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High-Dimensional Kuramoto Models on Stiefel Manifolds Synchronize Complex Networks Almost Globally Markdahl, Johan ; ; Goncalves, Jorge in Automatica (2020) Detailed reference viewed: 74 (3 UL)Decentralized cooperative tracking subject to motion constraints ; Markdahl, Johan ; et al in Automatica (2018), 96 This paper addresses the formation control problem, where three agents are tasked with moving an object cooperatively along a desired trajectory while also adjusting its posture to some desired attitudes ... [more ▼] This paper addresses the formation control problem, where three agents are tasked with moving an object cooperatively along a desired trajectory while also adjusting its posture to some desired attitudes, i.e. position and attitude tracking. Two decentralized control laws based on locally available information are proposed. The first control law maintains constant inter-agent distances over time, i.e. the formation of agents moves as a single rigid-body. The second control law relaxes this constraint by only maintaining similarity of the agent formation as a polygon in Euclidean space. [less ▲] Detailed reference viewed: 153 (1 UL)Dynamic controllers for column synchronization of rotation matrices: a QR-factorization approach Thunberg, Johan ; Markdahl, Johan ; Goncalves, Jorge in Automatica (2018), 93 In the multi-agent systems setting, this paper addresses continuous-time distributed synchronization of columns of rotation matrices. More precisely, k specific columns shall be synchronized and only the ... [more ▼] In the multi-agent systems setting, this paper addresses continuous-time distributed synchronization of columns of rotation matrices. More precisely, k specific columns shall be synchronized and only the corresponding k columns of the relative rotations between the agents are assumed to be available for the control design. When one specific column is considered, the problem is equivalent to synchronization on the (d-1)-dimensional unit sphere and when all the columns are considered, the problem is equivalent to synchronization on SO(d). We design dynamic control laws for these synchronization problems. The control laws are based on the introduction of auxiliary variables in combination with a QR-factorization approach. The benefit of this QR-factorization approach is that we can decouple the dynamics for the $k$ columns from the remaining d-k ones. Under the control scheme, the closed loop system achieves almost global convergence to synchronization for quasi-strong interaction graph topologies. [less ▲] Detailed reference viewed: 165 (2 UL)A lifting method for analyzing distributed synchronization on the unit sphere Thunberg, Johan ; Markdahl, Johan ; et al in Automatica (2018) This paper introduces a new lifting method for analyzing convergence of continuous-time distributed synchronization/consensus systems on the unit sphere. Points on the d-dimensional unit sphere are lifted ... [more ▼] This paper introduces a new lifting method for analyzing convergence of continuous-time distributed synchronization/consensus systems on the unit sphere. Points on the d-dimensional unit sphere are lifted to the (d+1)-dimensional Euclidean space. The consensus protocol on the unit sphere is the classical one, where agents move toward weighted averages of their neighbors in their respective tangent planes. Only local and relative state information is used. The directed interaction graph topologies are allowed to switch as a function of time. The dynamics of the lifted variables are governed by a nonlinear consensus protocol for which the weights contain ratios of the norms of state variables. We generalize previous convergence results for hemispheres. For a large class of consensus protocols defined for switching uniformly quasi-strongly connected time-varying graphs, we show that the consensus manifold is uniformly asymptotically stable relative to closed balls contained in a hemisphere. Compared to earlier projection based approaches used in this context such as the gnomonic projection, which is defined for hemispheres only, the lifting method applies globally. With that, the hope is that this method can be useful for future investigations on global convergence. [less ▲] Detailed reference viewed: 100 (1 UL)Intrinsic reduced attitude formation with ring inter-agent graph ; Markdahl, Johan ; et al in Automatica (2017), 85 This paper investigates the reduced attitude formation control problem for a group of rigid-body agents using feedback based on relative attitude information. Under both undirected and directed cycle ... [more ▼] This paper investigates the reduced attitude formation control problem for a group of rigid-body agents using feedback based on relative attitude information. Under both undirected and directed cycle graph topologies, it is shown that reversing the sign of a classic consensus protocol yields asymptotical convergence to formations whose shape depends on the parity of the group size. Specifically, in the case of even parity the reduced attitudes converge asymptotically to a pair of antipodal points and distribute equidistantly on a great circle in the case of odd parity. Moreover, when the inter-agent graph is an undirected ring, the desired formation is shown to be achieved from almost all initial states. [less ▲] Detailed reference viewed: 82 (0 UL)Distributed methods for synchronization of orthogonal matrices over graphs Thunberg, Johan ; Bernard, Florian ; Goncalves, Jorge in Automatica (2017), 80 This paper addresses the problem of synchronizing orthogonal matrices over directed graphs. For synchronized