scholarly journals Application of the State-Dependent Riccati Equation and Kalman Filter Techniques to the Design of a Satellite Control System

2012 ◽  
Vol 19 (5) ◽  
pp. 939-946 ◽  
Author(s):  
L.C.G. Souza ◽  
R.G. Gonzáles
Keyword(s):  
Kalman Filter ◽  
Control System ◽  
Riccati Equation ◽  
The State ◽  
State Dependent ◽  
Satellite Control

scholarly journals Optimal Factorization of the State-Dependent Riccati Equation Technique in a Satellite Attitude and Orbit Control System

2021 ◽  
Vol 20 ◽  
pp. 98-107
Author(s):  
Alessandro Gerlinger Romero ◽  
Luiz Carlos Gadelha De Souza
Keyword(s):  
Control System ◽  
Riccati Equation ◽  
The State ◽  
Linear Control ◽  
Control Techniques ◽  
Orbit Control ◽  
Satellite Attitude ◽  
Modified Rodrigues Parameters ◽  
State Dependent ◽  
Attitude Maneuver

The satellite attitude and orbit control system (AOCS) can be designed with success by linear control theory if the satellite has slow angular motions and small attitude maneuver. However, for large and fast maneuvers, the linearized models are not able to represent all the perturbations due to the effects of the nonlinear terms present in the dynamics and in the actuators (e.g., saturation). Therefore, in such cases, it is expected that nonlinear control techniques yield better performance than the linear control techniques. One candidate technique for the design of AOCS control law under a large maneuver is the State-Dependent Riccati Equation (SDRE). SDRE entails factorization (that is, parameterization) of the nonlinear dynamics into the state vector and the product of a matrix-valued function that depends on the state itself. In doing so, SDRE brings the nonlinear system to a (nonunique) linear structure having state-dependent coefficient (SDC) matrices and then it minimizes a nonlinear performance index having a quadratic-like structure. The nonuniqueness of the SDC matrices creates extra degrees of freedom, which can be used to enhance controller performance, however, it poses challenges since not all SDC matrices fulfill the SDRE requirements. Moreover, regarding the satellite's kinematics, there is a plethora of options, e.g., Euler angles, Gibbs vector, modified Rodrigues parameters (MRPs), quaternions, etc. Once again, some kinematics formulation of the AOCS do not fulfill the SDRE requirements. In this paper, we evaluate the factorization options (SDC matrices) for the AOCS exploring the requirements of the SDRE technique. Considering a Brazilian National Institute for Space Research (INPE) typical mission, in which the AOCS must stabilize a satellite in three-axis, the application of the SDRE technique equipped with the optimal SDC matrices can yield gains in the missions. The initial results show that MRPs for kinematics provides an optimal SDC matrix.

Development of a novel nonlinear estimator based on state-dependent Riccati equation technique for articulated vehicles

2018 ◽  
Vol 233 (3) ◽  
pp. 516-530 ◽  
Author(s):  
Hamze Ahmadi Jeyed ◽  
Ali Ghaffari
Keyword(s):  
Kalman Filter ◽  
Riccati Equation ◽  
High Speed ◽  
The State ◽  
Heavy Vehicle ◽  
Lane Change ◽  
Heavy Vehicles ◽  
State Dependent ◽  
Articulated Vehicle ◽  
Filter Approach

In this article, for the first time, a novel nonlinear estimator based on state-dependent Riccati equation filter technique is developed for state estimation of the articulated heavy vehicles. The state-dependent Riccati equation filter approach has a structure similar to the Kalman filter, and compared to the Kalman filter, which is based on linearization, the state-dependent Riccati equation filter is based on parameterization. Also, the state-dependent Riccati equation approach due to the nonuniqueness of the state-dependent coefficient matrix prevented singularity (uncontrollability or unobservability), and this advantage can be used to improve the efficiency of the system. For this purpose, using the Newton's method, a ten-degrees-of-freedom nonlinear model of the articulated heavy vehicle including the longitudinal, lateral and yaw motion of the tractor, the articulation angle, and rotational motion of each wheel is developed. Then, the developed model of articulated heavy vehicle is verified using nonlinear TruckSim model in high-speed lane change maneuver. The vehicle model validation results indicated that the development model is near to the actual articulated vehicle nonlinear model and can be utilized in the nonlinear estimator design. Then, using the state-dependent Riccati equation filter approach, the state variable estimation algorithm based on parametrization is designed and the articulated vehicle states are estimated online. In order to assess the performance and the efficiency of the developed estimator, the simulations with two standard maneuvers including low-speed 90 ° turn maneuver and high-speed lane change maneuver in the slippery road are performed. The simulation results indicate the remarkable impacts of the developed estimator based on state-dependent Riccati equation filter technique on the state estimation of the articulated heavy vehicles.

Hardware-In-the-Loop Simulations of spacecraft attitude synchronization using the State-Dependent Riccati Equation technique

2013 ◽  
Vol 51 (3) ◽  
pp. 434-449 ◽  
Author(s):  
Junoh Jung ◽  
Sang-Young Park ◽  
Sung-Woo Kim ◽  
Youngho Eun ◽  
Young-Keun Chang
Keyword(s):  
Riccati Equation ◽  
The State ◽  
Spacecraft Attitude ◽  
Hardware In The Loop ◽  
State Dependent ◽  
Attitude Synchronization

Chaos control and chaos synchronization using the state-dependent Riccati equation techniques

2018 ◽  
Vol 41 (2) ◽  
pp. 311-320 ◽  
Author(s):  
Yazdan Batmani
Keyword(s):  
Riccati Equation ◽  
Chaos Synchronization ◽  
Chaos Control ◽  
Design Procedure ◽  
The State ◽  
Suboptimal Control ◽  
Control Law ◽  
Closed Loop System ◽  
Infinite Time ◽  
State Dependent

In this paper, the problems of chaos control and chaos synchronization are solved using the state-dependent Riccati equation methods. In the former problem, a nonlinear suboptimal control law is found, which leads to a stable closed-loop system. In the latter, an optimal infinite-time horizon tracking problem is defined and solved using the state-dependent Riccati equation technique. It is shown that the synchronization error between the slave and the master systems converges asymptotically to zero under some mild conditions. Three numerical simulations are provided to demonstrate the design procedure and the flexibility of the methods.

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