Robust nonlinear control : from continuous time to sampled-data with aerospace applications.

Abstract : The dissertation deals with the problems of stabilization and control of nonlinear systems with deterministic model uncertainties. First, in the context of uncertain systems analysis, we introduce and explain the basic concepts of robust stability and stabilizability. Then, we propose a method of stabilization via state-feedback in presence of unmatched uncertainties in the dynamics. The recursive backstepping approach allows to compensate the uncertain terms acting outside the control span and to construct a robust control Lyapunov function, which is exploited in the subsequent design of a compensator for the matched uncertainties. The obtained controller is called recursive Lyapunov redesign. Next, we introduce the stabilization technique through Immersion \& Invariance (I\&I) as a tool to improve the robustness of a given nonlinear controller with respect to unmodeled dynamics. The recursive Lyapunov redesign is then applied to the attitude stabilization of a spacecraft with flexible appendages and to the autopilot design of an asymmetric air-to-air missile. Contextually, we develop a systematic method to rapidly evaluate the aerodynamic perturbation terms exploiting the deterministic model of the uncertainty. The effectiveness of the proposed controller is highlighted through several simulations in the second case-study considered. In the final part of the work, the technique of I\& I is reformulated in the digital setting in the case of a special class of systems in feedback form, for which constructive continuous-time solutions exist, by means of backstepping and nonlinear domination arguments. The sampled-data implementation is based on a multi-rate control solution, whose existence is guaranteed for the class of systems considered. The digital controller guarantees, under sampling, the properties of manifold attractivity and trajectory boundedness. The control law, computed by finite approximation of a series expansion, is finally validated through numerical simulations in two academic examples and in two case-studies, namely the cart-pendulum system and the rigid spacecraft.
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Submitted on : Tuesday, September 1, 2015 - 3:52:05 PM
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  • HAL Id : tel-01191084, version 1

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Giovanni Mattei. Robust nonlinear control : from continuous time to sampled-data with aerospace applications.. Automatic. Université Paris Sud - Paris XI, 2015. English. ⟨NNT : 2015PA112025⟩. ⟨tel-01191084⟩

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