393 research outputs found
Relative controllability of multiagent systems with pairwise different delays in states
In this manuscript, relative controllability of leader–follower multiagent systems with pairwise different delays in states and fixed interaction topology is considered. The interaction topology of the group of agents is modeled by a directed graph. The agents with unidirectional information flows are selected as leaders, and the others are followers. Dynamics of each follower obeys a generic time-invariant delay differential equation, and the delays of agents, which satisfy a specified condition, are different one another because of the degeneration or burn-in of sensors. With a neighbor-based protocol steering, the dynamics of followers become a compact form with multiple delays. Solution of the multidelayed system without pairwise matrices permutation is obtained by improving the method in the references, and relative controllability is established via Gramian criterion. Further rank criterion of a single delay system is dealt with. Simulation illustrates the theoretical deduction
Leader-following Consensus Control of a Distributed Linear Multi-agent System using a Sliding Mode Strategy
A distributed leader-following consensus control framework is proposed for a linear system. The linear system is first transformed into a regular form. Then a linear sliding mode is designed to provide high robustness, and the corresponding consensus protocol is proposed in a fully distributed fashion. When matched disturbances are present, it can be demonstrated that the system states reach the sliding mode in finite time and consensus can be achieved asymptotically using Lyapunov theory and the invariant set theorem. Simulation results validate the effectiveness of the proposed algorithm
Leader-following Consensus Control of a Distributed Linear Multi-agent System using a Sliding Mode Strategy
A distributed leader-following consensus control framework is proposed for a linear system. The linear system is first transformed into a regular form. Then a linear sliding mode is designed to provide high robustness, and the corresponding consensus protocol is proposed in a fully distributed fashion. When matched disturbances are present, it can be demonstrated that the system states reach the sliding mode in finite time and consensus can be achieved asymptotically using Lyapunov theory and the invariant set theorem. Simulation results validate the effectiveness of the proposed algorithm
Event-triggered pinning control of switching networks
This paper investigates event-triggered pinning control for the synchronization of complex networks of nonlinear dynamical systems. We consider networks described by time-varying weighted graphs and featuring generic linear interaction protocols. Sufficient conditions for the absence of Zeno behavior are derived and exponential convergence of a global normed error function is proven. Static networks are considered as a special case, wherein the existence of a lower bound for interevent times is also proven. Numerical examples demonstrate the effectiveness of the proposed control strategy
Opinion Dynamics and the Evolution of Social Power in Social Networks
A fundamental aspect of society is the exchange and discussion of
opinions between individuals, occurring in mediums and situations
as varied as company boardrooms, elementary school classrooms and
online social media. This thesis studies several mathematical
models of how an individual’s opinion(s) evolves via
interaction with others in a social network, developed to reflect
and capture different socio-psychological processes that occur
during the interactions.
In the first part, and inspired by Solomon E. Asch’s seminal
experiments on conformity, a novel discrete-time model of opinion
dynamics is proposed, with each individual having both an
expressed and a private opinion on the same topic. Crucially, an
individual’s expressed opinion is altered from the
individual’s private opinion due to pressures to conform to the
majority opinion of the social network. Exponential convergence
of the opinion dynamical system to a unique configuration is
established for general networks. Several conclusions are
established, including how differences between an individual’s
expressed and private opinions arise, and how to estimate
disagreement among the private opinions at equilibrium. Asch’s
experiments are revisited and re-examined, and then it is shown
that a few extremists can create “pluralistic ignorance”,
where people believe there is majority support for a position but
in fact the position is privately rejected by the majority of
individuals!
The second part builds on the recently proposed discrete-time
DeGroot–Friedkin model, which describes the evolution of an
individual’s self-confidence (termed social power) in his/her
opinion over the discussion of a sequence of issues. Using
nonlinear contraction analysis, exponential convergence to a
unique equilibrium is established for networks with constant
topology. Networks with issue-varying topology (which remain
constant for any given issue) are then studied; exponential
convergence to a unique limiting trajectory is established. In a
social context, this means that each individual forgets his/her
initial social power exponentially fast; in the limit, his/her
social power for a given issue depends only on the previously
occurring sequence of dynamic topology. Two further related works
are considered; a network modification problem, and a different
convergence proof based on Lefschetz Fixed Point Theory.