transformations (or matrices), composite transformations over loops equal the identity. We ... [more ▼] This paper addresses the problem of synchronizing orthogonal matrices over directed graphs. For synchronized transformations (or matrices), composite transformations over loops equal the identity. We formulate the synchronization problem as a least-squares optimization problem with nonlinear constraints. The synchronization problem appears as one of the key components in applications ranging from 3D-localization to image registration. The main contributions of this work can be summarized as the introduction of two novel algorithms; one for symmetric graphs and one for graphs that are possibly asymmetric. Under general conditions, the former has guaranteed convergence to the solution of a spectral relaxation to the synchronization problem. The latter is stable for small step sizes when the graph is quasi-strongly connected. The proposed methods are verified in numerical simulations. [less ▲] Detailed reference viewed: 141 (3 UL)Sparse Network Identifiability via Compressed Sensing Goncalves, Jorge ; ; et al in Automatica (2016), 68 Detailed reference viewed: 297 (18 UL)New unified H-infinity dynamic observer design for linear systems with unknown inputs ; ; Voos, Holger et al in Automatica (2016), 65 In this paper, a unified dynamic observer (UO) is proposed for a class of linear systems in the presence of unknown inputs and disturbances. It generalizes the existing results on the proportional ... [more ▼] In this paper, a unified dynamic observer (UO) is proposed for a class of linear systems in the presence of unknown inputs and disturbances. It generalizes the existing results on the proportional observer (PO), the proportional integral observer (PIO) and the dynamic observer (DO). The design approach of the UO is derived from the solution of the linear matrix inequality (LMI), based on the new dynamic observer formulation and the solution of the algebraic constraints obtained from the unbiased estimation error. A numerical example is provided to show the applicability and the performance of our results. [less ▲] Detailed reference viewed: 127 (13 UL)Exact solutions to a class of feedback systems on SO(n) Markdahl, Johan ; in Automatica (2016), 63 This paper provides a novel approach to the problem of attitude tracking for a class of almost globally asymptotically stable feedback laws on View the MathML source. The closed-loop systems are solved ... [more ▼] This paper provides a novel approach to the problem of attitude tracking for a class of almost globally asymptotically stable feedback laws on View the MathML source. The closed-loop systems are solved exactly for the rotation matrices as explicit functions of time, the initial conditions, and the gain parameters of the control laws. The exact solutions provide insight into the transient dynamics of the system and can be used to prove almost global attractiveness of the identity matrix. Applications of these results are found in model predictive control problems where detailed insight into the transient attitude dynamics is utilized to approximately complete a task of secondary importance. Knowledge of the future trajectory of the states can also be used as an alternative to the zero-order hold in systems where the attitude is sampled at discrete time instances. [less ▲] Detailed reference viewed: 99 (3 UL)Consensus and Formation Control on SE(3) for Switching Topologies Thunberg, Johan ; Goncalves, Jorge ; in Automatica (2016), 66 This paper addresses the consensus problem and the formation problem on SE(3) in multi-agent systems with directed and switching interconnection topologies. Several control laws are introduced for the ... [more ▼] This paper addresses the consensus problem and the formation problem on SE(3) in multi-agent systems with directed and switching interconnection topologies. Several control laws are introduced for the consensus problem. By a simple transformation, it is shown that the proposed control laws can be used for the formation problem. The design is first conducted on the kinematic level, where the velocities are the control laws. Then, for rigid bodies in space, the design is conducted on the dynamic level, where the torques and the forces are the control laws. On the kinematic level, first two control laws are introduced that explicitly use Euclidean transformations, then separate control laws are defined for the rotations and the translations. In the special case of purely rotational motion, the consensus problem is referred to as consensus on SO(3) or attitude synchronization. In this problem, for a broad class of local representations or parameterizations of SO(3), including the Axis–Angle Representation, the Rodrigues Parameters and the Modified Rodrigues Parameters, two types of control laws are presented that look structurally the same for any choice of local representation. For these two control laws we provide conditions on the initial rotations and the connectivity of the graph such that the system reaches consensus on SO(3). Among the contributions of this paper, there are conditions for when exponential rate of convergence occurs. A theorem is provided showing that for any choice of local representation for the rotations, there is a change of coordinates such that the transformed system has a well known structure. [less ▲] Detailed reference viewed: 118 (12 UL)Optimal output consensus for linear systems: a topology free approach Thunberg, Johan ; in Automatica (2016), 68 In this paper, for any homogeneous system of agents with linear continuous time dynamics, we formulate an optimal control problem. In this problem