Output Agreement Problem Research Articles

A new look at distributed optimal output agreement of multi-agent systems

This paper studies the distributed optimal output agreement problem for multi-agent systems with the agents admitting the essential reference-tracking capability characterized by the well-known notion of system types. In the present system setup, the agents know only the gradient values of their corresponding local objective functions, and distributed optimizers are designed to generate reference signals for the agents. Under mild assumptions on the local objective functions and the connectivity between the agents, it is shown that the agents’ outputs can be steered to the global optimum of the total objective function as long as the system type of each agent is not less than one. A numerical example on the simultaneous formation and source seeking of a group of vertical take-off and landing (VTOL) vehicles is employed to verify the effectiveness of the proposed approach.

Distributed Optimization of Nonlinear Multiagent Systems: A Small-Gain Approach

This article studies the distributed optimal output agreement problem for multiagent systems described by uncertain nonlinear models. By using the partial information of an objective function, the design aims to steer the outputs of the agents to an agreement on the optimal solution to the objective function. To solve this problem, this article introduces distributed coordinators to calculate the desired outputs, and designs reference-tracking controllers for the agents to follow the desired outputs. To deal with the nonlinear uncertain dynamics, the closed-loop multiagent system is considered as a dynamical network, and Sontag's input-to-state stability is employed to characterize the interconnections. It is shown that output agreement in multiagent nonlinear systems is achievable by means of distributed optimal controllers via a small-gain approach. The proposed design features a three-layer architecture, and the reference-tracking controllers can be implemented as successive nonlinear proportional-integral loops. A numerical example is employed to show the effectiveness of the design.

Cooperative Formation Control Under Switching Topology: An Experimental Case Study in Multirotors.

This article presents a novel design algorithm for the cooperative formation control of multirotors with directed and switching topology. A key strategy is to transform the formation control problem into an output agreement problem for which a class of cooperative controllers with successive loops is developed to achieve output agreement. For practical implementation, velocities and accelerations of the controlled multirotors are restricted to within desired ranges by introducing appropriate saturations to the loops. It is proved that each controlled multirotor admits an invariant set property, and the formation control objective can be achieved if a mild joint connectivity condition is satisfied by the switching topology. Along the way, this article also proves a result of independent interest in the output agreement problem subject to both velocity and control input constraints with switching topology. Numerical simulations and physical experiments are employed to verify the effectiveness of the proposed design.

Robust Output Agreement of Multi-Agent Systems with Flexible Topologies

This paper studies the robust output agreement problem for second-order multi-agent systems with flexible topologies subject to measurement disturbances. A new distributed control law is proposed to guarantee the robust output agreement in the sense of input-to-state stability (ISS) as long as the union of the interconnection graphs satisfies a standard connectivity condition. It is proved that, robust output agreement can be achieved in the presence of any bounded measurement disturbances if the functions of the distributed control laws are radially unbounded, and a local result can still be guaranteed if the condition of radial unboundedness is not satisfied. Numerical simulations are employed to show the effectiveness of the main result.

An internal model approach to (optimal) frequency regulation in power grids with time-varying voltages

This paper studies the problem of frequency regulation in power grids under unknown and possible time-varying load changes, while minimizing the generation costs. We formulate this problem as an output agreement problem for distribution networks and address it using incremental passivity and distributed internal-model-based controllers. Incremental passivity enables a systematic approach to study convergence to the steady state with zero frequency deviation and to design the controller in the presence of time-varying voltages, whereas the internal-model principle is applied to tackle the uncertain nature of the loads.

Distributed control of nonlinear uncertain systems: A cyclic-small-gain approach

This paper presents a cyclic-small-gain approach to distributed control of nonlinear multi-agent systems for output agreement. Through a novel nonlinear control law design, the output agreement problem is transformed into a stabilization problem, and the closed-loop multi-agent system is transformed into a large-scale system composed of input-to-state stability (ISS) subsystems which are interconnected with each other through redefined outputs. By forcing the redefined outputs to go to arbitrarily small neighborhoods of the origin, practical consensus is achieved for the agents in the sense that their outputs ultimately converge to each other within an arbitrarily small region. A recently developed cyclic-small-gain result is adopted to assign appropriately the ISS gains to the transformed interconnected system. Moreover, if the system is disturbance-free, then consensus can be guaranteed. Interestingly, the closed-loop multi-agent system is also robust to bounded time-delays and disturbances in information exchange.

Internal models for nonlinear output agreement and optimal flow control

This paper studies the problem of output agreement in networks of nonlinear dynamical systems under time-varying disturbances. Necessary and sufficient conditions for output agreement are derived for the class of incrementally passive systems. Following this, it is shown that the optimal distribution problem in dynamic inventory systems with time-varying supply and demand can be cast as a special version of the output agreement problem. We show in particular that the time-varying optimal distribution problem can be solved by applying an internal model controller to the dual variables of a certain convex network optimization problem.