arXiv subjects

Dimitra Panagou

Publications and source records attributed to Dimitra Panagou.

122 records · Page 7Linked to original sources

arXiv2019

Resilient Leader-Follower Consensus to Arbitrary Reference Values in Time-Varying Graphs

Several algorithms in prior literature have been proposed which guarantee consensus of normally behaving agents in a network that may contain adversarially behaving agents. These algorithms guarantee that the consensus value lies within the convex hull of initial normal agents' states, with the exact consensus value possibly being unknown. In leader-follower consensus problems however, the objective is for normally behaving agents to track a reference state that may take on values outside of this convex hull. In this paper we present methods for agents in time-varying graphs with discrete-time dynamics to resiliently track a reference state propagated by a set of leaders despite a bounded subset of the leaders and followers behaving adversarially. Our results are demonstrated through simulations.

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arXiv2019

Finite-Time Stability of Hybrid Systems: A Multiple Generalized Lyapunov Functions Approach

This paper studies finite-time stability of a class of hybrid systems. We present sufficient conditions in terms of multiple generalized Lyapunov functions for the origin of the hybrid system to be finite-time stable. More specifically, we show that even if the value of the generalized Lyapunov functions increase between consecutive switches, finite-time stability can be guaranteed if the finite-time convergent mode is active long enough. In contrast to earlier work where the Lyapunov functions are required to be decreasing during the continuous flows and non-increasing at the discrete jumps, we allow the generalized Lyapunov functions to increase \emph{both} during the continuous flows and the discrete jumps. As thus, the derived stability results are less conservative compared to the related literature. Numerical example demonstrates the efficacy of the proposed methods.

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arXiv2019

Prescribed-time convergence with input constraints: A control Lyapunov function based approach

In this paper, we present a control framework for a general class of control-affine nonlinear systems under spatiotemporal and input constraints. Specifically, the proposed control architecture addresses the problem of reaching a given final set $S$ in a prescribed (user-defined) time with bounded control inputs. To this end, a time transformation technique is utilized to transform the system subject to temporal constraints into an equivalent form without temporal constraints. The transformation is defined so that asymptotic convergence in the transformed time scale results into prescribed-time convergence in the original time scale. To incorporate input constraints, we characterize a set of initial conditions $D_M$ such that starting from this set, the closed-loop trajectories reach the set $S$ within the prescribed time. We further show that starting from outside the set $D_M$, the system trajectories reach the set $D_M$ in a finite time that depends upon the initial conditions and the control input bounds. We use a novel parameter $μ$ in the controller, that controls the convergence-rate of the closed-loop trajectories and dictates the size of the set $D_M$. Finally, we present a numerical example to showcase the efficacy of our proposed method.

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arXiv2019

Herding an Adversarial Attacker to a Safe Area for Defending Safety-Critical Infrastructure

This paper investigates a problem of defending safety-critical infrastructure from an adversarial aerial attacker in an urban environment. A circular arc formation of defenders is formed around the attacker, and vector-field based guidance laws herd the attacker to a predefined safe area in the presence of rectangular obstacles. The defenders' formation is defined based on a novel vector field that imposes super-elliptic contours around the obstacles, to closely resemble their rectangular shape. A novel finite-time stabilizing controller is proposed to guide the defenders to their desired formation while avoiding obstacles and inter-agent collisions. The efficiency of the approach is demonstrated via simulation results.

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arXiv2018

Hybrid Planning and Control for Multiple Fixed-Wing Aircraft under Input Constraints

This paper presents a novel hybrid control protocol for de-conflicting multiple vehicles with constraints on control inputs. We consider turning rate and linear speed constraints to represent fixed-wing or car-like vehicles. A set of state-feedback controllers along with a state-dependent switching logic are synthesized in a hybrid system to generate collision-free trajectories that converge to the desired destinations of the vehicles. The switching law is designed so that the safety can be guaranteed while no Zeno behavior can occur. A novel temporary goal assignment technique is also designed to guarantee convergence. We analyze the individual modes for safety and the closed-loop hybrid system for convergence. The theoretical developments are demonstrated via simulation results.

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arXiv2018

New Results on Finite-Time Stability: Geometric Conditions and Finite-Time Controllers

This paper presents novel controllers that yield finite-time stability for linear systems. We first present a sufficient condition for the origin of a scalar system to be finite-time stable. Then we present novel finite-time controllers based on vector fields and barrier functions to demonstrate the utility of this geometric condition. We also consider the general class of linear controllable systems, and present a continuous feedback control law to stabilize the system in finite time. Finally, we present simulation results for each of these cases, showing the efficacy of the designed control laws.

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arXiv2018

Finite-Time Resilient Formation Control with Bounded Inputs

In this paper we consider the problem of a multi-agent system achieving a formation in the presence of misbehaving or adversarial agents. We introduce a novel continuous time resilient controller to guarantee that normally behaving agents can converge to a formation with respect to a set of leaders. The controller employs a norm-based filtering mechanism, and unlike most prior algorithms, also incorporates input bounds. In addition, the controller is shown to guarantee convergence in finite time. A sufficient condition for the controller to guarantee convergence is shown to be a graph theoretical structure which we denote as Resilient Directed Acyclic Graph (RDAG). Further, we employ our filtering mechanism on a discrete time system which is shown to have exponential convergence. Our results are demonstrated through simulations.

