Control design for discrete-time stochastic nonlinear processes with a nonquadratic performance objective

A performance-oriented controller synthesis technique for discrete-time stochastic nonlinear processes is proposed. When the objective for design is specified as the expected value of a nonsymmetric, nonquadratic loss functional, it is necessary to relate closed-loop process dynamics to the stationary probability density function (PDF) to properly address the problem. Since explicit relationships are available for only a few special cases, solution of the general optimal control problem is not possible. An approximate dynamics-PDF relationship is developed using parameterized structures to represent both process dynamics and PDF. The multivariate Gram-Charlier basis is presented as a practical and flexible tool for PDF parameterization. Application of the approximation technique in the optimal control framework results in regulatory control laws suboptimal with respect to the design objective. Application of the technique to an example process is illustrated through simulation.