arXiv subjects

Dimitra Panagou

Publications and source records attributed to Dimitra Panagou.

At least 109 records · Page 6Linked to original sources

arXiv2020

Finite-Time Stability of Adaptive Parameter Estimation and Control

This paper presents extensions of finite-time stability results to some prototypical adaptive control and estimation frameworks. First, we present a novel scheme of online parameter estimation that guarantees convergence of the estimation error in a fixed time under a relaxed persistence of excitation condition. Subsequently, we design a novel Model Reference Adaptive Control (MRAC) for a scalar system with finite-time convergence guarantees for both the state- and the parameter-error. Lastly, for a general class of strict-feedback systems with unknown parameters, we propose a finite-time stabilizing control based on adaptive backstepping techniques. We also present some numerical examples demonstrating the efficacy of our scheme.

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arXiv2020

A Quadratic Program based Control Synthesis under Spatiotemporal Constraints and Non-vanishing Disturbances

In this paper, we study the effect of non-vanishing disturbances on the stability of fixed-time stable (FxTS) systems. We present a new result on FxTS, which allows a positive term in the time derivative of the Lyapunov function with the aim to model bounded, non-vanishing disturbances in the system dynamics. We characterize the neighborhood to which the system trajectories converge, as well the time of convergence to this neighborhood, in terms of the positive and negative terms that appear in the time derivative of the Lyapunov function. Then, we use the new FxTS result and formulate a quadratic program (QP) that yields control inputs which drive the trajectories of a class of nonlinear, control-affine systems to a goal set in the presence of control input constraints and non-vanishing, bounded disturbances in the system dynamics. We consider an overtaking problem on a highway as a case study, and discuss how to setup the QP for the considered problem, and how to make a decision on when to start the overtake maneuver, in the presence of sensing errors.

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arXiv2020

Adaptive Active-Passive Networked Multiagent Systems

Active-passive multiagent systems consist of agents subject to inputs (active agents) and agents with no inputs (passive agents), where active and passive agent roles are considered to be interchangeable in order to capture a wide array of applications. A challenge in the control of active-passive multiagent systems is the presence of information exchange uncertainties that can yield to undesirable closed-loop system performance. Motivated by this standpoint, this paper proposes an adaptive control algorithm for this class of multiagent systems to suppress the negative effects of information exchange uncertainties. Specifically, by estimating these uncertainties, the proposed adaptive control architecture has the ability to recover the active-passive multiagent system performance in a distributed manner. As a result, the agents converge to a user-adjustable neighborhood of the average of the applied inputs to the active agents. The efficacy of the proposed control architecture is also validated from a human-robot collaboration perspective, where a human is visiting several task locations, and the multiagent system identifies these locations and moves toward them as a coverage control problem.

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arXiv2020

Robust Distributed Fixed-Time Economic Dispatch under Time-Varying Topology

The centralized power generation infrastructure that defines the North American electric grid is slowly moving to the distributed architecture due to the explosion in use of renewable generation and distributed energy resources (DERs), such as residential solar, wind turbines and battery storage. Furthermore, variable pricing policies and profusion of flexible loads entail frequent and severe changes in power outputs required from the individual generation units, requiring fast availability of power allocation. To this end, a fixed-time convergent, fully distributed economic dispatch algorithm for scheduling optimal power generation among a set of DERs is proposed. The proposed algorithm incorporates both load balance and generation capacity constraints.

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arXiv2020

Approximate Time-Optimal Trajectories for Damped Double Integrator in 2D Obstacle Environments under Bounded Inputs

This article provides extensions to existing path-velocity decomposition based time optimal trajectory planning algorithm \cite{kant1986toward} to scenarios in which agents move in 2D obstacle environment under double integrator dynamics with drag term (damped double integrator). Particularly, we extend the idea of a tangent graph \cite{liu1992path} to $\calC^1$-Tangent graph to find continuously differentiable ($\calC^1$) shortest path between any two points. $\calC^1$-Tangent graph has a continuously differentiable ($\calC^1$) path between any two nodes. We also provide analytical expressions for a near time-optimal velocity profile for an agent moving on these shortest paths under the damped double integrator with bounded acceleration.

