Qing Hui

Finite-Time Semistability and Consensus for Nonlinear Dynamical Networks

This paper focuses on semistability and finite-time stability analysis and synthesis of systems having a continuum of equilibria. Semistability is the property whereby the solutions of a dynamical system converge to Lyapunov stable equilibrium points determined by the system initial conditions. In this paper, we merge the theories of semistability and finite-time stability to develop a rigorous framework for finite-time semistability. In particular, finite-time semistability for a continuum of equilibria of continuous autonomous systems is established. Continuity of the settling-time function as well as Lyapunov and converse Lyapunov theorems for semistability are also developed. In addition, necessary and sufficient conditions for finite-time semistability of homogeneous systems are addressed by exploiting the fact that a homogeneous system is finite-time semistable if and only if it is semistable and has a negative degree of homogeneity. Unlike previous work on homogeneous systems, our results involve homogeneity with respect to semistable dynamics, and require us to adopt a geometric description of homogeneity. Finally, we use these results to develop a general framework for designing semistable protocols in dynamical networks for achieving coordination tasks in finite time.

Brief paper: Distributed nonlinear control algorithms for network consensus

In this paper, we develop a thermodynamic framework for addressing consensus problems for nonlinear multiagent dynamical systems with fixed and switching topologies. Specifically, we present distributed nonlinear static and dynamic controller architectures for multiagent coordination. The proposed controller architectures are predicated on system thermodynamic notions resulting in controller architectures involving the exchange of information between agents that guarantee that the closed-loop dynamical network is consistent with basic thermodynamic principles.

Semistability, Finite-Time Stability, Differential Inclusions, and Discontinuous Dynamical Systems Having a Continuum of Equilibria

This paper focuses on semistability and finite-time semistability for discontinuous dynamical systems having a continuum of equilibria. Semistability is the property whereby the solutions of a dynamical system converge to Lyapunov stable equilibrium points determined by the system initial conditions. In this paper, we extend the theory of semistability to discontinuous autonomous dynamical systems. In particular, Lyapunov-based tests for semistability and finite-time semistability for autonomous differential inclusions are established.

Finite-time stabilization of nonlinear dynamical systems via control vector Lyapunov functions

Finite-time stability involves dynamical systems whose trajectories converge to an equilibrium state in finite time. Since finite-time convergence implies nonuniqueness of system solutions in reverse time, such systems possess non-Lipschitzian dynamics. Sufficient conditions for finite-time stability have been developed in the literature using holder continuous Lyapunov functions. In this paper, we develop a general framework for finite-time stability analysis based on vector Lyapunov functions. Specifically, we construct a vector comparison system whose solution is finite-time stable and relate this finite-time stability property to the stability properties of a nonlinear dynamical system using a vector comparison principle. Furthermore, we design a universal decentralized finite-time stabilizer for large-scale dynamical systems that is robust against full modeling uncertainty.

H 2 optimal semistable stabilization for linear discrete-time dynamical systems with applications to network consensus

In this paper, we develop H2 semistability theory for linear discrete-time dynamical systems. Using this theory, we design H2 optimal semistable controllers for linear dynamical systems. Unlike the standard H2 optimal control problem, a complicating feature of the H2 optimal semistable stabilization problem is that the closed-loop Lyapunov equation guaranteeing semistability can admit multiple solutions. An interesting feature of the proposed approach, however, is that a least squares solution over all possible semistabilizing solutions corresponds to the H2 optimal solution. It is shown that this least squares solution can be characterized by a linear matrix inequality minimization problem. Finally, the proposed framework is used to develop H2 optimal semistable controllers for addressing the consensus control problem in networks of dynamic agents.

Energy- and Entropy-Based Stabilization for Lossless Dynamical Systems via Hybrid Controllers

A novel class of dynamic, energy-based hybrid controllers is proposed as a means for achieving enhanced energy dissipation in lossless dynamical systems. These dynamic controllers combine a logical switching architecture with continuous dynamics to guarantee that the system plant energy is strictly decreasing across switchings. The general framework leads to closed-loop systems described by impulsive differential equations. In addition, we construct hybrid dynamic controllers that guarantee that the closed-loop system is consistent with basic thermodynamic principles. In particular, the existence of an entropy function for the closed-loop system is established that satisfies a hybrid Clausius-type inequality. Special cases of energy-based and entropy-based hybrid controllers involving state-dependent switching are described.

Hybrid consensus protocols: an impulsive dynamical system approach

In this paper, we develop a novel hybrid control framework for addressing consensus problems for multiagent dynamical systems. Specifically, we present hybrid distributed controller architectures for multiagent coordination. The proposed controller architectures are predicated on system thermodynamic notions resulting in thermodynamically consistent hybrid controller architectures involving the exchange of information between agents that guarantee that the closed-loop dynamical network is consistent with basic thermodynamic principles. A unique feature of the proposed framework is that the proposed controller architectures are hybrid and can achieve finite-time coordination. The overall closed-loop dynamics under any of these controller algorithms achieving consensus possesses discontinuous flows since the controller algorithms combine logical switchings with continuous dynamics, leading to impulsive differential equations.

Semistability theory for differential inclusions with applications to consensus problems in dynamical networks with switching topology

This paper focuses on semistability and finite-time semistability for discontinuous dynamical systems. Semistability is the property whereby the solutions of a dynamical system converge to Lyapunov stable equilibrium points determined by the system initial conditions. Using these results we develop a framework for designing semistable protocols in dynamical networks with switching topologies. Specifically, we present distributed nonlinear static and dynamic output feedback controller architectures for multiagent network consensus with dynamic communication topologies.

Modeling the Vulnerability of Feedback-Control Based Internet Services to Low-Rate DoS Attacks

Feedback control is a critical element in many Internet services (e.g., quality-of-service aware applications). Recent research has demonstrated the vulnerability of some feedback-control based applications to low-rate denial-of-service (LRDoS) attacks, which send high-intensity requests in an ON/OFF pattern to degrade the victims performance and evade the detection designed for traditional DoS attacks. However, the intricate interaction between LRDoS attacks and the feedback control mechanism remains largely unknown. In this paper, we address two fundamental questions: 1) what is the impact of an LRDoS attack on a general feedback-control based system and 2) how to conduct a systematic evaluation of the impact of an LRDoS attack on specific feedback-control based systems. To tackle these problems, we model the system under attack as a switched system and then examine its properties. We conduct the first theoretical investigation on the impact of the LRDoS attack on a general feedback control system. We formally show that the attack can make the systems steady-state error oscillate along with the attack period, and prove the existence of LRDoS attacks that can force the system to be far off the desired state. In addition, we propose a novel methodology to systematically characterize the impact of an LRDoS attack on specific systems, and apply it to a web server and an IBM Notes server. This investigation obtains many new insights, such as new attack scenarios, the bound of the systems states, the relationship between the bound and the LRDoS attacks, the close-formed equations for quantifying the impact, and so on. The extensive experimental results are congruent with the theoretical analysis.

H2 optimal semistable control for linear dynamical systems: An LMI approach☆

Abstract In this paper, we develop H 2 semistability theory for linear dynamical systems. Using this theory, we design H 2 optimal semistable controllers for linear dynamical systems. Unlike the standard H 2 optimal control problem, a complicating feature of the H 2 optimal semistable stabilization problem is that the closed-loop Lyapunov equation guaranteeing semistability can admit multiple solutions. An interesting feature of the proposed approach, however, is that a least squares solution over all possible semistabilizing solutions corresponds to the H 2 optimal solution. It is shown that this least squares solution can be characterized by a linear matrix inequality minimization problem.