the H-infinity -norm estimation problem. The approach presented in this paper is iterative and corresponds to the combination of two state-of-the-art methods: Power Iterations and Weighted Thompson Sampling. The combination is done by means of a well-known technique in communications known as a cyclic prefix, in which the last points of a signal are prepended to it. This allows to take considerably more exact measurements of the frequency response of the system at a set of equispaced frequencies. The discussion is complemented with a simulation study, showing that the proposed algorithm has an increased speed of convergence to the quantity of interest., QC 20220121

This paper presents a distributed learning model predictive control (DLMPC) scheme for distributed linear time invariant systems with coupled dynamics and state constraints. The proposed solution method is based on an online distributed optimization scheme with nearest-neighbor communication. If the control task is iterative and data from previous feasible iterations are available, local data are exploited by the subsystems in order to construct the local terminal set and terminal cost, which guarantee recursive feasibility and asymptotic stability, as well as performance improvement over iterations. In case a first feasible trajectory is difficult to obtain, or the task is non-iterative, we further propose an algorithm that efficiently explores the state-space and generates the data required for the construction of the terminal cost and terminal constraint in the MPC problem in a safe and distributed way. In contrast to other distributed MPC schemes which use structured positive invariant sets, the proposed approach involves a control invariant set as the terminal set, on which we do not impose any distributed structure. The proposed iterative scheme converges to the global optimal solution of the underlying infinite horizon optimal control problem under mild conditions. Numerical experiments demonstrate the effectiveness of the proposed DLMPC scheme., QC 20220121