a convex cost functional of the control signals of the ... [more ▼] In this paper, for any homogeneous system of agents with linear continuous time dynamics, we formulate an optimal control problem. In this problem a convex cost functional of the control signals of the agents shall be minimized, while the outputs of the agents shall coincide at some given finite time. This is an instance of the rendezvous or finite time consensus problem. We solve this problem without any constraints on the communication topology and provide a solution as an explicit feedback control law for the case when the dynamics of the agents is output controllable. It turns out that the communication graph topology induced by the solution is complete. Based on this solution for the finite time consensus problem, we provide a solution to the case of infinite time horizon. Furthermore, we investigate under what circumstances it is possible to express the controller as a feedback control law of the output instead of the states. [less ▲] Detailed reference viewed: 130 (5 UL)Online Fault Diagnosis for Nonlinear Power Systems Pan, Wei ; ; et al in Automatica (2015), 55 In this paper, automatic fault diagnosis in large scale power networks described by second-order nonlinear swing equations is studied. This work focuses on a class of faults that occur in the transmission ... [more ▼] In this paper, automatic fault diagnosis in large scale power networks described by second-order nonlinear swing equations is studied. This work focuses on a class of faults that occur in the transmission lines. Transmission line protection is an important issue in power system engineering because a large portion of power system faults is occurring in transmission lines. This paper presents a novel technique to detect, isolate and identify the faults on transmissions using only a small number of observations. We formulate the problem of fault diagnosis of nonlinear power network into a compressive sensing framework and derive an optimisationbased formulation of the fault identification problem. An iterative reweighted `1-minimisation algorithm is finally derived to solve the detection problem efficiently. Under the proposed framework, a real-time fault monitoring scheme can be built using only measurements of phase angles of nonlinear power networks. [less ▲] Detailed reference viewed: 146 (14 UL)On minimal realisations of dynamical structure functions ; ; Goncalves, Jorge in Automatica (2015), 55 Motivated by the fact that transfer functions do not contain structural information about networks, dynamical structure functions were introduced to capture causal relationships between measured nodes in ... [more ▼] Motivated by the fact that transfer functions do not contain structural information about networks, dynamical structure functions were introduced to capture causal relationships between measured nodes in networks. From the dynamical structure functions, a) we show that the actual number of hidden states can be larger than the number of hidden states estimated from the corresponding transfer function; b) we can obtain partial information about the true state-space equation, which cannot in general be obtained from the transfer function. Based on these properties, this paper proposes algorithms to find minimal realisations for a given dynamical structure function. This helps to estimate the minimal number of hidden states, to better understand the complexity of the network, and to identify potential targets for new measurements. [less ▲] Detailed reference viewed: 192 (21 UL)Distributed attitude synchronization control of multi-agent systems with switching topologies Thunberg, Johan ; ; et al in Automatica (2014), 50(3), 832-840 This paper addresses the attitude synchronization problem in multi-agent systems with directed and switching interconnection topologies. Two cases for the synchronization problem are discussed under ... [more ▼] This paper addresses the attitude synchronization problem in multi-agent systems with directed and switching interconnection topologies. Two cases for the synchronization problem are discussed under different assumptions about the measurable information. In the first case the agents can measure their rotations relative to a global reference coordinate frame, whilst in the second case they can only measure the relative rotations between each other. Two intuitive distributed control laws based on the axis–angle representations of the rotations are proposed for the two cases, respectively. The invariance of convex balls in SO(3) is guaranteed. Moreover, attitude synchronization is ensured under the well-known mild switching assumptions, the joint strong connection for the first case and joint quasi-strong connection for the second case. To show the effectiveness of the proposed control schemes, illustrative examples are provided. [less ▲] Detailed reference viewed: 110 (2 UL)Decentralised minimum-time consensus ; ; et al in Automatica (2013), 49(5), 1227-1235 We consider the discrete-time dynamics of a network of agents that exchange information according to a nearest-neighbour protocol under which all agents are guaranteed to reach consensus asymptotically ... [more ▼] We consider the discrete-time dynamics of a network of agents that exchange information according to a nearest-neighbour protocol under which all agents are guaranteed to reach consensus asymptotically. We present a fully decentralised algorithm that allows any agent to compute the final consensus value of the whole network in finite time using the minimum number of successive values of its own state history. We show that the minimum number of steps is related