Ordinal Potential Differential Games to Model Human-Machine Interaction in Vehicle-Manipulators

Varga, Balint; Inga, Jairo; Lemmer, Markus; Hohmann, Sören

doi:10.1109/ccta48906.2021.9658788

Cited by 5 publications

(8 citation statements)

References 24 publications

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“…This makes the optimization robust against measurement noise and disturbance. According to [15], the condition for an OPDG, cf. (15), can be reformulated, leading to Lemma 1.…”

Section: Trajectory-free Lmi Optimizationmentioning

confidence: 99%

“…To establish a baseline for the analysis, we utilize the identification method proposed in [15] and compare it with the two novel approaches. This state-of-the-art identification is referred to as Input-Dependent Optimization (IDO).…”

Section: Input Dependent Optimizationmentioning

confidence: 99%

“…The minimization of (32a) ensures that the necessary condition OPDG cf. [15]. The constraint (32b) is necessary for the optimum of J (p) meaning that u (p) is the result of the optimal control problem.…”

Section: Input Dependent Optimizationmentioning

confidence: 99%

“…elements in main diagonal are identical for all players, see [10] or Example 4 in [14]. To allow a broader usage, the subclass of OPDGs has been introduced in [15]. Definition 3 (Ordinal Potential Differential Game [15]).…”

Section: Ordinal Potential Differential Gamesmentioning

confidence: 99%

“…To allow a broader usage, the subclass of linear quadratic (LQ) ordinal potential differential games (OPDGs) has been previously introduced in literature [15]. While the core idea of this subclass has already been discussed, a systematic identification method for OPDGs is still absent from the literature.…”

Section: Introductionmentioning

confidence: 99%

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Identification Methods for Ordinal Potential Differential Games

Varga,

Huang,

Hohmann

2024

Preprint

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This paper introduces two new identification methods for the class of linear quadratic (LQ) ordinal potential differential games (OPDGs). Potential games are notable for their benefits, including the computability and guaranteed existence of Nash Equilibria. Previous literature has explored the analysis of static ordinal potential games, yet their applicability to various engineering applications remains limited. Despite the previous introduction of the core idea of OPDGs, a systematic method for identifying a potential game for a given LQ differential game has not been developed yet. To address this research gap, this paper proposes two identification methods that provide the quadratic potential cost function for the given LQ differential game. Both identification methods are based on linear matrix inequalities. The first identification method aims to minimize the condition number of the potential cost function's parameters, providing a faster and more precise technique compared to earlier solutions. In addition, an evaluation regarding the feasibility of system structure requirements is presented. With a less rigid formulation, the second identification technique can successfully identify LQ OPDGs in instances where the first method fails. These two novel identification methods are verified through simulations. The results demonstrate their advantages and potential in designing and analyzing cooperative control systems.

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“…This makes the optimization robust against measurement noise and disturbance. According to [15], the condition for an OPDG, cf. (15), can be reformulated, leading to Lemma 1.…”

Section: Trajectory-free Lmi Optimizationmentioning

confidence: 99%

Section: Input Dependent Optimizationmentioning

confidence: 99%

Section: Input Dependent Optimizationmentioning

confidence: 99%

Section: Ordinal Potential Differential Gamesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Identification Methods for Ordinal Potential Differential Games

Varga,

Huang,

Hohmann

2024

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Identification methods for ordinal potential differential games

Varga,

Huang,

Hohmann

2024

Comp. Appl. Math.

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This paper introduces two new identification methods for linear quadratic (LQ) ordinal potential differential games (OPDGs). Potential games are notable for their benefits, such as the computability and guaranteed existence of Nash Equilibria. While previous research has analyzed ordinal potential static games, their applicability to various engineering applications remains limited. Despite the earlier introduction of OPDGs, a systematic method for identifying a potential game for a given LQ differential game has not yet been developed. To address this gap, we propose two identification methods to provide the quadratic potential cost function for a given LQ differential game. Both methods are based on linear matrix inequalities (LMIs). The first method aims to minimize the condition number of the potential cost function’s parameters, offering a faster and more precise technique compared to earlier solutions. In addition, we present an evaluation of the feasibility of the structural requirements of the system. The second method, with a less rigid formulation, can identify LQ OPDGs in cases where the first method fails. These novel identification methods are verified through simulations, demonstrating their advantages and potential in designing and analyzing cooperative control systems.

show abstract

Open-Loop and Feedback LQ Potential Differential Games for Multi-Agent Systems

Scarpa,

Mylvaganam

2023

2023 62nd IEEE Conference on Decision and Control (CDC)

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Ordinal Potential Differential Games to Model Human-Machine Interaction in Vehicle-Manipulators

Cited by 5 publications

References 24 publications

Identification Methods for Ordinal Potential Differential Games

Identification Methods for Ordinal Potential Differential Games

Identification methods for ordinal potential differential games

Open-Loop and Feedback LQ Potential Differential Games for Multi-Agent Systems

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