Distributed Extremum Seeking Control Research Articles

Cooperative distributed extremum seeking control for coupled multiagent systems based on distributed identification‐gradient tracking

SummaryThis paper proposes a cooperative distributed extremum seeking control (ESC) approach for solving distributed optimization problems in static and dynamical multiagent systems, where the agents' coupled dynamics are unknown and only local cost values can be measured. The approach begins with each agent estimating the local gradient information of the unknown local cost function through recursive identification using measured local cost values. Subsequently, the distributed identification‐gradient tracking (DIGT) algorithm is employed to enable each agent to track the global gradient information of the global cost function, utilizing the estimated local gradient information from itself and its neighbors in the network. The proposed cooperative distributed ESC method enables the multiagent system to reach the extreme point of the global cost function under model‐free scenarios. Furthermore, the convergence properties of the approach are established for both static and dynamical multiagent systems. Finally, numerical examples are presented to demonstrate the effectiveness and stability of the proposed approach.

Distributed extremum-seeking control with nonlinear gain for a class of optimization problems

We propose a distributed extremum seeking controller with a nonlinear gain to solve a class of real-time optimization problems. Each dynamic agent in the network has unknown dynamics, and it is assumed that each agent only knows its own local cost measurement. The nonlinear gain term makes the practical implementation of the controller more feasible. It ensures that the gain is large enough to achieve convergence to the optimum and eliminates the issue of tuning the controller gain. The proposed method is illustrated using a simulation example.

Traffic Congestion Control Using Distributed Extremum Seeking and Filtered Feedback Linearization Control Approaches

This letter presents a hierarchical infrastructure-based control algorithm to manage mainstream traffic flow on freeways. At the upper level, a distributed Extremum-Seeking control approach is employed to determine the optimal density of vehicles in a congested cell. The local objective function is defined such that the average flow within the target cell is maximized to resolve the congestion, and the flow difference with its upstream cell is minimized to prevent back-propagating the congestion. At the lower level, a distributed Filtered Feedback Linearization controller is used to update the suggested velocity communicated to the vehicles so that the desired density determined by the upper level can be achieved in each cell. We adopted the METANET model to describe the aggregated dynamics of the traffic network. We tested the performance of these controllers via a MATLAB-VISSIM COM interface. The results demonstrate that the designed distributed controllers can achieve the desired closed-loop performance despite unknown disturbances in an uncertain large-scale traffic network.

Distributed extremum seeking control of multi-agent systems with unknown dynamics for optimal resource allocation

The paper considers a class of equality constrained resource allocation problems for dynamically coupled multi-agent systems. It is assumed that the mathematical structure of each agent’s dynamics and its local cost function are unknown but depend on the entire resource allocation vector. A distributed dual-mode extremum seeking control is proposed. It is shown that the distributed approach decouples the local contribution of each agent locally while guaranteeing a solution of the network wide optimization problem subject to the resource allocation constraints. The agents operate over a communication network which enables the application of a dynamic consensus algorithm to generate local estimates of the total network cost. Locally, each agent implements a parameter estimation routine to estimate the gradient of the total cost with respect to the local action. Each agent uses its local gradient estimate to implement a dual mode extremum seeking controller that guarantees satisfaction of the resource allocation constraints. Two simulation examples are provided to demonstrate the effectiveness of the proposed technique.

Distributed extremum-seeking control over networks of dynamically coupled unstable dynamic agents

In this paper, a distributed extremum seeking control technique is proposed to solve a class of real-time optimization problems over a network of dynamic agents with unknown unstable dynamics. Each dynamic agent measures a cost that is shared over a network. A dynamic average consensus approach is used to provide each agent with an estimate of the total network cost. The extremum seeking controller operates at each agent to allow each agent to contribute to the optimization of the total cost, in a cooperative fashion. The extremum seeking control technique is based on a proportional–integral approach that provides improvements in transient performance over standard techniques. The contribution of the proposed technique is to solve the simultaneous stabilization and real-time optimization. A dynamic network simulation example is presented to demonstrate the effectiveness of the technique.

Power Maximization of Wind Farms using Discrete-time Distributed Extremum Seeking Control

The use of a model independent control approach to tackle the problem of wind farm power maximization under constant and varying free stream wind speed and direction is considered. In this paper, a time-varying extremum seeking control (TVESC) for discrete-time systems is utilized in a distributed and a collaborative manner. Each controller monitors the actions of a wind turbine and the objective is to maximize the farm wide power capture. To address this task, the distributed controllers ensure that the turbines share local information over an undirected connected communication network. Also, with the use of a discretized version of a continuous-time dynamic average consensus estimator, the controllers help the turbines estimate the mean of the overall power generated in the wind farm. The dynamics of each turbine power estimate is parameterized and the unknown gradient is estimated as a time-varying parameter using a tailored estimation routine. This information is used in the design of the extremum seeking controller. The problem to be solved is addressed via numerical simulations, results are provided to show the effectiveness of this technique.

Distributed Extremum Seeking Control for Wind Farm Power Maximization

A cooperative extremum seeking control technique is employed to overcome the need for accurate models of aerodynamic wake interactions among wind turbines thereby providing an effective technique for farm wide power capture. In this paper, a time-varying extremum seeking control (TVESC) approach is employed in a distributed fashion to maximize the power production of an array of wind turbines under constant and varying free stream wind speeds and directions. Each wind turbine (identified as an agent) has access to the measurement of its unknown local power generation. The goal is to maximize the unknown total power capture in the wind farm. A cooperative approach is employed where the agents work together to maximize this overall objective function. This approach requires every agent to exchange information with its neighbours over an undirected connected communication network. Each agent is also expected to estimate the mean of the overall cost function and this is achieved using a dynamic average consensus estimator. The dynamics of each agent’s cost estimate is parametrized and a parameter estimation routine is used to estimate the unknown gradient information. A distributed extremum seeking controller is designed to ensure that the overall cost is maximized. This problem is tackled via numerical simulations, results are provided to show the effectiveness of this technique.

Distributed extremum-seeking control over networks of unstable dynamic agents

In this paper, a distributed extremum seeking control technique is proposed to solve a class of real-time optimization problems over a network of dynamic agents with unknown unstable dynamics. Each dynamic agent measures a cost that is shared over a network. A dynamic average consensus approach is used to provide each agent with an estimate of the total network cost. The extremum seeking controller uses the local estimate of the total cost to adjust the value of the local decision variables. The contribution of the proposed technique is the simultaneous stabilization of the network dynamics and the distributed optimization of the total network cost. A dynamic network simulation example is presented to demonstrate the effectiveness of the technique.