OBC: Stochastic Systems

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Receding Horizon Control Stochastic Systems Kalman Filtering

In this chapter we present a focused review of stochastic systems, oriented toward the material that is required in Chapters 5 and 6. After a brief review of random variables, we define discrete-time and continuous-time random processes, including the expectation, (co-)variance and correlation functions for a random process. These definitions are used to describe linear stochastic systems (in continuous time) and the stochastic response of a linear system to a random process (e.g., noise). We initially derive the relevant quantities in the state space, followed by a presentation of the equivalent frequency domain concepts.