to a Jordan block decomposition of the network dynamics, and present an algorithm to compute the final consensus value in the minimum number of steps by checking a rank condition of a Hankel matrix of local observations. Furthermore, we prove that the minimum number of steps is related to graph theoretical notions that can be directly computed from the Laplacian matrix of the graph and from the minimum external equitable partition. [less ▲] Detailed reference viewed: 189 (4 UL)Robust stabilization of uncertain descriptor fractional-order systems Ndoye, Ibrahima ; ; et al in Automatica (2013) This paper presents sufficient conditions for the robust asymptotical stabilization of uncertain descriptor fractional-order systems with the fractional order α satisfying 0<\alpha<2. The results are ... [more ▼] This paper presents sufficient conditions for the robust asymptotical stabilization of uncertain descriptor fractional-order systems with the fractional order α satisfying 0<\alpha<2. The results are obtained in terms of linear matrix inequalities. The parameter uncertainties are assumed to be time-invariant and norm-bounded appearing in the state matrix. A necessary and sufficient condition for the normalization of uncertain descriptor fractional-order systems is given via linear matrix inequality (LMI) formulation. The state feedback control to robustly stabilize such uncertain descriptor fractional-order systems with the fractional order \alpha belonging to 0</alpha<2 is derived. Two numerical examples are given to demonstrate the applicability of the proposed approach. [less ▲] Detailed reference viewed: 160 (5 UL)Robust dynamical network structure reconstruction ; ; et al in Automatica (2011), 47(6), This paper addresses the problem of network reconstruction from data. Previous work identified necessary and sufficient conditions for network reconstruction of LTI systems, assuming perfect measurements ... [more ▼] This paper addresses the problem of network reconstruction from data. Previous work identified necessary and sufficient conditions for network reconstruction of LTI systems, assuming perfect measurements (no noise) and perfect system identification. This paper assumes that the conditions for network reconstruction have been met but here we additionally take into account noise and unmodelled dynamics (including nonlinearities). In order to identify the network structure that generated the data, we compute the smallest distances between the measured data and the data that would have been generated by particular network structures. We conclude with biologically inspired network reconstruction examples which include noise and nonlinearities. [less ▲] Detailed reference viewed: 123 (0 UL)An adaptive high-gain observer for nonlinear systems Boizot, Nicolas ; ; in Automatica (2010), 46(9), 1483-1488 In this paper the authors provide a solution to the noise sensitivity of high-gain observers. The resulting nonlinear observer possesses simultaneously 1) extended Kalman filter's good noise filtering ... [more ▼] In this paper the authors provide a solution to the noise sensitivity of high-gain observers. The resulting nonlinear observer possesses simultaneously 1) extended Kalman filter's good noise filtering properties, and 2) the reactivity of the high-gain extended Kalman filter with respect to large perturbations. The authors introduce innovation as the quantity that drives the gain adaptation. They prove a general convergence result, propose guidelines to practical implementation and show simulation results for an example. [less ▲] Detailed reference viewed: 200 (1 UL)Reachability analysis of continuous-time piecewise affine systems ; Goncalves, Jorge in Automatica (2008), 44(12), 3189-3194 This paper proposes an algorithm for the characterization of reachable sets of states for continuous-time piecewise affine systems. Given a model of the system and a bounded set of possible initial states ... [more ▼] This paper proposes an algorithm for the characterization of reachable sets of states for continuous-time piecewise affine systems. Given a model of the system and a bounded set of possible initial states, the algorithm employs an LMI approach to compute both upper and lower bounds on reachable regions. Rather than performing computations in the state-space, this method uses impact maps to find the reachable sets on the switching surfaces of the system. This tool can then be used to deduce safety and performance results about the system. [less ▲] Detailed reference viewed: 124 (1 UL)Necessary conditions for robust stability of a class of nonlinear systems Goncalves, Jorge ; in Automatica (1998), 34(6), 705-714 Input-output stability results for feedback systems are developed. Robust stability conditions are presented for nonlinear systems with nonlinear uncertainty defined by some function (with argument equal ... [more ▼] Input-output stability results for feedback systems are developed. Robust stability conditions are presented for nonlinear systems with nonlinear uncertainty defined by some function (with argument equal to the norm of the input) that bounds its output norm. A sufficient small gain theorem for a class of these systems is known. Here, necessary conditions are presented for the vector space (L- infinity ll . ll infinity). These results capture the conservatism of the small gain theorem as it is applied to systems that do not have linear gain. The theory is also developed for the case of L2 signal norms, indicating some difficulties which make this case less natural than L-infinity. [less ▲] Detailed reference viewed: 81 (2 UL) |
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