Nonlinear optimal control with disturbance rejection for asteroid landing

seungsik, kang; Wang, Jianan; Li, Chaoyong; Shan, Jiayuan

doi:10.1016/j.jfranklin.2018.06.028

Cited by 6 publications

(4 citation statements)

References 24 publications

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“…Thus we consider the dual problem of the linear-quadratic problem of the form Q N +1 in the next section. 4 The primal linear-quadratic optimal control problem…”

Section: Quasilinearization Technique For Problem(np)mentioning

confidence: 99%

“…Optimal control is a subject that aims at controlling a given dynamic system over a period of time such that a specified performance index is minimized while any other constraints are satisfied in the process. Optimal control problems are widely encountered as mathematical models in such areas as industrial engineering [1,2], medical science [3] and aerospace science [4].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Solutions of Nonlinear Optimal Control Problems Using Quasilinearization and Fenchel Duality

Wang¹,

Wu²,

Yu³

2022

Preprint

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In this paper, we consider a special class of nonlinear optimal control problems, where the control variables are box-constrained and the objective functional is strongly convex corresponding to control variables and separable with respect to the state variables and control variables. We convert solving the original nonlinear problem into solving a sequence of constrained linear-quadratic optimal control problems by quasilinearization method. In order to solve each linear-quadratic problem efficiently we turn to study its dual problem. We formulate dual problem by the scheme of Fenchel duality, the strong duality property and the saddle point property corresponding to primal and dual problem are also proved, which together ensure that solving dual problem is effective. Thus solving the sequence of control constrained linear-quadratic optimal control problems obtained by quasilinearization technique is substituted by solving the sequence of their dual problem. We solve the sequence of dual problem and obtain the solution to primal control constrained linear-quadratic problem by the saddle point property. Furthermore, the fact that solution to each subproblem finally converges to the solution to the optimality conditions of original nonlinear problem is also proved. After that we carry out numerical experiments using present approach, for each subproblem we formulate the discretized primal and dual problem by Euler discretization scheme in our experiments. Efficiency of the present method is validated by numerical results.

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“…Thus we consider the dual problem of the linear-quadratic problem of the form Q N +1 in the next section. 4 The primal linear-quadratic optimal control problem…”

Section: Quasilinearization Technique For Problem(np)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Solutions of Nonlinear Optimal Control Problems Using Quasilinearization and Fenchel Duality

Wang¹,

Wu²,

Yu³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…For most nonlinear systems, the analytical solution of the associated HJB equation is difficult or even impossible to find, for which researchers try to find an approximate optimal solution by using methods like adaptive dynamic programming [25]- [31]. The optimal control of nonlinear systems subject to periodic external disturbances is a challenging issue, for which only a few results have been reported [32], [33]. Tang and Gao [32] proposed an optimal control method for nonlinear systems with fully known sinusoidal disturbances and system dynamics, which transforms the original problem into a sequence of nonhomogeneous linear two-point boundary value problems.…”

Section: Introductionmentioning

confidence: 99%

“…Tang and Gao [32] proposed an optimal control method for nonlinear systems with fully known sinusoidal disturbances and system dynamics, which transforms the original problem into a sequence of nonhomogeneous linear two-point boundary value problems. However, the methods in [32], [33] require that the system parameters are fully known.…”

Section: Introductionmentioning

confidence: 99%

Learning and Near-Optimal Control of Underactuated Surface Vessels With Periodic Disturbances

Zhang

Weng

2022

IEEE Trans. Cybern.

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In this paper, we propose a novel learning and near-optimal control approach for underactuated surface vessels with unknown mismatched periodic external disturbances and unknown hydrodynamic parameters. Given a prior knowledge of the periods of the disturbances, an analytical near-optimal control law is derived through approximation of the integraltype quadratic performance index with respect to the tracking error, where the equivalent unknown parameters are generated online by an auxiliary system that can learn the dynamics of the controlled system. It is proved that the state differences between the auxiliary system and the corresponding controlled underactuated surface vessel are globally asymptotically convergent to zero. Besides, the approach theoretically guarantees asymptotic optimality of the performance index. The efficacy of the method is demonstrated via simulations based on the real parameters of an underactuated surface vessel.

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Twistor-based pose control for asteroid landing with path constraints

Zhang

Cai

2020

Nonlinear Dyn

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Nonlinear optimal control with disturbance rejection for asteroid landing

Cited by 6 publications

References 24 publications

Solutions of Nonlinear Optimal Control Problems Using Quasilinearization and Fenchel Duality

Solutions of Nonlinear Optimal Control Problems Using Quasilinearization and Fenchel Duality

Learning and Near-Optimal Control of Underactuated Surface Vessels With Periodic Disturbances

Twistor-based pose control for asteroid landing with path constraints

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