Extremum-seeking Control Approach Research Articles

An Extremum-Seeking Controller for Distributed Optimization Over Sensor Networks

In this study, a distributed extremum-seeking control approach is proposed to solve a class of constrained real-time optimization problems. Each agent operates over a sensor network. The agents have access to the measurement of a local cost and local constraints which it can communicate to neighbouring agents over the network. A dynamic consensus algorithm is used to provide all agents with an estimate of the total network cost and global constraints. A local extremum seeking controller is used to manipulate local input variables. It is shown that the distributed extremum-seeking control system achieves the optimization of the total network cost.

Online Optimization Applied to a Shockless Explosion Combustor

Changing the combustion process of a gas turbine from a constant-pressure to a pressure-increasing approximate constant-volume combustion (aCVC) is one of the most promising ways to increase the efficiency of turbines in the future. In this paper, a newly proposed method to achieve such an aCVC is considered. The so-called shockless explosion combustion (SEC) uses auto-ignition and a fuel stratification to achieve a spatially homogeneous ignition. The homogeneity of the ignition can be adjusted by the mixing of fuel and air. A proper filling profile, however, also depends on changing parameters, such as temperature, that cannot be measured in detail due to the harsh conditions inside the combustion tube. Therefore, a closed-loop control is required to obtain an adequate injection profile and to reject such unknown disturbances. For this, an optimization problem is set up and a novel formulation of a discrete extremum seeking controller is presented. By approximating the cost function with a parabola, the first derivative and a Hessian matrix are estimated, allowing the controller to use Newton steps to converge to the optimal control trajectory. The controller is applied to an atmospheric test rig, where the auto-ignition process can be investigated for single ignitions. In the set-up, dimethyl ether is injected into a preheated air stream using a controlled proportional valve. Optical measurements are used to evaluate the auto-ignition process and to show that using the extremum seeking control approach, the homogeneity of the ignition process can be increased significantly.

A proportional integral extremum-seeking control approach for discrete-time nonlinear systems

ABSTRACTThis paper proposes a proportional-integral extremum-seeking control technique for a class of discrete-time nonlinear dynamical systems with unknown dynamics. The technique is a generalisation of existing time-varying extremum-seeking control (ESC) techniques that provides fast transient performance of the closed-loop system to the optimum equilibrium of a measured objective function. The main contribution of the proposed technique is the addition of a proportional action that can be used to minimise the impact of a time-scale separation on the transient performance of the ESC system. The integral action fulfils the role of standard ESC techniques to identify optimal equilibrium conditions. The effectiveness of the proposed approach is demonstrated using a simulation example.

An extremum-seeking control approach for constrained robotic motion tasks

In this paper, we propose two adaptive control schemes for multiple-input systems for execution of robot end-effector movements in the presence of parametric system uncertainties. The design of these schemes is based on Model Reference Adaptive Control (MRAC) while the adaptation of the controller parameters is achieved by Extremum Seeking Control (ESC). The two control schemes, which are called Multiple-Input ESC–MRAC and Multiple-Input Adaptive-Dynamic-Inversion ESC–MRAC, are suitable for linear and nonlinear systems respectively. Lyapunov and averaging analysis shows that the proposed schemes achieve practical asymptotic reference state tracking. The proposed methods are evaluated in simulations and in a real-world robotic experiment.

An extremum-seeking control approach for observer design

Abstract: In this study, we propose to circumvent the difficulties associated with the computation of the observer gain for nonlinear systems by using an extremum-seeking control approach to generate optimal observer gains for a general class of nonlinear systems. This paper proposes a proportional-integral extremum-seeking control (PIESC) technique for the design of nonlinear observers. The PIESC technique is a generalization of the standard perturbation based techniques that provides fast transient performance of the closed-loop system to the optimum equilibrium of a measured objective function. In this application of PIESC, the gain of the nonlinear observer is computed in real-time to minimize the least-squares output prediction error. Two examples are used to demonstrate the effectiveness of this technique.

On the dynamic optimization of methane production in anaerobic digestion via extremum-seeking control approach

This paper proposes an extremum-seeking control approach based on sliding mode to achieve the dynamic optimization of methane outflow rate in anaerobic digestion processes. Open-loop analysis for a two-population model shown that the system becomes unstable due at the accumulation of volatile fatty acids (VFA). Then the controller is designed to achieve the regulation of VFA concentration close to the optimal set-point while maximizing the methane production. The control law is based on a variable-structure feedback to iteratively extremize the methane outflow rate and converges to the neighborhood of the optimum with sliding mode motions. In contrast with previous works on extremum-seeking control with sliding mode, the control scheme includes an observer-based uncertain estimator which computes the unknown terms related to the growth kinetics and the inlet composition. Practical stabilizability for the closed-loop system around to unknown optimal set-point is analyzed. Numerical experiments illustrate the effectiveness of the proposed approach.

