In this paper, we study the H∞-norm of linear systems over graphs, which is used to model distribution networks. In particular, we aim to minimize the H∞-norm subject to allocation of the weights on the edges. The optimization problem is formulated with LMI (Linear-Matrix-Inequality) constraints. For distribution networks with one port, i.e., SISO systems, we show that the H∞-norm coincides with the effective resistance between the nodes in the port. Moreover, we derive an upper bound of the H∞-norm, which is in terms of the algebraic connectivity of the graph on which the distribution network is defined.

In this paper, we consider the classic car overtake problem. There are three cars, two moving along the same direction in the same lane while the third car moves in the direction opposite to that of the first two cars in the adjacent lane. The objective of the trailing car is to overtake the car in front of it avoiding collision with the other cars in the scenario. The information available to the trailing car is the relative position, relative velocities with respect to other cars and its position and past actions. The relative position and relative velocity information is corrupted by noise. Given this information, the car needs to make a decision as to whether it wants to overtake or not. We present a control algorithm for the car which minimizes the probability of collision with both the cars. We also present the results obtained by simulating the above scenario with the control algorithm. Through simulations, we study the effect of the variance of the measurement noise and the time at which the decision is made on the probability of collision.

We study the deployment of a first-order multi-agent system over a desired smooth curve in 2D or 3D space. We assume that the agents have access to the local information of the desired curve and their relative positions with respect to their closest neighbors, whereas in addition a leader is able to measure his relative position with respect to the desired curve. For the case of an open C-2 curve, we consider two boundary leaders that use boundary instantaneous static output-feedback controllers. For the case of a closed C-2 curve we assume that the leader transmits his measurement to other agents through a communication network. The resulting closed-loop system is modeled as a heat equation with a delayed (due to the communication) boundary state, where the state is the relative position of the agents with respect to the desired curve. By choosing appropriate controller gains (the diffusion coefficient and the gain multiplying the leader state), we can achieve any desired decay rate provided the delay is small enough. The advantage of our approach is in the simplicity of the control law and the conditions. Numerical example illustrates the efficiency of the method.

We study the deployment of a first-order multi-agent system over a desired smooth curve in 3D space. We assume that the agents have access to the local information of the desired curve and their displacements with respect to their closest neighbors, whereas in addition a leader is able to measure his absolute displacement with respect to the desired curve. In this paper we consider the case that the desired curve is a closed C-2 curve and we assume that the leader transmit his measurement to other agents through a communication network. We start the algorithm with displacement-based formation control protocol. Connections from this ODE model to a PDE model (heat equation), which can be seen as a reduced model, are then established. The resulting closed-loop system is modeled as a heat equation with delay (due to the communication). The boundary condition is periodic since the desired curve is closed. By choosing appropriate controller gains (the diffusion coefficient and the gain multiplying the leader state), we can achieve any desired decay rate provided the delay is small enough. The advantage of our approach is in the simplicity of the control law and the conditions. Numerical example illustrates the efficiency of the method.

We consider an extension of the Rescorla-Wagner model which bridges the gap between conditioning and learning on a neural-cognitive, individual psychological level, and the social population level. In this model, the interaction among individuals is captured by a Markov process. The resulting human-social behavior model is a recurrent iterated function system which behaves differently from the classical Rescorla-Wagner model due to randomness. A sufficient condition for the convergence of the forward process starting with arbitrary initial distribution is provided. Furthermore, the ergodicity properties of the internal states of agents in the proposed model are studied.

In this paper, the attitude tracking problem is considered using the rotation matrices. Due to the inherent topological restriction, it is impossible to achieve global attractivity with any continuous attitude control system on SO(3). Hence in this work, we propose some control protocols achieving almost global tracking asymptotically and in finite time, respectively. In these protocols, no world frame is needed and only relative state information are requested. For finitetime tracking case, Filippov solutions and non-smooth analysis techniques are adopted to handle the discontinuities. Simulation examples are provided to verify the performances of the control protocols designed in this paper.

This paper studies multi-agent systems with nonlinear consensus protocols, i.e., only nonlinear measurements of the states are available to agents. The solutions of these systems are understood in Filippov sense since the possible discontinuity of the nonlinear controllers. Under the condition that the nonlinear functions are monotonic increasing without any continuous constraints, asymptotic stability is derived for systems defines on both directed and undirected graphs. The results can be applied to quantized consensus which extend some existing results from undirected graphs to directed ones.

Nonlinearities are present in all real applications. Two types of general nonlinear consensus protocols are considered in this paper, namely, the systems with nonlinear communication and actuator constraints. The solutions of the systems are understood in the sense of Filippov to handle the possible discontinuity of the controllers. For each case, we prove the asymptotic stability of the systems with minimal assumptions on the nonlinearity, for both directed and undirected graphs. These results extend the literature to more general nonlinear dynamics and topologies. As applications of established theorems, we interpret the results on quantized consensus protocols.

A finite-time attitude synchronization problem is considered in this paper where the rotation of each rigid body is expressed using the axis-angle representation. One simple discontinuous and distributed controller using the vectorized signum function is proposed. This controller only involves the sign of the state differences of adjacent neighbors. In order to avoid the singularity introduced by the axis-angular representation, an extra constraint is added to the initial condition. It is proved that for some initial conditions, the control law achieves finite-time attitude synchronization. One simulated example is provided to verify the usage of the control protocol designed in this paper.

The finite-time attitude synchronization problem is considered in this paper, where the rotation of each rigid body is expressed using the axis-angle representation. Two discontinuous and distributed controllers using the vectorized signum function are proposed, which guarantee almost global and local convergence, respectively. Filippov solutions and non-smooth analysis techniques are adopted to handle the discontinuities. Sufficient conditions are provided to guarantee finite-time convergence and boundedness of the solutions. Simulation examples are provided to verify the performances of the control protocols designed in this paper.

In this paper, a projected primal-dual gradient flow of augmented Lagrangian is presented to solve convex optimization problems that are not necessarily strictly convex. The optimization variables are restricted by a convex set with computable projection operation on its tangent cone as well as equality constraints. As a supplement of the analysis in Niederlander and Cortes (2016), we show that the projected dynamical system converges to one of the saddle points and hence finding an optimal solution. Moreover, the problem of distributedly maximizing the algebraic connectivity of an undirected network by optimizing the port gains of each nodes (base stations) is considered. The original semi-definite programming (SDP) problem is relaxed into a nonlinear programming (NP) problem that will be solved by the aforementioned projected dynamical system. Numerical examples show the convergence of the aforementioned algorithm to one of the optimal solutions. The effect of the relaxation is illustrated empirically with numerical examples. A methodology is presented so that the number of iterations needed to reach the equilibrium is suppressed. Complexity per iteration of the algorithm is illustrated with numerical examples.