On solving hybrid optimal control problems with higher index DAEs

Pytlak, R.; Suski, Damian

doi:10.1080/10556788.2017.1288730

Cited by 10 publications

(22 citation statements)

References 33 publications

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“…Below, we present the results of applying the presented algorithm to solving two optimal control problems based on hybrid systems. They have been previously discussed in (Pytlak and Suski, 2017), but here we show results for different versions of these problems. Please note, that the purpose of these examples is purely illustrative within the discussion of capabilities of the implemented solver and they do not necessarily represent sensible problems of real engineering importance or application.…”

Section: Examplesmentioning

confidence: 83%

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Defining and Solving Hybrid Optimal Control Problems with Higher Index DAEs

Pytlak

Suski

Tarnawski

et al. 2017

Linköping Electronic Conference Proceedings

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The paper deals with optimal control problems defined for hybrid systems described by higher index DAEs. We present a prototype solution that supports the whole process from defining such problem to solving it and presenting results. Problem's definition is done with Dynamic Optimization Modeling Language (DOML) which is based directly on Modelica. The proposed numerical procedure for solving the problems of interest has the following features: 1) it is based on the appropriately defined adjoint equations formulated for the discretized equations being the result of the numerical integration of system equations by an implicit Runge-Kutta method; 2) initialization for higher index DAEs is performed with the help of Pantelides' algorithm; 3) it does not require the system to be transformed to ODEs (through differentiation of some algebraic equations). The paper presents numerical examples related to hybrid systems described by index three DAEs, showing the validity of the proposed approach. All software components needed to carry out the computations, i.e. the code editor, compiler, numerical libraries and GUI for presenting results are prepared as parts of a combined platform: Interactive Dynamic Optimization Server (IDOS).

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Section: Examplesmentioning

confidence: 83%

“…analogical to formulas (32)-(33). The formulae (44)-(45) are derived in (Pytlak and Suski, 2017). To solve the optimal control problem, we replace control functions by their piecewise constant approximations and follow the optimization procedure outlined below.…”

Section: Numerical Proceduresmentioning

confidence: 99%

Defining and Solving Hybrid Optimal Control Problems with Higher Index DAEs

Pytlak

Suski

Tarnawski

et al. 2017

Linköping Electronic Conference Proceedings

Self Cite

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“…The numerical procedure which we used to solve the problem (9), (1)–(8),(10)–(15) is described, to much extent, in [20] and [21]. The main features of the procedure are: it is based on the Radau IIa version of a Runge–Kutta method for integrating differential equations,it uses adjoint equations to evaluate gradients of functions defining the optimization problem.…”

Section: Methodsmentioning

confidence: 99%

Application of dynamic optimisation for planning a haemodialysis process

et al. 2019

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Background The aim of the study is to show that optimization tools can be used in planning the haemodialysis process in order to obtain the most effective treatment aimed at removing both urea and phosphorus. To this end we use the IV–compartment model of phosphorus kinetics. Methods The use of the IV–compartment model of phosphorus kinetics forces us to apply new numerical tools which cope with a rebound phenomenon that can occur during haemodialysis. The proposed algorithm solves optimization problems with various constraints imposed on concentrations of urea and phosphorus. Results We show that the optimization tools are effective in planning haemodialysis processes aimed at achieving desired levels of urea and phosphorus concentrations at the end of these processes. One of the numerical experiments reported in the paper concerns patients data who experienced a rebound phenomenon during haemodialysis due to a low level of phosphorus concentration. Conclusion In order to plan haemodialysis processes one should take into account the fact that these processes, in general, are described by different equations in different regions determined by phosphorus concentrations. This follows from the fact that mechanisms modelled by IV–compartment model are activated during dialysis. Therefore, advanced numerical tools have to be used in order to simulate and optimize these processes. The paper shows that these tools can be constructed and effectively applied in planning haemodialysis processes.

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“…To avoid additional Newton iterations for integration, we can use the implicit function theorem [3,6]. Specifically, k n is a function of ξ n from (8). Then, we can obtain from the implicit function theorem that…”

Section: Gradient Evaluation By Adjoint Sensitivity Propagationmentioning

confidence: 99%

“…Gradients were evaluated by propagating adjoint sensitivity in discrete time. Then, this method was extended to higher-index DAEs [7,8]. This method is more efficient than forward one when the number of constraints is less than that of optimization variables [2].…”

Section: Introductionmentioning

confidence: 99%

Implicit integration with adjoint sensitivity propagation for optimal control problems involving differential-algebraic equations

Jiang

Xie

Guo

et al. 2017

2017 36th Chinese Control Conference (CCC)

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For the solution of optimal control problem involving an index-1 differential-algebraic equation, an efficient function evaluation algorithm is proposed in this paper. In the evaluation procedure, the state equation is propagated forwards, then, adjoint sensitivity is propagated backwards. Thus, it is computationally more efficient than forward sensitivity propagation when the number of constraints is less than that of optimization variables. In order to reduce Newton iterations, the adjoint sensitivity is derived utilizing the implicit function theorem, and the integration procedure is accelerated by incorporating a predictor-corrector strategy. This algorithm is integrated with a nonlinear programming solver Ipopt to solve sequentially the point-to-point optimal control for a Delta robot with constrained motor torque. Numerical experiments demonstrate the efficiency of this algorithm.

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On solving hybrid optimal control problems with higher index DAEs

Cited by 10 publications

References 33 publications

Defining and Solving Hybrid Optimal Control Problems with Higher Index DAEs

Defining and Solving Hybrid Optimal Control Problems with Higher Index DAEs

Application of dynamic optimisation for planning a haemodialysis process

Implicit integration with adjoint sensitivity propagation for optimal control problems involving differential-algebraic equations

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