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arXiv2020

Multi-Swarm Herding: Protecting against Adversarial Swarms

This paper studies a defense approach against one or more swarms of adversarial agents. In our earlier work, we employ a closed formation (`StringNet') of defending agents (defenders) around a swarm of adversarial agents (attackers) to confine their motion within given bounds, and guide them to a safe area. The control design relies on the assumption that the adversarial agents remain close enough to each other, i.e., within a prescribed connectivity region. To handle situations when the attackers no longer stay within such a connectivity region, but rather split into smaller swarms (clusters) to maximize the chance or impact of attack, this paper proposes an approach to learn the attacking sub-swarms and reassign defenders towards the attackers. We use a `Density-based Spatial Clustering of Application with Noise (DBSCAN)' algorithm to identify the spatially distributed swarms of the attackers. Then, the defenders are assigned to each identified swarm of attackers by solving a constrained generalized assignment problem. Simulations are provided to demonstrate the effectiveness of the approach.

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arXiv2020

Fixed-Time Stable Gradient Flows: Applications to Continuous-Time Optimization

This paper proposes novel gradient-flow schemes that yield convergence to the optimal point of a convex optimization problem within a \textit{fixed} time from any given initial condition for unconstrained optimization, constrained optimization, and min-max problems. The application of the modified gradient flow to unconstrained optimization problems is studied under the assumption of gradient-dominance. Then, a modified Newton's method is presented that exhibits fixed-time convergence under some mild conditions on the objective function. Building upon this method, a novel technique for solving convex optimization problems with linear equality constraints that yields convergence to the optimal point in fixed time is developed. More specifically, constrained optimization problems formulated as min-max problems are considered, and a novel method for computing the optimal solution in fixed-time is proposed using the Lagrangian dual. Finally, the general min-max problem is considered, and a modified scheme to obtain the optimal solution of saddle-point dynamics in fixed time is developed. Numerical illustrations that compare the performance of the proposed method against Newton's method, rescaled-gradient method, and Nesterov's accelerated method are included to corroborate the efficacy and applicability of the modified gradient flows in constrained and unconstrained optimization problems.

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arXiv2020

Safety-Critical Adaptive Control with Nonlinear Reference Model Systems

In this paper, a model reference adaptive control architecture is proposed for uncertain nonlinear systems to achieve prescribed performance guarantees. Specifically, a general nonlinear reference model system is considered that captures an ideal and safe system behavior. An adaptive control architecture is then proposed to suppress the effects of system uncertainties without any prior knowledge of their magnitude and rate upper bounds. More importantly, the proposed control architecture enforces the system state trajectories to evolve within a user-specified prescribed distance from the reference system trajectories, satisfying the safety constraints. This eliminates the ad-hoc tuning process for the adaptation rate that is conventionally required in model reference adaptive control to ensure safety. The efficacy of the proposed control architecture is also demonstrated through an illustrative numerical example.

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arXiv2020

Strong Invariance Using Control Barrier Functions: A Clarke Tangent Cone Approach

Many control applications require that a system be constrained to a particular set of states, often termed as safe set. A practical and flexible method for rendering safe sets forward-invariant involves computing control input using Control Barrier Functions and Quadratic Programming methods. Many prior results however require the resulting control input to be continuous, which requires strong assumptions or can be difficult to demonstrate theoretically. In this paper we use differential inclusion methods to show that simultaneously rendering multiple sets invariant can be accomplished using a discontinuous control input. We present an optimization formulation which computes such control inputs and which can be posed in multiple forms, including a feasibility problem, a linear program, or a quadratic program. In addition, we discuss conditions under which the optimization problem is feasible and show that any feasible solution of the considered optimization problem which is measurable renders the multiple safe sets forward invariant.

