Global Output-Feedback Control by Exploiting High-Gain Dynamic-Compensation Mechanisms

SIAM Journal on Control and Optimization, Volume 62, Issue 2, Page 1122-1151, April 2024.
Abstract. Currently, output-feedback control still necessitates severe constraints on systems, e.g., system nonlinearities cannot exceed certain degree and uncertainties should belong to specific types. In this paper, by exploiting dynamic-compensation mechanisms, we essentially extend system nonlinearities and uncertainties. Specifically, the nonlinearities heavily rely on unmeasured states and particularly have unknown arbitrary function-of-output growth rates. Unknown control coefficients whether with known or unknown bounds are admitted, which have been excluded before in the context of such inclusive nonlinearities. The key to our novel solution lies in realizing the potential of filter-based observers, dynamic high gains, design/analysis parameter designation, and composite Lyapunov functions. In detail, two dynamic-high-gain filters are worked out to provide available states for controller design. The filter states, after weighted by the unknown control coefficient, also make up the estimated states which lead to control-free and tractable error dynamics. Two dynamic high gains with new dynamics are put forward to counteract the nonlinearities and uncertainties and, meanwhile, to enable the adaptive controller to own a concise structure. During the controller design, crucial design parameters can no longer be expressed explicitly due to unknown control coefficients, but rather need to be pursued through a recursive algorithm. With a set of analysis parameters, important (dynamic-high-gain) input-to-state stable properties of some vital variables are uncovered, and exhaustive Lyapunov analysis is performed for the closed-loop boundedness and convergence.