H∞-constrained quasi-linear quadratic Gaussian control with loop transfer recovery

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In this paper we propose a new nonlinear controller design method, called quasi-linear quadratic Gaussian/H-infinity/loop transfer recovery (QLQG/H∞/LTR), for nonlinear multivariable, systems with hard nonlinearities such as Coulomb friction and dead-zones. We consider H∞-constraints for the optimization of statistically linearized systems, by replacing the covariance Lyapunov equation by a modified Riccati equation, whose solution leads to an upper bound QLQG performance. As a result, the nonlinear correction term is included in the Riccati equation which, in general, is excessively difficult to solve numerically. To solve this problem, we use the modified loop shaping technique and derive analytic proofs of the LTR condition. Finally, the H∞-constrained, nonlinear controller is synthesized by an inverse random input describing function technique (IRIDF). The proposed design method for a hard nonlinear multivariable systems has better robustness to unstructured uncertainty and hard nonlinearities than the QLQG/LTR method. A flexible link system with Coulomb frictions serves as a design example for our methodology.