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arXiv2020

Resilient Finite Time Consensus: A Discontinuous Systems Perspective

Many algorithms have been proposed in prior literature to guarantee resilient multi-agent consensus in the presence of adversarial attacks or faults. The majority of prior work present excellent results that focus on discrete-time or discretized continuous-time systems. Fewer authors have explored applying similar resilient techniques to continuous-time systems without discretization. These prior works typically consider asymptotic convergence and make assumptions such as continuity of adversarial signals, the existence of a dwell time between switching instances for the system dynamics, or the existence of trusted agents that do not misbehave. In this paper, we expand the study of resilient continuous-time systems by removing many of these assumptions and using discontinuous systems theory to provide conditions for normally-behaving agents with nonlinear dynamics to achieve consensus in finite time despite the presence of adversarial agents.

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arXiv2019

Finite-Time Stability of Switched and Hybrid Systems with Unstable Modes

In this work, we study finite-time stability of switched and hybrid systems in the presence of unstable modes. We present sufficient conditions in terms of multiple Lyapunov functions for the origin of the system to be finite time stable. More specifically, we show that even if the value of the Lyapunov function increases in between two switches, i.e., if there are unstable modes in the system, finite-time stability can still 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 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 earlier results in the related literature, and in effect allow the hybrid system to have unstable modes. Then, we illustrate how the proposed finite-time stability conditions specialize for a class of switched systems, and present a method on the synthesis of a finite-time stabilizing switching signal for switched linear systems. As a case study, we design a finite-time stable output feedback controller for a linear switched system, in which only one of the modes is controllable and observable. Numerical example demonstrates the efficacy of the proposed methods.

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arXiv2019

Decentralized Goal Assignment and Safe Trajectory Generation in Multi-Robot Networks via Multiple Lyapunov Functions

This paper considers the problem of decentralized goal assignment and trajectory generation for multi-robot networks when only local communication is available, and proposes an approach based on methods related to switched systems and set invariance. A family of Lyapunov-like functions is employed to encode the (local) decision making among candidate goal assignments, under which a group of connected agents chooses the assignment that results in the shortest total distance to the goals. An additional family of Lyapunov-like barrier functions is activated in the case when the optimal assignment may lead to colliding trajectories, maintaining thus system safety while preserving the convergence guarantees. The proposed switching strategies give rise to feedback control policies that are computationally efficient and scalable with the number of agents, and therefore suitable for applications including first-response deployment of robotic networks under limited information sharing. The efficacy of the proposed method is demonstrated via simulation results and experiments with six ground robots.

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arXiv2019

Herding an Adversarial Swarm in an Obstacle Environment

This paper studies a defense approach against a swarm of adversarial agents. We employ a closed formation (`StringNet') of defending agents around the adversarial agents to restrict their motion and guide them to a safe area while navigating in an obstacle-populated environment. Control laws for forming the StringNet and guiding it to a safe area are developed, and the stability of the closed-loop system is analyzed formally. The adversarial swarm is assumed to move as a flock in the presence of rectangular obstacles. Simulation results are provided to demonstrate the efficacy of the approach.

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arXiv2019

Control-Lyapunov and Control-Barrier Functions based Quadratic Program for Spatio-temporal Specifications

