Controller Design for Discrete-Time Stochastic Processes With Nonquadratic Loss

Abstract

The problem of optimal controller synthesis for discrete-time stochastic nonlinear processes is examined. When the objective for design is specified as the expected value of a nonsymmetric, nonquadratic loss functional, it is necessary to relate the closed-loop process dynamics to the stationary probability density function (pdf). Because explicit relationships are available for only a few special cases, a general solution to the problem is not possible. In this work a technique for developing approximations of the optimal control law by application of a dynamics–pdf approximation is presented. Numerical simulations illustrate application of the proposed technique.

KEY WORDS :

• Feedback control method
• Nonlinear process
• Nonnormal process
• Probability density function
• Stationarity