Application of linear gauss pseudospectral method in model predictive control

Yang, Liang; Zhang, Hao; Chen, Wanchun

doi:10.1016/j.actaastro.2013.11.038

Cited by 46 publications

(27 citation statements)

References 15 publications

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“…It costs a lot of computing time and may lead to the numerical instability phenomenon to solve the time-intensive backward integration of the matrix Riccati differential equation by the traditional numerical methods such as the tool function ''lqr'' in MATLAB. Here, the indirect pseudospectral method is employed to obtain the optimal feedback control for the linear time-varying system (35). For details on the indirect pseudospectral method, the readers can refer to Refs.…”

Section: Indirect Pseudospectral Methodsmentioning

confidence: 99%

“…The trajectory state regulation problem is stated as an optimal control problem, i.e., find the required control inputs duðtÞ and corresponding state variables dxðtÞ which satisfies Eq. (35) and minimizes the following quadratic performance index…”

Section: Two-point Boundary Value Problemmentioning

confidence: 99%

“…However, LPM is an open-loop control method which is sensitive to system parameter uncertainties and external disturbances. Therefore, serial feedback control schemes are proposed to modify the reference trajectory obtained by LPM and guarantee the system's robustness against the uncertainties and disturbances [31][32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

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Optimal reorientation of a free-floating space robot subject to initial state uncertainties

Yao

2018

J Braz. Soc. Mech. Sci. Eng.

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This paper focuses on the dynamics and optimal reorientation of a free-floating space robot system in the presence of initial state uncertainties. A control strategy combining optimal motion planning and feedback control is presented based on the dynamic model of the system. In the design of the optimal motion planning, Legendre pseudospectral method (LPM) is used to transform the optimal reorientation problem into a nonlinear programming problem. Then, sequential quadratic programming algorithm is employed to solve the nonlinear programming problem and off-line generate the optimal reference trajectory of the system. In the design of feedback control, the state equation is linearized around the reference trajectory obtained by LPM. The tracking control problem is converted into a two-point boundary value problem based on Pontryagin's maximum principle. Then LPM is used to discretize the two-point boundary value problem and transform it into a set of linear algebraic equations. This process does not require any integration calculations and has good performance in real time. Numerical simulations indicate that the control strategy is effective with good robustness.

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Section: Indirect Pseudospectral Methodsmentioning

confidence: 99%

Section: Two-point Boundary Value Problemmentioning

confidence: 99%

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Optimal reorientation of a free-floating space robot subject to initial state uncertainties

Yao

2018

J Braz. Soc. Mech. Sci. Eng.

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“…The pseudospectral model predictive control (PMPC) method, which was first presented by Yang Liang et al [17], combines MPC (Model Predictive Control) and GPM (Gauss Pseudospectral Method). In this approach, the state and control variables are approximated by using LG (Legendre Gauss) points, and the system dynamics are approximated on the LG collocation points.…”

Section: Pseudospectral Model Predictive Controlmentioning

confidence: 99%

“…Here, equation (14) is the transversatility condition which includes the effect of the predicted state deviation Ψ on the terminal states x f [17]; ν is a Lagrange multiplier. If the desired terminal state is restricted to some specific value, the first part of the transversatility condition is used.…”

Section: T R T B T T T Q a T T Bu Tmentioning

confidence: 99%

Pseudospectral Model Predictive Control for Exo-atmospheric Guidance

Rahman¹,

Zhang²,

Yang³

et al. 2015

International Journal of Aeronautical and Space Sciences

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This paper suggests applying pseudospectral model predictive method for exo-atmospheric guidance. The method is a fusion of pseudospectral law and model predictive control, in which a two point boundary value problem is formulated using model predictive approach and solved by applying pseudospectral law. In this work, the method is applied to exo-atmospheric guidance with specific target requirement. The existing exo-atmospheric guidance methods suffice general requirements for guidance, but cannot ensure specific target constraints; whereas, the presented method is able to do so. The proposed guidance law is assessed through simulation of perturbed cases, and the tests suggest that the method is able to operate semiautonomously under control and thrust vector perturbations.

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Ascent adaptive energy management method for solid rocket‐powered hypersonic vehicle under uncertainties

Liu

Wang

et al. 2023

Adaptive Control & Signal

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Summary The solid rocket booster is widely used in the launch mission for hypersonic vehicles nowadays, whose ascent energy management is still a challenging problem due to the inherent dynamic nonlinearity. This paper casts the problem into an equivalent ascent guidance one and proposes a model predictive static programming (MPSP) based solution. The MPSP‐based method is a computationally efficient solver that adapts to different energy demands while guaranteeing the satisfaction of terminal constraints. To further improve the performance of MPSP in this problem, a Bézier spline guidance method is proposed to generate high‐quality reference trajectories such that the MPSP can converge with high accuracy while satisfying the real‐time requirement. Additionally, an online parameter estimation based on the extended Kalman filter is employed to avoid large terminal state deviations incurred by parametric uncertainties during the Bézier curve computation and linearization in MPSP. Numerical simulations with different hard terminal constraints and uncertainties are conducted to demonstrate the effectiveness and robustness of the proposed algorithm. The simulation results show that our proposed algorithm can guide the hypersonic vehicle to a given terminal state under uncertainties and outperforms several existing ascent energy management methods.

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Application of linear gauss pseudospectral method in model predictive control

Cited by 46 publications

References 15 publications

Optimal reorientation of a free-floating space robot subject to initial state uncertainties

Optimal reorientation of a free-floating space robot subject to initial state uncertainties

Pseudospectral Model Predictive Control for Exo-atmospheric Guidance

Ascent adaptive energy management method for solid rocket‐powered hypersonic vehicle under uncertainties

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