ABSTRACT
This chapter introduces stochastic control ideas and the linear quadratic Gaussian (LQG) control problem. A distributed and decentralized control algorithm is proposed as a solution to the limitations of fully connected decentralized control systems. The chapter describes the optimal stochastic control problem and its solution. The two principles imply that the problem of seeking a linear control law for a linear dynamical system with Gaussian measurement noise subject to a quadratic performance index can be cast in terms of two separate problems: Optimal deterministic control, and Optimal stochastic estimation. Under the LQG assumptions, the design of the optimal stochastic controller can be completely separated into the design of the appropriate information filter and the design of an optimal deterministic controller associated with the original problem. The separation and certainty equivalence principles do not hold for nonlinear systems. Just as in the multisensor data fusion case, there are three broad categories of multiactuator control architectures: centralized, hierarchical and decentralized.
