Local First-Order Algorithms for Constrained Nonlinear Dynamic Games

2020 ◽  
Author(s):  
Bolei Di ◽  
Andrew Lamperski
Keyword(s):  
Nonlinear Dynamic ◽  
Dynamic Games ◽  
First Order

scholarly journals Differential Neural Networks for Identification and Filtering in Nonlinear Dynamic Games

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Emmanuel García ◽  
Daishi Alfredo Murano
Keyword(s):  
Neural Networks ◽  
Nonlinear Dynamic ◽  
Dynamic Games ◽  
Perfect State ◽  
State Information ◽  
State Identification ◽  
New Learning ◽  
Information Pattern ◽  
The Stability ◽  
The Mathematical Model

This paper deals with the problem of identifying and filtering a class of continuous-time nonlinear dynamic games (nonlinear differential games) subject to additive and undesired deterministic perturbations. Moreover, the mathematical model of this class is completely unknown with the exception of the control actions of each player, and even though the deterministic noises are known, their power (or their effect) is not. Therefore, two differential neural networks are designed in order to obtain a feedback (perfect state) information pattern for the mentioned class of games. In this way, the stability conditions for two state identification errors and for a filtering error are established, the upper bounds of these errors are obtained, and two new learning laws for each neural network are suggested. Finally, an illustrating example shows the applicability of this approach.

Rationalization and Incomplete Information

2003 ◽  
Vol 3 (1) ◽  
Author(s):  
Pierpaolo Battigalli ◽  
Marciano Siniscalchi
Keyword(s):  
Incomplete Information ◽  
Dynamic Games ◽  
Form Solution ◽  
Forward Induction ◽  
First Order ◽  
Bayesian Equilibrium ◽  
Incomplete Information Games ◽  
Games With Incomplete Information ◽  
Intuitive Criterion ◽  
Signalling Games

We analyze a family of extensive-form solution procedures for games with incomplete information that do not require the specification of an epistemic type space a la Harsanyi, but can accommodate a (commonly known) collection of explicit restrictions D on first-order beliefs. For any fixed D we obtain a solution called D-rationalizability.In static games, D-rationalizability characterizes the set of outcomes (combinations of payoff types and strategies) that may occur in any Bayesian equilibrium model consistent with D; these are precisely the outcomes consistent with common certainty of rationality and of the restrictions D. Hence, our approach to the analysis of incomplete-information games is consistent with Harsanyi's, and it may be viewed as capturing the robust implications of Bayesian equilibrium analysis.In dynamic games, D-rationalizability yields a forward-induction refinement of this set of Bayesian equilibrium outcomes. Focusing on the restriction that first-order beliefs be consistent with a given distribution on terminal nodes, we obtain a refinement of self-confirming equilibrium. In signalling games, this refinement coincides with the Iterated Intuitive Criterion.

First-order nonlinear dynamic initial value problems

2021 ◽  
Vol 11 (3/4) ◽  
pp. 241
Author(s):  
Iguer Luis Domini Dos Santos ◽  
Sanket Tikare ◽  
Martin Bohner
Keyword(s):  
Nonlinear Dynamic ◽  
Initial Value Problems ◽  
Initial Value ◽  
First Order

Nonlinear Dynamic Behavior of Functionally Graded Truncated Conical Shell Under Complex Loads

2015 ◽  
Vol 25 (02) ◽  
pp. 1550025 ◽  
Author(s):  
S. W. Yang ◽  
Y. X. Hao ◽  
W. Zhang ◽  
S. B. Li
Keyword(s):  
Nonlinear Dynamics ◽  
Conical Shell ◽  
Nonlinear Dynamic ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Phase Portraits ◽  
Vertex Angle ◽  
First Order ◽  
Aerodynamic Pressure ◽  
Truncated Conical Shell

Nonlinear dynamic behaviors of ceramic-metal graded truncated conical shell subjected to complex loads are investigated. The shell is modeled by first-order shear deformation theory. The nonlinear partial differential governing equation in terms of transverse displacements of the FGM truncated conical shell is derived from the Hamilton's principle. Galerkin's method is then utilized to discretize the partial governing equations to a two-degree-of-freedom nonlinear ordinary differential equation. The temperature-dependent materials properties of the constituents are graded in the radial direction in accordance with a power-law distribution. The aerodynamic pressure can be calculated by using the first-order piston theory. The temperature field is assumed to be a steady-state constant-temperature distribution. Bifurcation diagrams, the maximum Lyapunov exponents, wave forms and phase portraits are obtained by numerical simulation to demonstrate the complex nonlinear dynamics response of the FGM truncated conical shell. The influences of the semi-vertex angle, the material gradient index, in-plane and aerodynamic load on the nonlinear dynamics are studied.

First-order nonlinear dynamic initial value problems

2021 ◽  
Vol 11 (3/4) ◽  
pp. 241
Author(s):  
Martin Bohner ◽  
Sanket Tikare ◽  
Iguer Luis Domini Dos Santos
Keyword(s):  
Nonlinear Dynamic ◽  
Initial Value Problems ◽  
Initial Value ◽  
First Order

Convergence and stability analysis of active disturbance rejection control for first-order nonlinear dynamic systems

2018 ◽  
Vol 41 (7) ◽  
pp. 2064-2076 ◽  
Author(s):  
Zengqiang Chen ◽  
Yongshuai Wang ◽  
Mingwei Sun ◽  
Qinglin Sun
Keyword(s):  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Disturbance Rejection ◽  
Nonlinear Dynamic Systems ◽  
Stable Region ◽  
Feasible Region ◽  
Active Disturbance Rejection Control ◽  
First Order ◽  
Active Disturbance Rejection ◽  
Disturbance Rejection Control

To quantitatively investigate the correlation between parameters, disturbance and stability of the linear active disturbance rejection control (LADRC) technique, this paper provides a perspective of first-order nonlinear dynamic systems, and obtains the stable region of LADRC and reduced-order LADRC according to the Lyapunov function and the Markus–Yamabe theorem, along with mathematical proofs for global stability and asymptotic regulation. To be specific, regardless of whether plant dynamics are exactly known or unknown, the control bandwidth can be chosen arbitrarily from the obtained feasible region as long as the derivative of the disturbance satisfies a Lipschitz condition, or some knowledge of the boundary is available. Moreover, simulations are presented to testify the reliability of the results for different disturbances that are probably known or unknown when designing the extended state observer. The results show the validity and feasibility of this analysis.

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