Optimization Criteria for Human Trajectory Formation in Dynamic Virtual Environments

Albrecht, Sebastian; Passenberg, Carolina; Sobotka, Marion; Peer, Angelika; Buss, Martin; Ulbrich, Michael

doi:10.1007/978-3-642-14075-4_37

Cited by 10 publications

(3 citation statements)

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“…This particular instance of bilevel optimal control may therefore be also called inverse optimal control. In [2,3,4,25,45], inverse optimal control problems of ODEs are considered in the context of human locomotion. Some more theoretical results for such problems are presented in [26,56,57].…”

Section: What Is Bilevel Optimal Control?mentioning

confidence: 99%

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Bilevel optimal control: existence results and stationarity conditions

Mehlitz¹,

Wachsmuth²

2019

Preprint

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The mathematical modeling of numerous real-world applications results in hierarchical optimization problems with two decision makers where at least one of them has to solve an optimal control problem of ordinary or partial differential equations. Such models are referred to as bilevel optimal control problems. Here, we first review some different features of bilevel optimal control including important applications, existence results, solution approaches, and optimality conditions. Afterwards, we focus on a specific problem class where parameters appearing in the objective functional of an optimal control problem of partial differential equations have to be reconstructed. After verifying the existence of solutions, necessary optimality conditions are derived by exploiting the optimal value function of the underlying parametric optimal control problem in the context of a relaxation approach.

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Section: What Is Bilevel Optimal Control?mentioning

confidence: 99%

“…be a bounded Lipschitz domain. We fix p ∈(3,6) as in[32, Theorem 0.5]. Let us set Y := W 1, p 0 (Ω) and W := W −1, p (Ω).…”

mentioning

confidence: 99%

Bilevel optimal control: existence results and stationarity conditions

Mehlitz¹,

Wachsmuth²

2019

Preprint

View full text Add to dashboard Cite

show abstract

“…Flash and Hogan (1985); Uno et al (1989)), but further research showed that each of the cost functions can only explain a limited range of motions (Todorov (2004)). Thus, we consider a parameterized family of cost functions and search for the optimal parameters to reproduce the characteristics of a task at hand (Albrecht et al (2012(Albrecht et al ( , 2011(Albrecht et al ( , 2010).…”

Section: Introductionmentioning

confidence: 99%