Rigid spacecraft robust optimal attitude stabilization under actuator misalignments

Abstract Optimal control techniques and related robust controller extensions have been widely studied for rigid spacecraft, but these methods cannot effectively handle the attitude stabilization problem under actuator misalignments. In this paper, a robust optimal controller is proposed for the spacecraft attitude stabilization problem under actuator misalignments. It is proved that the robust attitude stabilization problem under actuator misalignments and disturbances can be reformulated into the problem of solving the Hamilton-Jacobi-Bellman (HJB) equation. However, numerically solving the HJB equation suffers from the curse of dimensionality. By proving its positive definiteness, the value function for Sontag's formula is taken as the substitute for the solution of the HJB equation to analytically construct the robust optimal controller. Thus the computational burden of implementing the controller is significantly reduced. Simulation results also demonstrate the effectiveness and efficiency of the proposed controller.

[1]  Randal W. Beard,et al.  Galerkin approximations of the generalized Hamilton-Jacobi-Bellman equation , 1997, Autom..

[2]  Dario Spiller,et al.  Inverse dynamics particle swarm optimization applied to constrained minimum-time maneuvers using reaction wheels , 2018 .

[3]  Zhihua Qu,et al.  Robust Control of Nonlinear Uncertain Systems Under Generalized Matching Conditions , 1993, 1993 American Control Conference.

[4]  Ming Xin,et al.  Indirect Robust Control of Spacecraft via Optimal Control Solution , 2012, IEEE Transactions on Aerospace and Electronic Systems.

[5]  Shihua Li,et al.  Global set stabilization of the spacecraft attitude control problem based on quaternion , 2010 .

[6]  P. Tsiotras.  Stabilization and optimality results for the attitude control problem , 1996 .

[7]  Bo Li,et al.  Disturbance observer based finite-time attitude control for rigid spacecraft under input saturation , 2014 .

[8]  Guang-Hong Yang,et al.  Data-based fault-tolerant control for affine nonlinear systems with actuator faults. , 2016, ISA transactions.

[9]  Feng Lin,et al.  An optimal control approach to robust control of robot manipulators , 1998, IEEE Trans. Robotics Autom..

[10]  Chutiphon Pukdeboon,et al.  Control Lyapunov function optimal sliding mode controllers for attitude tracking of spacecraft , 2012, J. Frankl. Inst..

[11]  Haiyan Hu,et al.  Infinite-Horizon Control for Retrieving a Tethered Subsatellite via an Elastic Tether , 2008 .

[12]  Danwei Wang,et al.  Attitude Tracking Control of Rigid Spacecraft With Actuator Misalignment and Fault , 2013, IEEE Transactions on Control Systems Technology.

[13]  Miroslav Krstic,et al.  Inverse optimal stabilization of a rigid spacecraft , 1999, IEEE Trans. Autom. Control..

[14]  Eduardo Sontag.  A universal construction of Artstein's theorem on nonlinear stabilization , 1989 .

[15]  Christopher Liu Darby,et al.  hp-Pseudospectral method for solving continuous-time nonlinear optimal control problems , 2011 .

[16]  R. Freeman,et al.  Control Lyapunov functions: new ideas from an old source , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[17]  Hiroshi Yamakawa,et al.  New Lambert Algorithm Using the Hamilton-Jacobi-Bellman Equation , 2010 .

[18]  Paul Williams,et al.  Application of Pseudospectral Methods for Receding Horizon Control , 2004 .

[19]  Bo Li,et al.  Robust finite-time control allocation in spacecraft attitude stabilization under actuator misalignment , 2013 .

[20]  Hansheng Wu,et al.  Adaptive robust tracking and model following of uncertain dynamical systems with multiple time delays , 2004, IEEE Trans. Autom. Control..

[21]  R. Freeman,et al.  Robust Nonlinear Control Design: State-Space and Lyapunov Techniques , 1996 .

[22]  Feng-Yi Lin.  Robust Control Design: An Optimal Control Approach , 2007 .

[23]  F.L. Lewis,et al.  Reinforcement learning and adaptive dynamic programming for feedback control , 2009, IEEE Circuits and Systems Magazine.

[24]  Tao Sheng,et al.  A novel three-axis attitude stabilization method using in-plane internal mass-shifting , 2019, Aerospace Science and Technology.

[25]  Zhijie Liu,et al.  Disturbance observer based attitude control for flexible spacecraft with input magnitude and rate constraints , 2018 .

[26]  John Doyle,et al.  A receding horizon generalization of pointwise min-norm controllers , 2000, IEEE Trans. Autom. Control..

[27]  Guanghong Yang,et al.  Approximate guaranteed cost fault-tolerant control of unknown nonlinear systems with time-varying actuator faults , 2016 .

[28]  Mrdjan J. Jankovic,et al.  Constructive Nonlinear Control , 2011 .

[29]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[30]  I. Michael Ross,et al.  A review of pseudospectral optimal control: From theory to flight , 2012, Annu. Rev. Control..

[31]  I. Michael Ross,et al.  Fast Mesh Refinement in Pseudospectral Optimal Control , 2019, Journal of Guidance, Control, and Dynamics.

[32]  Panagiotis Tsiotras.  Further passivity results for the attitude control problem , 1998, IEEE Trans. Autom. Control..

[33]  Guang-Hong Yang,et al.  Decentralized adaptive fault-tolerant control for large-scale systems with external disturbances and actuator faults , 2017, Autom..

[34]  Youmin Zhang,et al.  Adaptive Sliding Mode Fault Tolerant Attitude Tracking Control for Flexible Spacecraft Under Actuator Saturation , 2012, IEEE Transactions on Control Systems Technology.

[35]  Bo Li,et al.  Spacecraft attitude tracking control under actuator magnitude deviation and misalignment , 2013 .

[36]  Z. Artstein.  Stabilization with relaxed controls , 1983 .

[37]  Poom Kumam,et al.  Robust optimal sliding mode control for spacecraft position and attitude maneuvers , 2015 .

[38]  Daero Lee,et al.  Nonlinear disturbance observer-based robust control for spacecraft formation flying , 2018 .

[39]  Indra Narayan Kar,et al.  Finite-time robust control of robot manipulator: a SDDRE based approach , 2015, AIR '15.

[40]  Zhigang Wu,et al.  Symplectic Approaches for Solving Two-Point Boundary-Value Problems , 2012 .

[41]  Derong Liu,et al.  Data-Based Adaptive Critic Designs for Nonlinear Robust Optimal Control With Uncertain Dynamics , 2016, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[42]  Qinglei Hu,et al.  Observer-based fault tolerant control and experimental verification for rigid spacecraft , 2019, Aerospace Science and Technology.

[43]  J. Betts.  Survey of Numerical Methods for Trajectory Optimization , 1998 .

[44]  Ming Xin,et al.  Nonlinear robust and optimal control of robot manipulators , 2014 .

[45]  Lei Guo,et al.  Finite-Horizon Approximate Optimal Guaranteed Cost Control of Uncertain Nonlinear Systems With Application to Mars Entry Guidance , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[46]  P. Singla,et al.  Sparse Approximation-Based Collocation Scheme for Nonlinear Optimal Feedback Control Design , 2017 .

[47]  Bing Huang,et al.  Robust Saturated Finite-Time Attitude Control for Spacecraft Using Integral Sliding Mode , 2019, Journal of Guidance, Control, and Dynamics.

[48]  Yao Meng,et al.  Adaptive backstepping control for air-breathing hypersonic vehicle with actuator dynamics , 2017 .