Analysis of systems with shot noise

✍ Scribed by Prentiss Robinson

• Publisher: Elsevier Science
• Year: 1972
• Tongue: English
• Weight: 430 KB
• Volume: 293
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(72)90059-2

✦ Synopsis

If a system has a set of random inputs which are Poisson impulse processes (shot noise), then the performance index of this system satisfies an integral partialdiflerential equation. The problem considered here is the solution of this equation. It is shown that this equation is equivalent to an integral equation which can be solved by the method of successive approximations. Since shot noise tends to a Gaussian process as the density increases, the results of this paper can be used to solve the Gaussian noise problem. In th,is context, regarding the optimal control problem for system with Gaussian noise, the results of this paper can be used to apply the method of quasi-linearization to solve Bellman's _functionaE equation, which is a nonlinear parabolic partial-differential equation. * This model is used to simplify the notation. The method can easily be extended to the more general model given on p. 18 of Ref. (3).