Control parametrization: A unified approach to optimal control problems with general constraints

Goh, C. J.; Teo, Kok Lay

doi:10.1016/0005-1098(88)90003-9

Cited by 344 publications

(196 citation statements)

References 33 publications

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“…control vector parameterization method (CVP) [15], to solve the defined dynamic optimization problem. This method transforms formerly infinite-dimensional dynamic optimization problem into a finite-dimensional form of NLP problem by apply-ing a piece-wise polynomial approximation of the control variables.…”

Section: Dynamic Optimizationmentioning

confidence: 99%

Analysis of optimal operation of a fed-batch emulsion copolymerization reactor used for production of particles with core–shell morphology

Paulen

Benyahia

Latifi

et al. 2014

Computers & Chemical Engineering

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Section: Dynamic Optimizationmentioning

confidence: 99%

Analysis of optimal operation of a fed-batch emulsion copolymerization reactor used for production of particles with core–shell morphology

Paulen

Benyahia

Latifi

et al. 2014

Computers & Chemical Engineering

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“…In the simultaneous method, also known as orthogonal collocation approach [4,5,52], the state trajectories are parameterized and the residuals of the differential equations are enforced as constraints at specified collocation times. In the sequential method [6,22], the state trajectories are regarded as functions of the control decision variables. In the direct multiple shooting method [8], the state trajectories are formed by piecing together those of finite single shooting problems on the corresponding subintervals over which the param-eterized control is applied (see p.243 in [8]).…”

Section: Introductionmentioning

confidence: 99%

Local optimization of dynamic programs with guaranteed satisfaction of path constraints

Faust

Chachuat

et al. 2015

Automatica

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An algorithm is proposed for locating a feasible point satisfying the KKT conditions to a specified tolerance of feasible inequalitypath-constrained dynamic programs (PCDP) within a finite number of iterations. The algorithm is based on iteratively approximating the PCDP by restricting the right-hand side of the path constraints and enforcing the path constraints at finitely many time points. The main contribution of this article is an adaptation of the semi-infinite program (SIP) algorithm proposed in [Mitsos, Optimization, 2011, 60(10-11):1291-1308] to PCDP. It is proved that the algorithm terminates finitely with a guaranteed feasible point which satisfies the first-order KKT conditions of the PCDP to a specified tolerance. The main assumptions are: i) availability of a nonlinear program (NLP) local solver that generates a KKT point of the constructed approximation to PCDP at each iteration if this problem is indeed feasible; ii) existence of a Slater point of the PCDP that also satisfies the first-order KKT conditions of the PCDP to a specified tolerance; iii) all KKT multipliers are nonnegative and uniformly bounded with respect to all iterations. The performance of the algorithm is analyzed through two numerical case studies.

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“…This can be implemented by discretization of the controls and/or the states, depending on the selected discretization approach, and solving the problem using one of the nonlinear programming algorithms such as sequential quadratic programming (SQP), interior points, genetic algorithm (GA) etc. Although its ease and robustness, this method can only give suboptimal/approximate solution [6]- [9]. One of the preferred methods of the direct approaches is the inverse dynamics-based optimization which has three distinctive features: (a) it does not need the inverse mass matrix, (b) only the states of the target system are discretized, and (c)the ability to convert the original optimal control into algebraic equations which are easy to deal with.…”

Section: Introductionmentioning

confidence: 99%

Finite Difference-Based Suboptimal Trajectory Planning of Biped Robot with Continuous Dynamic Response

Al-Shuka¹,

Corves²,

Vanderborght³

et al. 2013

IJMO

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Abstract-One of the clear problems encountered in the dynamic response of the biped robot is the discontinuity of the actuating torques/ground reaction forces at the transition instances during transferring form single support phase to double support phase and vice versa. Therefore, this paper suggests the linear transition function used in the biomechanics field for estimating the ground reaction forces during the double support phase such that gradual increase/decrease of the ground reaction forces can occur. The closure loop of the biped robot at the transition instances during DSP can be broken using the mentioned strategy. Consequently, the continuous dynamic response can be achieved. Two cases are simulated using the optimal control theory. The inverse dynamics-based optimization is preferred as a direct suboptimal tool because it can show less computation and easinessthan other optimal control approaches. Due to easiness of the finite difference approach, it is used for discretization of the dynamic equations and the imposed constraints to convert the dynamic optimal control problem into parameter optimization. The simulated case 1 have been used repeatedly in the literature, whereas the case 2 adopts the linear transition function of the ground reaction forces keeping the same generalized coordinates of the biped configuration at the transition instances. The results show the superiority of the suggested method to guarantee continuous actuating torques/ground reaction forces at the transition instances.

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Control parametrization: A unified approach to optimal control problems with general constraints

Cited by 344 publications

References 33 publications

Analysis of optimal operation of a fed-batch emulsion copolymerization reactor used for production of particles with core–shell morphology

Analysis of optimal operation of a fed-batch emulsion copolymerization reactor used for production of particles with core–shell morphology

Local optimization of dynamic programs with guaranteed satisfaction of path constraints

Finite Difference-Based Suboptimal Trajectory Planning of Biped Robot with Continuous Dynamic Response

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