Optimistic planning algorithms for state-constrained optimal control problems

Bokanowski, Olivier; Gammoudi, Nidhal; Zidani, Hasnaa

doi:10.1016/j.camwa.2022.01.016

Cited by 11 publications

(16 citation statements)

References 20 publications

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“…(i) Fix any x ∈ R n , ∈ R >0 , and u ∈ U M, x [0, t], and denote the corresponding near-optimal trajectory by ξ . = χ(x, u) as per (5). Applying (42) and Corollary 1,…”

Section: Theoremmentioning

confidence: 93%

“…] s is affine by (5), convexity of γ s,α x follows by inspection of (35), (7), and Lemma 13. 22) satisfy the following:…”

Section: Existence and Uniqueness Of The Optimal Controlsmentioning

confidence: 99%

“…Moreover, consistent approximations generated via temporal and spatial discretization provide the foundation for finite difference methods for numerical computation, see for example [7,9]. In the context of the curse-of-dimensionality, recent advances in optimization based approaches exploiting (for example) reproducing kernels [3] and optimistic planning [5] have provided very promising computational improvements over those earlier grid-based methods.…”

Section: Contextmentioning

confidence: 99%

“…3. Two preliminary lemmas concerning (1), (5) are included prior to commencing this development. Their proofs are standard and are omitted for brevity.…”

Section: State Constrained Linear Regulator Problemmentioning

confidence: 99%

“…Their proofs are standard and are omitted for brevity. (5) for all k ∈ N, the following properties hold:…”

Section: State Constrained Linear Regulator Problemmentioning

confidence: 99%

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A Game Representation for a Finite Horizon State Constrained Continuous Time Linear Regulator Problem

2023

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A supremum-of-quadratics representation for a class of extended real valued barrier functions is developed and applied in the context of solving a continuous time linear regulator problem subject to a single state constraint of bounded norm. It is shown that this very simple state constrained regulator problem can be equivalently formulated as an unconstrained two-player game. By demonstrating equivalence of the upper and lower values, and exploiting existence and uniqueness of the optimal actions for both players, state feedback characterizations for the corresponding optimal policies for both players are developed. These characterizations are illustrated by a simple example.

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“…(i) Fix any x ∈ R n , ∈ R >0 , and u ∈ U M, x [0, t], and denote the corresponding near-optimal trajectory by ξ . = χ(x, u) as per (5). Applying (42) and Corollary 1,…”

Section: Theoremmentioning

confidence: 93%

“…] s is affine by (5), convexity of γ s,α x follows by inspection of (35), (7), and Lemma 13. 22) satisfy the following:…”

Section: Existence and Uniqueness Of The Optimal Controlsmentioning

confidence: 99%

Section: Contextmentioning

confidence: 99%

“…3. Two preliminary lemmas concerning (1), (5) are included prior to commencing this development. Their proofs are standard and are omitted for brevity.…”

Section: State Constrained Linear Regulator Problemmentioning

confidence: 99%

“…Their proofs are standard and are omitted for brevity. (5) for all k ∈ N, the following properties hold:…”

Section: State Constrained Linear Regulator Problemmentioning

confidence: 99%

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