System Theory

Download Discrete–Time Stochastic Control and Dynamic Potential by David González-Sánchez, Onésimo Hernández-Lerma PDF

By David González-Sánchez, Onésimo Hernández-Lerma

​There are numerous concepts to review noncooperative dynamic video games, similar to dynamic programming and the utmost precept (also known as the Lagrange method). It seems, despite the fact that, that a technique to signify dynamic strength video games calls for to research inverse optimum regulate difficulties, and it's the following the place the Euler equation method is available in since it is very well–suited to resolve inverse difficulties. regardless of the significance of dynamic strength video games, there isn't any systematic examine approximately them. This monograph is the 1st try to offer a scientific, self–contained presentation of stochastic dynamic strength games.

Show description

Read or Download Discrete–Time Stochastic Control and Dynamic Potential Games: The Euler–Equation Approach PDF

Best system theory books

Nonholonomic Mechanics and Control

This ebook is meant for graduate and complex undergraduate scholars in arithmetic, physics and engineering who desire to research this topic and for researchers within the sector who are looking to increase their concepts.

Optimal control, stabilization and nonsmooth analysis

This edited booklet comprises chosen papers awarded on the Louisiana convention on Mathematical regulate conception (MCT'03), which introduced jointly over 35 well known international specialists in mathematical keep watch over conception and its purposes. The publication types a well-integrated exploration of these parts of mathematical keep an eye on thought within which nonsmooth research is having a massive impression.

Complex Adaptive Systems: An Introduction to Computational Models of Social Life

This publication presents the 1st transparent, accomplished, and available account of advanced adaptive social structures, by way of of the field's major specialists. Such systems--whether political events, inventory markets, or ant colonies--present the most interesting theoretical and functional demanding situations confronting the social sciences.

Statistical Mechanics of Complex Networks (Lecture Notes in Physics)

Networks supplies an invaluable version and picture photo valuable for the outline of a wide number of web-like constructions within the actual and man-made realms, e. g. protein networks, nutrients webs and the net. The contributions accrued within the current quantity supply either an creation to, and an summary of, the multifaceted phenomenology of advanced networks.

Extra resources for Discrete–Time Stochastic Control and Dynamic Potential Games: The Euler–Equation Approach

Example text

2. Our main results are stated in Sect. 3, and illustrated in Sect. 4 with a detailed example. In Sect. 5 we deal with the nonstationary case. 35 D. Gonz´alez-S´anchez and O. 1. We will use the line integrals introduced in the section on notation and acronyms. That is, if f : Rn → Rn is measurable with component functions f1 , f2 , . . , fn and φ : [0, 1] → Rn is a C 1 function with components φ1 , φ2 , . . , φn , then φ (1) φ (0) f (x)dx := 1 0 d φi n ∑ fi (φ (t)) dt (t) dt. i=1 The function f is said to be exact when this integral does not depend on the path φ .

We also have to require convexity of the set Φ (x0 , s0 ) and concavity of the function gt (·, ·, st ) for each st ∈ St (t = 0, 1, . ). 2 (A stochastic LQ problem). In this example we consider a stochastic version of the OCP studied in Sect. 5. We assume the dynamics xt+1 = α xt + γ ut + ξt , t = 0, 1, . . d. random variables with zero mean and variance σ 2 . Let q, r > 0, and 0 < β < 1. 59). Note that gt (x, y, s) = β t [qx2 + rγ −2 (y − α x − s)2 ]. 61) where Q := (α 2 r + γ 2 q)β . Let x¯t denote the expected value of xˆtπ for t = 0, 1, .

Where utj is chosen by player j in the control set U j ( j = 1, . . , n). In general, the set U j may depend on time t, the current state xt , the action uti of each player i = j, and the value st taken by ξt , for each t = 0, 1, . .. We suppose that player j wants to maximize a performance index (also known as reward or payoff function) of the form ∞ E ∑ rtj (xt , ut1 , . . 1) and the given initial pair (x0 , s0 ), which is supposed to be fixed throughout the following. At each time t = 0, 1, .

Download PDF sample

Rated 4.33 of 5 – based on 26 votes