scholarly journals Power Series Solution of the Hamilton-Jacobi-Bellman Equation for Time-varying Differential-Algebraic Equations

2006 ◽  
Author(s):  
Johan Sjoberg ◽  
Torkel Glad
Keyword(s):  
Power Series ◽  
Series Solution ◽  
Bellman Equation ◽  
Differential Algebraic Equations ◽  
Power Series Solution ◽  
Time Varying ◽  
Algebraic Equations ◽  
Hamilton Jacobi Bellman Equation ◽  
Hamilton Jacobi Bellman

scholarly journals Analytical Solution of a Nonlinear Index-Three DAEs System Modelling a Slider-Crank Mechanism

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Brahim Benhammouda ◽  
Hector Vazquez-Leal
Keyword(s):  
Analytical Solution ◽  
Series Solution ◽  
Perturbation Parameter ◽  
Differential Algebraic Equations ◽  
Modern Technology ◽  
Power Series Solution ◽  
System Modelling ◽  
Algebraic Equations ◽  
Transform Method ◽  
Crank Mechanism

The slider-crank mechanism (SCM) is one of the most important mechanisms in modern technology. It appears in most combustion engines including those of automobiles, trucks, and other small engines. The SCM model considered here is an index-three nonlinear system of differential-algebraic equations (DAEs), and therefore difficult to integrate numerically. In this work, we present the application of the differential transform method (DTM) to obtain an approximate analytical solution of the SCM model in convergent series form. In addition, we propose a posttreatment of the power series solution with the Padé resummation method to extend the domain of convergence of the approximate series solution. The main advantage of the proposed technique is that it does not require an index reduction and does not generate secular terms or depend on a perturbation parameter.

Optimal algebra and power series solution of fractional Black-Scholes pricing model

2021 ◽  
Vol 25 (8) ◽  
pp. 6075-6082
Author(s):  
Hemanta Mandal ◽  
B. Bira ◽  
D. Zeidan
Keyword(s):  
Power Series ◽  
Series Solution ◽  
Power Series Solution ◽  
Pricing Model ◽  
Black Scholes

Interception of automated adversarial drone swarms in partially observed environments

2021 ◽  
pp. 1-14
Author(s):  
Daniel Saranovic ◽  
Martin Pavlovski ◽  
William Power ◽  
Ivan Stojkovic ◽  
Zoran Obradovic
Keyword(s):  
Bellman Equation ◽  
Pid Controllers ◽  
Partially Observed ◽  
Hamilton Jacobi Bellman Equation ◽  
Partial Feedback ◽  
Point Solution ◽  
Physical Limitations ◽  
Defensive Mechanisms ◽  
Hamilton Jacobi Bellman ◽  
New Framework

As the prevalence of drones increases, understanding and preparing for possible adversarial uses of drones and drone swarms is of paramount importance. Correspondingly, developing defensive mechanisms in which swarms can be used to protect against adversarial Unmanned Aerial Vehicles (UAVs) is a problem that requires further attention. Prior work on intercepting UAVs relies mostly on utilizing additional sensors or uses the Hamilton-Jacobi-Bellman equation, for which strong conditions need to be met to guarantee the existence of a saddle-point solution. To that end, this work proposes a novel interception method that utilizes the swarm’s onboard PID controllers for setting the drones’ states during interception. The drone’s states are constrained only by their physical limitations, and only partial feedback of the adversarial drone’s positions is assumed. The new framework is evaluated in a virtual environment under different environmental and model settings, using random simulations of more than 165,000 swarm flights. For certain environmental settings, our results indicate that the interception performance of larger swarms under partial observation is comparable to that of a one-drone swarm under full observation of the adversarial drone.

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