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Dynamically re-optimized SNAC controller for robust wing rock suppression

Following the philosophy of adaptive optimal control, a new technique is presented in this paper for robust optimal regulation of a class of nonlinear systems. First, accounting for a nominal system model, a single network adaptive critic (SNAC) based multi-layered neural network (called as NN1) is synthesized offline for optimal regulation of the nominal system. However, another linear-in-weight neural network (called as NN2) is trained online and augmented to NN1 in such a manner that their combined output represent the desired optimal costate for the actual plant. To do this, the nominal model needs to be updated online to adapt to the actual plant, which done by synthesizing yet another linear-in-weight neural network (called as NN3) online. Training of NN3 is done by utilizing the error information between the nominal and actual states and carrying out the necessary Lyapunov stability analysis using a Sobolev norm based Lyapunov function so that both the unmodelled part of the dynamics as well as its partial derivatives with respect to the states are captured. This helps in training NN2 successfully to capture the required optimal relationship. The overall architecture is named as `Dynamically re-optimized single network adaptive critic (DR-SNAC)'. To demonstrate its effectiveness, the DR-SNAC technique is applied to suppress the wing rock phenomenon of slender delta wings in high angle of attack in presence of significant unmodelled dynamics and the results are quite promising.