Extremum seeking control for UAV close formation flight via improved pigeon-inspired optimization

This paper proposes a comprehensive design scheme for the extremum seeking control(ESC)of the unmanned aerial vehicle(UAV)close formation flight.The proposed design scheme combines a Newton-Raphson method with an extended Kalman filter(EKF)to dynamically estimate the optimal position of the following UAV relative to the leading UAV.To reflect the wake vortex effects reliably,the drag coefficient induced by the wake vortex is considered as a performance function.Then,the performance function is parameterized by the first-order and second-order terms of its Taylor series expansion.Given the excellent performance of nonlinear estimation,the EKF is used to estimate the gradient and the Hessian matrix of the parameterized performance function.The output feedback of the proposed scheme is determined by iterative calculation of the Newton-Raphson method.Compared with the traditional ESC and the classic ESC,the proposed design scheme avoids the slow continuous time integration of the gradient.This allows a faster convergence of relative position extremum.Furthermore,the proposed method can provide a smoother command during the seeking process as the second-order term of the performance function is taken into account.The convergence analysis of the proposed design scheme is accomplished by showing that the output feedback is a supermartingale sequence.To improve estimation performance of the EKF,a improved pigeon-inspired optimization(IPIO)is proposed to automatically tune the noise covariance matrix.Monte Carlo simulations for a three-UAV close formation show that the proposed design scheme is robust to the initial position of the following UAV.

A Novel Extremum Seeking Control to Enhance Convergence and Robustness in the Presence of Nonlinear Dynamic Sensors

This paper focuses on optimizing an unknown cost function through extremum seeking(ES)control in the presence of a slow nonlinear dynamic sensor responsible for measuring the cost.In contrast to traditional perturbation-based ES control,which often suffers from sluggish convergence,the proposed method eliminates the time-scale separation between sensor dynamics and ES control by using the relative degree of the nonlinear sensor system.To improve the convergence rate,the authors incorporate high-frequency dither signals and a differentiator.To enhance the robustness with the existence of rapid disturbances,an off-the-shelf linear high-gain differentiator is applied.The first result demonstrates that,for any desired convergence rate,with properly tuned parameters for the proposed ES algorithm,the input of the cost function can converge to an arbitrarily small neighborhood of the optimal solution,starting from any initial condition within any given compact set.Furthermore,the second result shows the robustness of the proposed ES control in the presence of sufficiently fast,zero-mean periodic disturbances.Simulation results substantiate these theoretical findings.

Fractional order extremum seeking approach for maximum power point tracking of photovoltaic panels

Due to the high interest in renewable energy and diversity of research regarding photovoltaic （PV） array, a great research effort is focusing nowadays on solar power generation and its performance improvement under various weather conditions. In this paper, an integrated framework was proposed, which achieved both maximum power point tracking （MPPT） and minimum ripple signals. The proposed control scheme was based on extremum- seeking （ES） combined with fractional order systems （FOS）. This auto-tuning strategy was developed to maximize the PV panel output power through the regulation of the voltage input to the DC/DC converter in order to lead the PV system steady-state to a stable oscillation behavior around the maximum power point （MPP）. It is shown that fractional order operators can improve the plant dynamics with respect to time response and disturbance rejection. The effectiveness of the proposed controller scheme is illustrated with simulations using measured solar radiation data.

Extremum seeking-based optimal EGR set-point design for combustion engines in lean-burn mode

In lean combustion mode,exhaust gas ratio(EGR)is a significant factor that affects fuel economy and combustion stability.A proper EGR level is beneficial for the fuel economy;however,the combustion stability(coefficient of variation(COV)in indicated mean effective pressure(IMEP))deteriorated monotonously with increasing EGR.The aim of this study is to achieve a trade-off between the fuel economy and combustion stability by optimizing the EGR set-point.A cost function(J)is designed to represent the trade-off and reduce the calibration burden for optimal EGR at different engine operating conditions.An extremum-seeking(ES)algorithm is adopted to search for the extreme value of J and obtain the optimal EGR at an operating point.Finally,a map of optimal EGR set-value is designed and experimentally validated on a real driving cycle.

Adaptive neural network observer for proton-exchange membrane fuel cell system

This paper develops an adaptive neural network(NN)observer for proton-exchange membrane fuel cells(PEMFCs).Indeed,information on the oxygen excess ratio(OER)value is crucial to ensure optimal management of the durability and reliability of the PEMFC.The OER indicator is computed from the mass of oxygen and nitrogen inside the PEMFC cathode.Unfortunately,the measurement process of both these masses is difficult and costly.To solve this problem,the design of a PEMFC state observer is attractive.However,the behaviour of the fuel cell system is highly non-linear and its modelling is complex.Due to this constraint,a multilayer perceptron neural network(MLPNN)-based observer is proposed in this paper to estimate the oxygen and nitrogen masses.One notable advantage of the suggested MLPNN observer is that it does not require a database to train the NN.Indeed,the weights of the NN are updated in real time using the output error.In addition,the observer parameters,namely the learning rate and the damping factor,are online adapted using the optimization tools of extremum seeking.Moreover,the proposed observer stability analysis is performed using the Lyapunov theory.The observer performances are validated by simulation under MATLAB®/Simulink®.The supremacy of the proposed adaptive MLPNN observer is highlighted by comparison with a fixed-parameter MLPNN observer and a classical high-gain observer(HGO).The mean rela-tive error value of the excess oxygen rate is considered the performance index,which is equal to 1.01%for an adaptive MLPNN and 3.95%and 9.95%for a fixed MLPNN and HGO,respectively.Finally,a robustness test of the proposed observer with respect to measurement noise is performed.

Cylinder pressure based combustion phase optimization and control in spark-ignited engines

Efficiency and emissions of spark-ignited engines are significantly affected by combustion phase which can usually be indicated by crank angle of 50% mass burnt （CA50）. Managing combustion phase at the optimal value at which the maximal efficiency can be achieved is a challenging issue due to the cyclic variations of combustion process. This paper addresses this issue in two loops： CA50 set-point optimization （outer loop） and set-point tracking （inner loop） by controlling spark advance （SA）. Extremum seeking approach maximizing thermal efficiency is employed in the CA50 set-point optimization. A proportional- integral （PI） controller is adopted to make the moving average value of CA50 tracking the optimal CA50 set-point determined in the outer loop. Moreover, in order to obtain fast responses at steady and transient operations, feed-forward maps are designed for extremum seeking controller and PI controller, respectively. Finally, experimental validations are conducted on a six-cylinder gasoline at steady and transient operations to show the effectiveness of proposed control scheme.

Online calibration of combustion phase in a diesel engine

In this work, an online calibration mechanism is proposed for the combustion phase in a diesel engine. In particular, a simplified event-based engine model, of which the output predicts the optimum combustion phase, is used to aid the calibration, and the model is updated online along with the engine operation to keep the integrity high so as to improve the quality of optimum combustion phase prediction. It is found this mechanism can be applied to develop an online automated calibration process when the engine system shifts to a new operating point. of the proposed mechanism. Engine test results are included to demonstrate the effectiveness