In the final part, a continuous-time model is proposed to capture
simultaneous discussion of logically interdependent topics; the
interdependence is captured by a “logic matrix”. When no
individual remains attached to his/her initial opinion, a
necessary and sufficient condition for the network to reach a
consensus of opinions is provided. This condition depends on the
interplay between the network interactions and the logic matrix;
if the network interactions are too strong when compared to the
logical couplings, instability can result. Last, when some
individuals remain attached to their initial opinions, sufficient
conditions are given for opinions to converge to a state of
persistent disagreement
Stability and Control in Complex Networks of Dynamical Systems
Stability analysis of networked dynamical systems has been of interest in many disciplines such as biology and physics and chemistry with applications such as LASER cooling and plasma stability. These large networks are often modeled to have a completely random (Erdös-Rényi) or semi-random (Small-World) topologies. The former model is often used due to mathematical tractability while the latter has been shown to be a better model for most real life networks. The recent emergence of cyber physical systems, and in particular the smart grid, has given rise to a number of engineering questions regarding the control and optimization of such networks. Some of the these questions are: How can the stability of a random network be characterized in probabilistic terms? Can the effects of network topology and system dynamics be separated? What does it take to control a large random network? Can decentralized (pinning) control be effective? If not, how large does the control network needs to be? How can decentralized or distributed controllers be designed? How the size of control network would scale with the size of networked system? Motivated by these questions, we began by studying the probability of stability of synchronization in random networks of oscillators. We developed a stability condition separating the effects of topology and node dynamics and evaluated bounds on the probability of stability for both Erdös-Rényi (ER) and Small-World (SW) network topology models. We then turned our attention to the more realistic scenario where the dynamics of the nodes and couplings are mismatched. Utilizing the concept of ε-synchronization, we have studied the probability of synchronization and showed that the synchronization error, ε, can be arbitrarily reduced using linear controllers. We have also considered the decentralized approach of pinning control to ensure stability in such complex networks. In the pinning method, decentralized controllers are used to control a fraction of the nodes in the network. This is different from traditional decentralized approaches where all the nodes have their own controllers. While the problem of selecting the minimum number of pinning nodes is known to be NP-hard and grows exponentially with the number of nodes in the network we have devised a suboptimal algorithm to select the pinning nodes which converges linearly with network size. We have also analyzed the effectiveness of the pinning approach for the synchronization of oscillators in the networks with fast switching, where the network links disconnect and reconnect quickly relative to the node dynamics. To address the scaling problem in the design of distributed control networks, we have employed a random control network to stabilize a random plant network. Our results show that for an ER plant network, the control network needs to grow linearly with the size of the plant network
Problems in Control, Estimation, and Learning in Complex Robotic Systems
In this dissertation, we consider a range of different problems in systems, control, and learning theory and practice. In Part I, we look at problems in control of complex networks. In Chapter 1, we consider the performance analysis of a class of linear noisy dynamical systems. In Chapter 2, we look at the optimal design problems for these networks. In Chapter 3, we consider dynamical networks where interactions between the networks occur randomly in time. And in the last chapter of this part, in Chapter 4, we look at dynamical networks wherein coupling between the subsystems (or agents) changes nonlinearly based on the difference between the state of the subsystems. In Part II, we consider estimation problems wherein we deal with a large body of variables (i.e., at large scale). This part starts with Chapter 5, in which we consider the problem of sampling from a dynamical network in space and time for initial state recovery. In Chapter 6, we consider a similar problem with the difference that the observations instead of point samples become continuous observations that happen in Lebesgue measurable observations. In Chapter 7, we consider an estimation problem in which the location of a robot during the navigation is estimated using the information of a large number of surrounding features and we would like to select the most informative features using an efficient algorithm. In Part III, we look at active perception problems, which are approached using reinforcement learning techniques. This part starts with Chapter 8, in which we tackle the problem of multi-agent reinforcement learning where the agents communicate and classify as a team. In Chapter 9, we consider a single agent version of the same problem, wherein a layered architecture replaces the architectures of the previous chapter. Then, we use reinforcement learning to design the meta-layer (to select goals), action-layer (to select local actions), and perception-layer (to conduct classification)
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