MIT and Queen's researchers unveil nonadaptive control for complex nonlinear systems

A new paper by Shimin Wang, Martin Guay, and Richard D. Braatz tackles a longstanding challenge in control theory: robust output regulation for nonlinear systems with high relative degree. The team, affiliated with MIT and Queen's University, introduces a nonadaptive design that combines an input-driven filter and a generic internal model with a recursive backstepping law. This recasts the regulation problem as a robust input-to-state stabilization of an augmented error system, eliminating the need for adaptive parameter estimation entirely.

The proposed method works under standard assumptions on the exosystem—such as purely imaginary eigenvalues—and a minimum-phase input-to-state stability condition on internal dynamics. Crucially, it guarantees global asymptotic regulation of estimation and tracking errors, even when the system dynamics are complex or only partially known. The authors derive explicit, verifiable inequalities for selecting design gains, simplifying implementation. The effectiveness is demonstrated on a benchmark controlled Duffing system, confirming that the nonadaptive approach matches or exceeds traditional adaptive techniques without the computational overhead.