Stabilization and Robustness Analysis for a Chain of Saturating Integrators With Imprecise Measurements

Abstract

We solve a challenging input-to-state stabilization problem for a chain of saturated integrators when the variables are not accurately measured. We use a recent backstepping approach with pointwise delays and no distributed terms.

Stabilization and Robustness Analysis for a Chain of Saturating Integrators Arising in the Visual Landing of Aircraft

“…Given any constant u > 0, our goal is to construct an output feedback u that is bounded by u and that is such that the closed loop system (1) is input-to-state stable with respect to δ = (δ 1 , δ 2 ), under the assumption that δ 2 < L 1 . This contrasts with the objectives in [12], which studied the same system (1) with a sampled version of the same outputs (2), because in [12], the control was not required to be bounded, and in addition, [12] required the more stringent conditionδ 2 < L 1 (1 − e −1 ) 2 /(40(1 + 2e −1 + e −2 )) as well as a scaling constant λ > 0 in the control, which are not needed here. Hence, the present paper provides potential advantages over [12], which are made possible by our new dynamical extension in this work which was not present in [12].…”

“…This paper continues our search for more effective feedback stabilization methods for cases where only imprecise output measurements are available for use in the control. This led to our novel backstepping approach in [14] and [15] where pointwise delays are present in the feedback even if current output values are available, and then our work [11], [12] that uses the preceding backstepping approach to solve a feedback control problem for a chain of saturated integrators with imprecise output measurements using an unbounded control. In the present work, we use our backstepping approach to solve a stabilization problem for a chain of saturating integrators with imprecise measurements using dynamic output feedback controls of arbitrarily small amplitude; see Section II for more on the potential advantages of this work as compared with the method in [11], [12].…”

Controls for a nonlinear system arising in vision‐based landing of airliners

“…We prove global asymptotic stability, using a model in Section 3, which contains numerical results that apply our result; see Reference 21 for an artificial delays approach for a complementary landing problem without coupling. This makes it possible to provide performance guarantees that ensure global asymptotic stability under uncertain delays and sampling in the output, by incorporating known bounds from the delays and sampling into the control design.…”

Robust Adaptive Stabilization by Delay Under State Parametric Uncertainty and Measurement Bias

“…It is important to note that there exist papers devoted to adaptive control of time-delay systems as, for example, [13], [14], [15] (the uncertain parameters appear in the state equation only), or papers dealt with adaptive/robust control for systems with multiplicative uncertain parameters in the output equation [16], [17] (without presence of time delays) or [18], but to the best of our knowledge there is no theory dealing with time-delay systems subjected to parametric uncertainty in the state dynamics and the output measurements simultaneously.…”