An hp symplectic pseudospectral method for nonlinear optimal control

Peng, Haijun; Wang, Xinwei; Li, Mingwu

doi:10.1016/j.cnsns.2016.06.023

Cited by 52 publications

(18 citation statements)

References 41 publications

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“…The constraint conservation effect of the symplectic algorithm was proved in Reference . In the area of optimal control systems, Peng and his coworkers proved that the symplectic algorithm has faster convergence and higher precision and efficiency in References . Inspired by the symplectic method and by Moreau's midpoint rule, in this article, a stable nonsmooth method for multibody systems with impact and friction is proposed.…”

Section: Introductionmentioning

confidence: 95%

A novel nonsmooth dynamics method for multibody systems with friction and impact based on the symplectic discrete format

Peng

Song

Kan

2019

Numerical Meth Engineering

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Summary As multibody systems often involve unilateral constraints, nonsmooth phenomena, such as impacts and friction, are common in engineering. Therefore, a valid nonsmooth dynamics method is highly important for multibody systems. An accuracy representation of multibody systems is an important performance indicator of numerical algorithms, and the energy balance can be used efficiently evaluate the performance of nonsmooth dynamics methods. In this article, differential algebraic equations (DAEs) of a multibody system are constructed using the D'Alembert's principle, and a novel nonsmooth dynamics method based on symplectic discrete format is proposed. The symplectic discrete format can maintain the energy conservation of a conservative system; this property is expected to extend to nonconservative systems with nonsmooth phenomena in this article. To evaluate the properties of the proposed method, several numerical examples are considered, and the results of the proposed method are compared with those of Moreau's midpoint rule. The results demonstrate that the solutions obtained using the proposed method, which is based on the symplectic discrete format, can realize a higher solution accuracy and lower numerical energy dissipation, even under a large time step.

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Section: Introductionmentioning

confidence: 95%

A novel nonsmooth dynamics method for multibody systems with friction and impact based on the symplectic discrete format

Peng

Song

Kan

2019

Numerical Meth Engineering

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“…The degrees of interpolation function in each subinterval are not necessarily to be identical. Thus, adaptive mesh‐refine technique can be easily implemented …”

Section: Introductionmentioning

confidence: 99%

“…Thus, adaptive mesh-refine technique can be easily implemented. 43 In this paper, we focus on the motion planning and tracking control of three-dimensional (3D) overhead crane systems and a symplectic pseudospectral MPC controller is developed. In practice, modern overhead crane systems are normally operated with the combination of many motions, eg, moving the trolley, moving the girder, and hoisting the payload, to increase their maneuverabilities.…”

Section: Introductionmentioning

confidence: 99%

A unified symplectic pseudospectral method for motion planning and tracking control of 3D underactuated overhead cranes

Wang

Liu

Zhang

et al. 2019

Intl J Robust & Nonlinear

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Summary In this paper, a unified symplectic pseudospectral method for motion planning and tracking control of 3D underactuated overhead cranes is proposed. A feasible reference trajectory taking constraints into consideration is first generated offline by the symplectic pseudospectral optimal control method. Then, a trajectory tracking model predictive controller also based on the symplectic pseudospectral method is developed to track the reference trajectory. At each sampling instant, the trajectory tracking controller works by solving an open‐loop optimal control problem where linearized system dynamics is used instead to improve the computational efficiency. Since the symplectic pseudospectral optimal control method is the core algorithm for both offline trajectory planning and online trajectory tracking, constraints on state variables and control inputs can be easily imposed and hence theoretically guaranteed in solutions. By selecting proper weighted matrices on tracking error and control, the developed controller could achieve control objectives in both accurate trolley positioning and fast suppressing of residual swing angles. Simulations for 3D overhead crane systems in the presence of perturbations in initial conditions, an abrupt variation of system parameter, and various external disturbances demonstrate that the developed controller is robust and of excellent control performance.

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“…They proved that these methods are equivalent, which means they use the same iterative formula to obtain the approximate/analytical solution. In the work of Peng et al, an adaptive symplectic pseudospectral method based on dual variational principle was successfully applied to solve the first‐order necessary conditions of continuous OCPs. In the work of Moghadasian and Roshanian, a simple approach to design semifeedback optimal control law for nonlinear problems has been proposed.…”

Section: Introductionmentioning

confidence: 99%

Optimal control of nonlinear dynamical systems based on a new parallel eigenvalue decomposition approach

Jajarmi

Băleanu

2018

Optim Control Appl Methods

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Summary This manuscript aims to investigate a new approach based on the modal series method and eigenvalue decomposition technique to solve a class of nonlinear optimal control problems. For this purpose, a sequence of decoupled linear two‐point boundary value problems is solved iteratively instead of solving the coupled nonlinear two‐point boundary value problem derived from the maximum principle. The convergence analysis of the suggested technique is also investigated. In addition, the problem that needs to be solved at each iteration is composed of lower‐order decoupled subproblems; hence, they can be solved in parallel. Thus, the new scheme has a parallel computing property improving its computational effectiveness. Numerical simulations and comparative results show that the proposed approach is efficient and provides satisfactory results.

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An hp symplectic pseudospectral method for nonlinear optimal control

Cited by 52 publications

References 41 publications

A novel nonsmooth dynamics method for multibody systems with friction and impact based on the symplectic discrete format

A novel nonsmooth dynamics method for multibody systems with friction and impact based on the symplectic discrete format

A unified symplectic pseudospectral method for motion planning and tracking control of 3D underactuated overhead cranes

Optimal control of nonlinear dynamical systems based on a new parallel eigenvalue decomposition approach

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