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arXiv2018

Resilient Leader-Follower Consensus to Arbitrary Reference Values

The problem of consensus in the presence of misbehaving agents has increasingly attracted attention in the literature. Prior results have established algorithms and graph structures for multi-agent networks which guarantee the consensus of normally behaving agents in the presence of a bounded number of misbehaving agents. The final consensus value is guaranteed to fall within the convex hull of initial agent states. However, the problem of consensus tracking considers consensus to arbitrary reference values which may not lie within such bounds. Conditions for consensus tracking in the presence of misbehaving agents has not been fully studied. This paper presents conditions for a network of agents using the W-MSR algorithm to achieve this objective.

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arXiv2018

Approximating the Region of Multi-Task Coordination via the Optimal Lyapunov-Like Barrier Function

We consider the multi-task coordination problem for multi-agent systems under the following objectives: 1. collision avoidance; 2. connectivity maintenance; 3. convergence to desired destinations. The paper focuses on the safety guaranteed region of multi-task coordination (SG-RMTC), i.e., the set of initial states from which all trajectories converge to the desired configuration, while at the same time achieve the multi-task coordination and avoid unsafe sets. In contrast to estimating the domain of attraction via Lyapunov functions, the main underlying idea is to employ the sublevel sets of Lyapunov-like barrier functions to approximate the SG-RMTC. Rather than using fixed Lyapunov-like barrier functions, a systematic way is proposed to search an optimal Lyapunov-like barrier function such that the under-estimate of SG-RMTC is maximized. Numerical examples illustrate the effectiveness of the proposed method.

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arXiv2018

Robust Semi-Cooperative Multi-Agent Coordination in the Presence of Stochastic Disturbances

This paper presents a robust distributed coordination protocol that achieves generation of collision-free trajectories for multiple unicycle agents in the presence of stochastic uncertainties. We build upon our earlier work on semi-cooperative coordination and we redesign the coordination controllers so that the agents counteract a class of state (wind) disturbances and measurement noise. Safety and convergence is proved analytically, while simulation results demonstrate the efficacy of the proposed solution.

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arXiv2017

r-Robustness and (r,s)-Robustness of Circulant Graphs

There has been recent growing interest in graph theoretical properties known as r- and (r,s)-robustness. These properties serve as sufficient conditions guaranteeing the success of certain consensus algorithms in networks with misbehaving agents present. Due to the complexity of determining the robustness for an arbitrary graph, several methods have previously been proposed for identifying the robustness of specific classes of graphs or constructing graphs with specified robustness levels. The majority of such approaches have focused on undirected graphs. In this paper we identify a class of scalable directed graphs whose edge set is determined by a parameter k and prove that the robustness of these graphs is also determined by k. We support our results through computer simulations.

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arXiv2017

Chebyshev Approximation and Higher Order Derivatives of Lyapunov Functions for Estimating the Domain of Attraction

Estimating the Domain of Attraction (DA) of non-polynomial systems is a challenging problem. Taylor expansion is widely adopted for transforming a nonlinear analytic function into a polynomial function, but the performance of Taylor expansion is not always satisfactory. This paper provides solvable ways for estimating the DA via Chebyshev approximation. Firstly, for Chebyshev approximation without the remainder, higher order derivatives of Lyapunov functions are used for estimating the DA, and the largest estimate is obtained by solving a generalized eigenvalue problem. Moreover, for Chebyshev approximation with the remainder, an uncertain polynomial system is reformulated, and a condition is proposed for ensuring the convergence to the largest estimate with a selected Lyapunov function. Numerical examples demonstrate that both accuracy and efficiency are improved compared to Taylor approximation.

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arXiv2017

Distributed Multi-task Formation Control under Parametric Communication Uncertainties

Formation control is a key problem in the coordination of multiple agents. It arises new challenges to traditional formation control strategy when the communication among agents is affected by uncertainties. This paper considers the robust multi-task formation control problem of multiple non-point agents whose communications are disturbed by uncertain parameters. The control objectives include 1. achieving the desired configuration; 2. avoiding collisions; 3. preserving the connectedness of uncertain topology. To achieve these objectives, firstly, a condition of Linear Matrix Inequalities (LMIs) is proposed for checking the connectedness of an uncertain communication topology. Then, by preserving the initial topological connectedness, a gradient-based distributed controller is designed via Lyapunov-like barrier functions. Two numerical examples illustrate the effectiveness of the proposed method.

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arXiv2014

Motion planning and Collision Avoidance using Non-Gradient Vector Fields. Technical Report

This paper presents a novel feedback method on the motion planning for unicycle robots in environments with static obstacles, along with an extension to the distributed planning and coordination in multi-robot systems. The method employs a family of 2-dimensional analytic vector fields, whose integral curves exhibit various patterns depending on the value of a parameter lambda. More specifically, for an a priori known value of lambda, the vector field has a unique singular point of dipole type and can be used to steer the unicycle to a goal configuration. Furthermore, for the unique value of lambda that the vector field has a continuum of singular points, the integral curves are used to define flows around obstacles. An almost global feedback motion plan can then be constructed by suitably blending attractive and repulsive vector fields in a static obstacle environment. The method does not suffer from the appearance of sinks (stable nodes) away from goal point. Compared to other similar methods which are free of local minima, the proposed approach does not require any parameter tuning to render the desired convergence properties. The paper also addresses the extension of the method to the distributed coordination and control of multiple robots, where each robot needs to navigate to a goal configuration while avoiding collisions with the remaining robots, and while using local information only. More specifically, based on the results which apply to the single-robot case, a motion coordination protocol is presented which guarantees the safety of the multi-robot system and the almost global convergence of the robots to their goal configurations. The efficacy of the proposed methodology is demonstrated via simulation results in static and dynamic environments.

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