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Control of constrained systems: closed-loop, open-loop, and hybrid solutions

Abstract : The presence of constraints in a dynamical system makes its feedback control challenging. Most notably, input constraints usually prevent the inversion of the system dynamics. This thesis is concerned with the design of control laws that steer to the origin the state of two classes of constrained dynamical systems (namely nonlinear systems in feedforward form and linear systems with amplitude and/or rate limited input). The considered constraints impose a gain limitation at the inputs, so that the classical approach to stabilize such systems is to use so-called low-gain designs. Those have the advantage of producing large regions of attraction but have the drawbacks of resulting in feedback systems presenting poor performance and a lack of important robustness properties. The contribution of this thesis is mainly to present new control designs to alleviate these drawbacks. The first contribution consists in the introduction of a new control law for the stabilization of the origin of feedforward systems, which is robust to the presence of some destabilizing feedback terms. The other contributions concern the control of linear systems with bounded input. The first one includes online optimization of some of the control parameters, which is known to be a key factor to improve the performance of static feedback solutions. At the same time, the online optimization is selected in such a way that the numerical cost of the control algorithm is not prohibitive and that stability of the closed-loop system can be proven. The last contribution of the thesis is the proof of convergence of an algorithm that computes the switching times of time-optimal control for linear systems with bounded input. The low numerical cost of this algorithm makes it an attractive solution for the model predictive control of input constrained linear systems.
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https://hal.inria.fr/tel-01091828
Contributor : Frédéric Grognard <>
Submitted on : Thursday, December 11, 2014 - 3:56:45 PM
Last modification on : Tuesday, March 22, 2016 - 1:25:08 AM
Long-term archiving on: : Thursday, March 12, 2015 - 10:06:22 AM

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  • HAL Id : tel-01091828, version 1

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Frédéric Grognard. Control of constrained systems: closed-loop, open-loop, and hybrid solutions. Optimization and Control [math.OC]. UCL Belgique, 2001. English. ⟨tel-01091828⟩

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