Distributed Collision-Free Motion Coordination on a Sphere: A Conic Control Barrier Function Approach

This letter studies a distributed collision avoidance control problem for a group of rigid bodies on a sphere. A rigid body network, consisting of multiple rigid bodies constrained to a spherical surface and an interconnection topology, is first formulated. In this formulation, it is shown that motion coordination on a sphere is equivalent to attitude coordination on the 3-dimensional Special Orthogonal group. Then, an angle-based control barrier function that can handle a geodesic distance constraint on a spherical surface is presented. The proposed control barrier function is then extended to a relative motion case and applied to a collision avoidance problem for a rigid body network operating on a sphere. Each rigid body chooses its control input by solving a distributed optimization problem to achieve a nominal distributed motion coordination strategy while satisfying constraints for collision avoidance. The proposed collision-free motion coordination law is validated via simulation

Semi-global leader-following consensus of linear multi-agent systems with input saturation via low gain feedback

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Distributed Collision-Free Motion Coordination on a Sphere: A Conic Control Barrier Function Approach

This letter studies a distributed collision avoidance control problem for a group of rigid bodies on a sphere. A rigid body network, consisting of multiple rigid bodies constrained to a spherical surface and an interconnection topology, is first formulated. In this formulation, it is shown that motion coordination on a sphere is equivalent to attitude coordination on the 3-dimensional Special Orthogonal group. Then, an angle-based control barrier function that can handle a geodesic distance constraint on a spherical surface is presented. The proposed control barrier function is then extended to a relative motion case and applied to a collision avoidance problem for a rigid body network operating on a sphere. Each rigid body chooses its control input by solving a distributed optimization problem to achieve a nominal distributed motion coordination strategy while satisfying constraints for collision avoidance. The proposed collision-free motion coordination law is validated via simulation

The practice of access pricing : telecommunications in the United Kingdom

Telecommunications was the first network utility to be privatized in the United Kingdom. Drawing on 15 years'experience and discussion in the field, the author shows the economic principles of regulation in general and access pricing in particular that have been implemented. British Telecommunications (BT), formed as a public enterprise in 1980-81, was privatized in 1984. Since then the approaches to regulation have changed in three broad periods: the duoply, the transition to competition, and the recently introduced normalization phase. Dealing with each period, the author focuses on how the actual implementation of access charges are determined, at the same time providing background needed on regulatory intervention generally. Rather than follow the model of competition for a common infrastructure, Oftel [the Office of Telecommunications, the regulatory agency]has encouraged competition between alternative networks, which benefits customers but involves duplication of fixed costs. As a result of Oftel's approach, customers have seen their bills reduced 50 percent in real terms since privatization. It is difficult to know how much to attribute this remarkable result to technological progress (BT halved its workforce in the same period), to regulatory intervention (Oftel set string caps until 1997), or to competition (there are hundreds of players in the market). The author contends more weight should probably be given to the first two. Entrants have not achieved big market shares, if one considers the asymmetric regulation that has been in place for more than a decade. Indirectly, at least, competition benefited consumers by applying discipline to BT's behavior. Oftel's approach was interventionist until 1997, when it began trying to normalize the industry, as authority overseeing competition. The odds on complete deregulation are slight, and some controls on industry will remain. In the longer term, Oftel should especially monitor anticompetitive practices and collusive behavior among the bigger players (BT, CWC, and cellulator operators), The United Kingdom's interconnection experience demonstrates the complexity of the problem and its relationship to other topics, such as tariff rebalancing, access deficit, and universal service. Although a bit ad hoc, the recent incentive regulation, with a network cap based on proper accounting procedures and engineering models, may represent the best practice available today in the telecommunications industry, says the author.Public Sector Economics&Finance,Decentralization,Knowledge Economy,Economic Theory&Research,Payment Systems&Infrastructure,Public Sector Economics&Finance,Education for the Knowledge Economy,Knowledge Economy,Economic Theory&Research,ICT Policy and Strategies

Distributed optimal and predictive control methods for networks of dynamic systems

Several recent approaches to distributed control design over networks of interconnected dynamic systems rely on certain assumptions, such as identical subsystem dynamics, absence of dynamical couplings, linear dynamics and undirected interaction schemes. In this thesis, we investigate systematic methods for relaxing a number of simplifying factors leading to a unifying approach for solving general distributed-control stabilization problems of networks of dynamic agents. We show that the gain-margin property of LQR control holds for complex multiplicative input perturbations and a generic symmetric positive definite input weighting matrix. Proving also that the potentially non-simple structure of the Laplacian matrix can be neglected for stability analysis and control design, we extend two well-known distributed LQR-based control methods originally established for undirected networks of identical linear systems, to the directed case. We then propose a distributed feedback method for tackling large-scale regulation problems of a general class of interconnected non-identical dynamic agents with undirected and directed topology. In particular, we assume that local agents share a minimal set of structural properties, such as input dimension, state dimension and controllability indices. Our approach relies on the solution of certain model matching type problems using local linear state-feedback and input matrix transformations which map the agent dynamics to a target system, selected to minimize the joint control effort of the local feedback-control schemes. By adapting well-established distributed LQR control design methodologies to our framework, the stabilization problem of a network of non-identical dynamical agents is solved. We thereafter consider a networked scheme synthesized by multiple agents with nonlinear dynamics. Assuming that agents are feedback linearizable in a neighborhood near their equilibrium points, we propose a nonlinear model matching control design for stabilizing networks of multiple heterogeneous nonlinear agents. Motivated by the structure of a large-scale LQR optimal problem, we propose a stabilizing distributed state-feedback controller for networks of identical dynamically coupled linear agents. First, a fully centralized controller is designed which is subsequently substituted by a distributed state-feedback gain with sparse structure. The control scheme is obtained byoptimizing an LQR performance index with a tuning parameter utilized to emphasize/deemphasize relative state difference between coupled systems. Sufficient conditions for stability of the proposed scheme are derived based on the inertia of a convex combination of two Hurwitz matrices. An extended simulation study involving distributed load frequency control design of a multi-area power network, illustrates the applicability of the proposed method. Finally, we propose a fully distributed consensus-based model matching scheme adapted to a model predictive control setting for tackling a structured receding horizon regulation problem