Probing and Duality in Stochastic Model Predictive Control

In a general nonlinear setting, stochastic optimal control involves the propagation of the conditional probability density of the state given the input signal and output measurements. This density is known as the information state in control circles and as the belief state in artificial intelligence and robotics squares. The choice of control signal affects the information state so that state observability becomes control-dependent. Thus, the feedback control law needs to include aspects of probing in addition to, or more accurately in competition with, its function in regulation. This is called duality of the control. In the linear case, this connection is not problematic since the control signal simply translates or recenters the conditional density without other effect. But for nonlinear systems, this complication renders all but the simplest optimal control problems computationally intractable.

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