A symplectic moving horizon estimation algorithm with its application to the Earth-Moon L2 libration point navigation

Accurate state estimations are perquisites of autonomous navigation and orbit maintenance missions.The extended Kalman lter(EKF)and the unscented Kalman lter(UKF),are the most commonly used method.However,the EKF results in poor estimation performance for systems are with high nonlinearity.As for the UKF,irregular sampling instants are required.In addition,both the EKF and the UKF cannot treat constraints.In this paper,a symplectic moving horizon estimation algorithm,where constraints can be considered,for nonlinear systems are developed.The estimation problem to be solved at each sampling instant is seen as a nonlinear constrained optimal control problem.The original nonlinear problem is transferred into a series of linear-quadratic problems and solved iteratively.A symplectic method based on the variational principle is proposed to solve such linear-quadratic problems,where the solution domain is divided into sub-intervals,and state,costate,and parametric variables are locally interpolated with linear approximation.The optimality conditions result in a linear complementarity problem which can be solved by the Lemke's method easily.The developed symplectic moving horizon estimation method is applied to the Earth-Moon L2 libration point navigation.And numerical simulations demonstrate that though more time-consuming,the proposed method results in better estimation performance than the EKF and the UKF.

Event-Triggered Moving Horizon Pose Estimation for Spacecraft Systems

An event-triggered moving horizon estimation strategy is proposed for spacecraft pose estimation.The error dual quaternion is used to describe the system state and construct the spacecraft attitude-orbit coupled model.In order to reduce the energy consumption on spacecraft,an event-triggered moving horizon estimator(MHE)is designed for real-time pose estimation with limited communication resources.The model mismatch caused by event-triggered is finally solved by solving the cost function of the min-max optimization problem.The system simulation model is built in Matlab/Simulink,and the spacecraft pose estimation simulation is carried out.The numerical results demonstrate that the designed estimator could ensure the estimation effect and save spacecraft communication and computing resources effectively.

Characteristics Extraction of Vehicle State Information Based on Entropy Calculation

A method of extracting and detecting vehicle stability state characteristics based on entropy is proposed.The vehicle’s longitudinal and lateral dynamics models are established for complex driving and maneuver conditions.The corresponding state observer is designed by adopting the moving horizon estimation algorithm,which realizes the observation of the vehicle stability state considering the global state information.Meanwhile,the Shannon entropy is modified to approximate entropy,and the approximate entropy value of the observed vehicle state is calculated.Furthermore,the optimal controller is designed to further validate the reliability of the entropy value as the reference of control system.Simulation results demonstrate that this method can quickly detect the instability state of the system during the process of vehicle driving,which provides a reference for risk prediction and active control.

Cloud-Based Optimal Control of Individual Borehole Heat Exchangers in a Geothermal Field

Integrating renewable energy sources is a crucial component in reducing CO_(2) emissions in the building sector. In particular, shallow geothermal energy is expected to play a significant role in the regenerative energy supply of buildings. An effective control strategy for the geothermal field is crucial to reduce the overall energy consumption. This paper analyzes the benefits of controlling an existing field’s individual borehole heat exchangers(BHE) using nonlinear model predictive control(NMPC) and moving horizon estimation. The considered geothermal field consists of 41 BHEs and is used for heating and cooling. Each BHE is equipped with temperature sensors for in-and outflow and has individually controllable valves, while a central hydraulic pump feeds all BHEs. The sensor measurements are accessed through a cloud platform, enabling also set point writing for the pump speed and the valve positions. To control the BHEs individually, we propose a two-stage process. In the calibration stage, a moving horizon estimator estimates the actual borehole and ground temperatures for each BHE. In the second stage, first, a nonlinear model predictive controller optimizes the number of active BHEs necessary to meet the buildings’ energy demand. With the estimated ground temperatures as a basis, it is determined which BHEs shall be(de)-activated. The active BHEs are fed with a fixed volume flow of 24 L/min to ensure turbulent heat transfer. To reduce the power usage of the pumps, an optimal control problem based on a simple hydraulic model of the geothermal field is used. The methodology is analyzed through simulations first and then validated experimentally. The results show that half or more of the BHEs could be deactivated most of the time, leading to 67% savings in electricity consumption by the hydraulic pump. The experimental validation confirms the high energy saving potential of the proposed methodology, reducing the consumption of electrical energy by 71%. Additionally, the deactivated BHEs regenerate faster and improve the field’s long-term behavior. In conclusion, the proposed strategy improves the short and long-term performance of the geothermal field.