329 research outputs found
Distributed Optimal State Consensus for Multiple Circuit Systems with Disturbance Rejection
This paper investigates the distributed optimal state consensus problem for an electronic system with a group of circuit units, where the dynamics of each unit is modeled by a Chua's circuit in the presence of disturbance generated by an external system. By means of the internal model approach and feedback control, a compensator-based continuous-time algorithm is proposed to minimize the sum of all cost functions associated with each individual unit in a cooperative manner. Supported by convex analysis, graph theory and Lyapunov theory, it is proved that the proposed algorithm is exponentially convergent. Compared with the centralized algorithms, the proposed protocol possesses remarkable superiority in improving scalability and reliability of multiple circuit systems. Moreover, we also study the distributed uncertain optimal state consensus problem and a linear regret bound is obtained in this case. Finally, a state synchronization example is provided to validate the effectiveness of the proposed algorithms
Uncertain Multi-Agent Systems with Distributed Constrained Optimization Missions and Event-Triggered Communications: Application to Resource Allocation
This paper deals with solving distributed optimization problems with equality
constraints by a class of uncertain nonlinear heterogeneous dynamic multi-agent
systems. It is assumed that each agent with an uncertain dynamic model has
limited information about the main problem and limited access to the
information of the state variables of the other agents. A distributed algorithm
that guarantees cooperative solving of the constrained optimization problem by
the agents is proposed. Via this algorithm, the agents do not need to
continuously broadcast their data. It is shown that the proposed algorithm can
be useful in solving resource allocation problems
Robust distributed linear programming
This paper presents a robust, distributed algorithm to solve general linear
programs. The algorithm design builds on the characterization of the solutions
of the linear program as saddle points of a modified Lagrangian function. We
show that the resulting continuous-time saddle-point algorithm is provably
correct but, in general, not distributed because of a global parameter
associated with the nonsmooth exact penalty function employed to encode the
inequality constraints of the linear program. This motivates the design of a
discontinuous saddle-point dynamics that, while enjoying the same convergence
guarantees, is fully distributed and scalable with the dimension of the
solution vector. We also characterize the robustness against disturbances and
link failures of the proposed dynamics. Specifically, we show that it is
integral-input-to-state stable but not input-to-state stable. The latter fact
is a consequence of a more general result, that we also establish, which states
that no algorithmic solution for linear programming is input-to-state stable
when uncertainty in the problem data affects the dynamics as a disturbance. Our
results allow us to establish the resilience of the proposed distributed
dynamics to disturbances of finite variation and recurrently disconnected
communication among the agents. Simulations in an optimal control application
illustrate the results
Finite-Time Consensus with Disturbance Rejection by Discontinuous Local Interactions in Directed Graphs
In this technical note we propose a decentralized discontinuous interaction rule which allows to achieve consensus in a network of agents modeled by continuous-time first-order integrator dynamics affected by bounded disturbances. The topology of the network is described by a directed graph. The proposed discontinuous interaction rule is capable of rejecting the effects of the disturbances and achieving consensus after a finite transient time. An upper bound to the convergence time is explicitly derived in the technical note. Simulation results, referring to a network of coupled Kuramoto-like oscillators, are illustrated to corroborate the theoretical analysis
Distributed optimization for multi-agent systems with communication delays and external disturbances under a directed network
This article studies the distributed optimization problem for multi-agent systems with communication delays and external disturbances in a directed network. Firstly, a distributed optimization algorithm is proposed based on the internal model principle in which the internal model term can effectively compensate for external environmental disturbances. Secondly, the relationship between the optimal solution and the equilibrium point of the system is discussed through the properties of the Laplacian matrix and graph theory. Some sufficient conditions are derived by using the Lyapunov–Razumikhin theory, which ensures all agents asymptotically reach the optimal value of the distributed optimization problem. Moreover, an aperiodic sampled-data control protocol is proposed, which can be well transformed into the proposed time-varying delay protocol and analyzed by using the Lyapunov–Razumikhin theory. Finally, an example is given to verify the effectiveness of the results
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