A Covariance Feedback Approach to Covariance Control of Nonlinear Stochastic Systems

Algorithm 1

Nonlinear covariance assignment strategy.

	If the small value of the measured matrix is selected and the strong filtering action (6) in statistical linearization is assumed or by input-state feedback linearization idea, finally, in both cases, the nonlinear system can be specified as follows (16a):
	Step 1: consider a state transform and feedback control input (16b) such that the nonlinear dynamic (2) or (11) would be transferred into the linear dynamic (16a).
	Step 2: online state covariance estimation of the main system (20).
	Step 3: rearrange and modify the covariance vector and from (26) and (27).
	Step 4: calculate the covariance control variable from ((29)–(32)).
	Step 5: modify the covariance matrix from as covariance of control signal .
	Step 6: generate the covariance control signal with covariance matrix from (33).