Nonlinear optimal controllers in stochastic systems with a linear plant and a quadratic functional (Q1083420)

The author considers the problem of determining the optimal control u for a time-invariant linear control system with additive disturbance by a generalized random process. The optimal control u(t) is assumed to be computable as a function of the system's states x(s) available for times \(s<t\) and has to minimize a cost functional which is the time average of the expected value of a quadratic form of x and u. The optimal controller generating u(t) is well known to be linear at least as long as the disturbances are Gaussian, otherwise it usually has to be nonlinear. The author presents a method for computing u(t) which uses nonlinear predictions of the disturbance. An illustrative example is given.