A time-varying extremum-seeking control approach

This paper considers the solution of a real-time optimization problem using adaptive extremum seeking control. It is assumed that the equations describing the dynamics of the nonlinear system and the cost function to be minimized are unknown and that the objective function is measured. The main contribution of the paper is to formulate the extremum-seeking problem as a time-varying estimation problem. The proposed approach is shown to avoid the need for averaging results which minimizes the impact of the choice of dither signal on the performance of the extremum seeking control system. Several examples are used to illustrate the effectiveness of the proposed technique.

A time-varying extremum-seeking control approach for discrete-time systems

This paper considers the solution of a real-time optimization problem using adaptive extremum seeking control for a class of unknown discrete-time nonlinear systems. It is assumed that the equations describing the dynamics of the nonlinear system and the cost function to be minimized are unknown and that the objective function is measured. The main contribution of the paper is to formulate the extremum-seeking problem as a time-varying discrete-time estimation problem. The proposed approach is shown to avoid the need for averaging results which minimizes the impact of the choice of dither signals on the performance of the extremum seeking control system. Several examples are used to illustrate the effectiveness of the proposed technique.

A proportional integral extremum-seeking control approach

This paper proposes an alternative extremum seeking control design technique for the solution of real-time optimization control problems. The technique considers a proportional-integral approach that avoids the need for a time-scale separation in the formulation of the ESC. It is assumed that the equations describing the dynamics of the nonlinear system and the cost function to be minimized are unknown and that the objective function is measured. The dynamics are assumed to be asymptotically stable and relative order one with respect to the objective function. The extremum-seeking problem is solved using a time-varying parameter estimation technique.

A time-varying extremum-seeking control approach for discrete-time systems with application to model predictive control

This paper considers the solution of a real-time optimization problem using adaptive extremum seeking control for a class of unknown discrete-time nonlinear systems. It is assumed that the equations describing the dynamics of the nonlinear system and the cost function to be minimized are unknown and that the objective function is measured. The main contribution of the paper is to formulate the extremum-seeking problem as a time-varying discrete-time estimation problem. The proposed approach is applied in the design of nonlinear model predictive control algorithms where the extremum-seeking controller is used to perform the real-time optimization of the MPC. A simulation study and an experimental study is presented that demonstrates the effectiveness of the proposed technique.

A new approach in MPPT for photovoltaic array based on Extremum Seeking Control under uniform and non-uniform irradiances

This work presents a Maximum Power Point Tracking (MPPT) based on analyzing the output characteristics of PV array under uniform irradiance and partial shading conditions. In order to carry out MPPT in PV panels, under partial shading conditions a method based on Extremum Seeking Control (ESC) is introduced. In contrast with classic ESC, in this method the double of dithering signal frequency is not used, consequently PV output power has a ripple of a lower frequency. Also the drop which occurs when MPPT system starts to operate in classic ESC method is minimized in this paper. The ESC approach for MPPT in this paper uses a series combination of a Low Pass Filter (LPF) and a High Pass Filter (HPF). These two filters act as a Band Pass Filter (BPF) and let a specific frequency of input power which includes the derivative of PV with respect to its voltage pass through. Finally, the system does not operate in local optimal points for efficient point will be global. The algorithm adds partial shadow judging conditions in ESC method. The system runs the variable step ESC method to realize MPPT when photovoltaic array is under uniform irradiance. Under Partial Shading Condition (PSC), the control method can eliminate the interference of local maximum power point (MPP) to make 23 the PV array running at global MPP. In addition, unlike other methods, the proposed MPPT operates on the global MPPs. The proposed MPP tracker does not add any extra complexity compared to the classical ones. However, it increases significantly the efficiency of the PV installation under PSC. We will show that under uniform irradiance, the proposed MPPT leads to faster performances than classical approaches.

Extremum Seeking Control with Second-Order Sliding Mode

The extremum seeking control (ESC) approach with a first-order sliding mode has been proposed for searching a setpoint by making a sliding mode occur, where a performance index tracks a reference signal to reach its extremum. The system dynamics is assumed to be much faster than the parameter updating rate determined by the ESC rule and thus is omitted in the stability analysis for the ESC system with a first-order sliding mode. As a result only a static optimization can be obtained. In this paper, an ESC approach with a second-order sliding mode is proposed with the consideration of the system dynamics such that the performance index can be optimized dynamically even if the system dynamics is not faster than the parameter updating rate for the extremum seeking. The asymptotic second-order sliding mode relay control algorithm is implemented to guarantee the asymptotic convergence to the second-order sliding mode without using the derivative of the performance index. Simulation results show that the second-order sliding mode can be reached asymptotically and the system converges to the setpoint on the second-order sliding mode in the speed determined by the reference signal.