Stochastic Systems

Abstract

Stochastic systems are described with emphasis on their use in stochastic control, filtering, and stochastic differential games. Some background is given for the Wiener process, stochastic calculus, and stochastic differential equations. The linear filtering problem is described. Some general notions of stochastic control are given and the linear–quadratic Gaussian control problem is solved. Weighted least‐squares estimation is applied to continuous‐time adaptive control and an adaptive control problem is solved. A solution is given for the linear–quadratic control problem with a general noise process. Stochastic differential games are described and both linear and nonlinear stochastic differential games are explicitly solved by determining optimal control strategies.