Control of Nonlinear Stochastic Systems: Model-Free Controllers versus Linear Quadratic Regulators

Classical linear controllers are widely used in the control of nonlinear stochastic systems and thus there is concern about the ability of the controller to adequately regulate the system. An alternative approach to cope with such systems is to avoid the need to build the traditional "open-loop" model for the system. Through the avoidance of model, controllers can be built for arbitrarily complex nonlinear systems via neural-networks trained by simultaneous perturbation stochastic approximation so that only the output error (between the plant and target outputs) is needed. In this paper, we discuss basic characteristics and limitations of both approaches and formally analyze this comparison in the case of linear quadratic regulators. The comparison is illustrated numerically on a simulated nonstationary multiple input, multiple output wastewater treatment system with stochastic effects