This paper presents a method for control synthesis under spatio-temporal constraints. First, we consider the problem of reaching a set $S$ in a user-defined or prescribed time $T$. We define a new class of control Lyapunov functions, called prescribed-time control Lyapunov functions (PT CLF), and present sufficient conditions on the existence of a controller for this problem in terms of PT CLF. Then, we formulate a quadratic program (QP) to compute a control input that satisfies these sufficient conditions. Next, we consider control synthesis under spatio-temporal objectives given as: the closed-loop trajectories remain in a given set $S_s$ at all times; and, remain in a specific set $S_i$ during the time interval $[t_i, t_{i+1})$ for $i = 0, 1, \cdots, N$; and, reach the set $S_{i+1}$ on or before $t = t_{i+1}$. We show that such spatio-temporal specifications can be translated into temporal logic formulas. We present sufficient conditions on the existence of a control input in terms of PT CLF and control barrier functions. Then, we present a QP to compute the control input efficiently, and show its feasibility under the assumptions of existence of a PT CLF. To the best of authors' knowledge, this is the first paper proposing a QP based method for the aforementioned problem of satisfying spatio-temporal specifications for nonlinear control-affine dynamics with input constraints. We also discuss the limitations of the proposed methods and directions of future work to overcome these limitations. We present numerical examples to corroborate our proposed methods.

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arXiv2019

Determining r- and (r,s)-Robustness of Digraphs Using Mixed Integer Linear Programming

There has been an increase in the use of resilient control algorithms based on the graph theoretic properties of $r$- and $(r,s)$-robustness. These algorithms guarantee consensus of normally behaving agents in the presence of a bounded number of arbitrarily misbehaving agents if the values of the integers $r$ and $s$ are sufficiently large. However, determining an arbitrary graph's robustness is a highly nontrivial problem. This paper introduces a novel method for determining the $r$- and $(r,s)$-robustness of digraphs using mixed integer linear programming; to the best of the authors' knowledge it is the first time that mixed integer programming methods have been applied to the robustness determination problem. The approach only requires knowledge of the graph Laplacian matrix, and can be formulated with binary integer variables. Mixed integer programming algorithms such as branch-and-bound are used to iteratively tighten the lower and upper bounds on $r$ and $s$. Simulations are presented which compare the performance of this approach to prior robustness determination algorithms.

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arXiv2019

A Hybrid Approach to Persistent Coverage in Stochastic Environments

This paper considers the persistent coverage of a 2-D manifold that has been embedded in 3-D space. The manifold is subject to continual impact by intruders which travel at constant velocities along arbitrarily oriented straight-line trajectories. The trajectories of intruders are estimated online with an extended Kalman filter and their predicted impact points contribute normally distributed decay terms to the coverage level. A formal hybrid control strategy is presented that allows for power-constrained 3-D free-flyer agents to persistently monitor the domain, track and intercept intruders, and periodically deploy from and return to a single charging station on the manifold. Guarantees on intruder interception with respect to agent power lifespans are formally proven. The efficacy of the algorithm is demonstrated through simulation.

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arXiv2019

Determining r-Robustness of Digraphs Using Mixed Integer Linear Programming

Convergence guarantees of many resilient consensus algorithms are based on the graph theoretic properties of $r$- and $(r,s)$-robustness. These algorithms guarantee consensus of normally behaving agents in the presence of a bounded number of arbitrarily misbehaving agents if the values of the integers $r$ and $s$ are sufficiently high. However, determining the largest integer $r$ for which an arbitrary digraph is $r$-robust is highly nontrivial. This paper introduces a novel method for calculating this value using mixed integer linear programming. The method only requires knowledge of the graph Laplacian matrix, and can be formulated with affine objective and constraints, except for the integer constraint. Integer programming methods such as branch-and-bound can allow both lower and upper bounds on $r$ to be iteratively tightened. Simulations suggest the proposed method demonstrates greater efficiency than prior algorithms.

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arXiv2019

Resilient Leader-Follower Consensus with Time-Varying Leaders in Discrete-Time Systems

The problem of consensus in the presence of adversarially behaving agents has been studied extensively in the literature. The proposed algorithms typically guarantee that the consensus value lies within the convex hull of initial normal agents' states. In leader-follower consensus problems however, the objective for normally behaving agents is to track a time-varying reference state that may take on values outside of this convex hull. In this paper we present a method for agents with discrete-time dynamics to resiliently track a set of leaders' common time-varying reference state despite a bounded subset of the leaders and followers behaving adversarially. The efficacy of our results are demonstrated through simulations.

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