Parametric variational solution of linear-quadratic optimal control problems with control inequality constraints

彭海军,; 张洪武,; 高强,; 吴志刚,; 钟万勰,

doi:10.1007/s10483-014-1858-6

Cited by 7 publications

(4 citation statements)

References 34 publications

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“…The above two sub-sections give the fast MPC without input saturation. In this sub-section, based on the parametric variational principle [45], the fast MPC with input saturation will be proposed, and then a linear complementary problem will be developed to replace the quadratic programming problem.…”

Section: Parametric Variational Principle For Mpc With Input Saturationmentioning

confidence: 99%

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A novel fast model predictive control with actuator saturation for large-scale structures

Peng

Zhang

2017

Computers & Structures

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One of the most critical issues faced in the application of active control to engineering structures is actuator saturation. In this paper, a novel fast model predictive control with actuator saturation for large-scale structures is proposed. First, based on the second-order dynamic equation, the explicit expression form of the Newmark-β method is derived. Then, according to the parametric variational principle, the explicit structure of the model predictive control (MPC) saturation controller is obtained. A linear complementary problem for the proposed fast MPC saturation controller is developed, replacing the quadratic programming problem for the original MPC saturation controller. The optimal control input can be achieved by solving one linear complementarity problem and one transient analysis problem. Particularly, the physical meaning of the explicit expression form of the Newmark-β method is discovered and applied for increasing computational efficiency and saving memory. Finally, numerical simulations of a plane adjacent frame building subjected to earthquake ground motion demonstrate that the proposed fast MPC saturation controller is highly efficient and can be applied under a large step-length, especially for large-scale structural dynamic control problems.

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Section: Parametric Variational Principle For Mpc With Input Saturationmentioning

confidence: 99%

“…According to the parametric variational principle [45], an expanded performance index e J can be given as (40) The control variables U can be explicitly expressed by the above equation, given as…”

Section: Parametric Variational Principle For Mpc With Input Saturationmentioning

confidence: 99%

A novel fast model predictive control with actuator saturation for large-scale structures

Peng

Zhang

2017

Computers & Structures

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“…The primary advantage of them is the warranty that the solution assures the first-order optimality conditions. 9 The most popular shooting and multiple shooting methods, 10,11 the symplectic methods 12–14 and the homotopic approaches 15–18 have successful experiences of using indirect methods in solving complicated optimal control problems. In this paper, an indirect method based on a pseudospectral approach for accurate solution of a class of switching optimal control problems is presented.…”

Section: Introductionmentioning

confidence: 99%

A modified pseudospectral method for indirect solving a class of switching optimal control problems

Mehrpouya

2020

Proceedings of the Institution of Mechanical Engineers, Part G:

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In the present paper, an efficient pseudospectral method for solving the Hamiltonian boundary value problems arising from a class of switching optimal control problems is presented. For this purpose, based on the Pontryagin's minimum principle, the first-order necessary conditions of optimality are derived. Then, by partitioning the time interval related to the problem under study into some subintervals, the states (and costates) and control functions are approximated on each subintervals with piecewise interpolating polynomials based on Legendre–Gauss–Radau points and a piecewise constant function, respectively. As a result, solution of the problem is turned into solution of a number of algebraic equations, in which the values of the states (and costates) and control functions at Legendre–Gauss–Radau points as well as switching and terminal points are allowed to be unknown. Numerical examples are presented at the end to show the efficiency of the proposed method.

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“…Many practical problems in engineering technology, information security, and so on can be solved by nonlinear equations [1,2]. Because the complex of nonlinear equations, it is difficult to solve them, especially for high-dimensional nonlinear equations.…”

Section: Introductionmentioning

confidence: 99%

A Velocity-Combined Local Best Particle Swarm Optimization Algorithm for Nonlinear Equations

Lian

Wang

Chen

2020

Mathematical Problems in Engineering

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Many people use traditional methods such as quasi-Newton method and Gauss–Newton-based BFGS to solve nonlinear equations. In this paper, we present an improved particle swarm optimization algorithm to solve nonlinear equations. The novel algorithm introduces the historical and local optimum information of particles to update a particle’s velocity. Five sets of typical nonlinear equations are employed to test the quality and reliability of the novel algorithm search comparing with the PSO algorithm. Numerical results show that the proposed method is effective for the given test problems. The new algorithm can be used as a new tool to solve nonlinear equations, continuous function optimization, etc., and the combinatorial optimization problem. The global convergence of the given method is established.

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Parametric variational solution of linear-quadratic optimal control problems with control inequality constraints

Cited by 7 publications

References 34 publications

A novel fast model predictive control with actuator saturation for large-scale structures

A novel fast model predictive control with actuator saturation for large-scale structures

A modified pseudospectral method for indirect solving a class of switching optimal control problems

A Velocity-Combined Local Best Particle Swarm Optimization Algorithm for Nonlinear Equations

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