This paper proposes a robust feedback controller using Linear Matrix Inequalities (LMIs) formulation for the stabilization of an underactuated mechanical system, namely the Inertia Wheel Inverted Pendulum (IWIP), in its upright position. Such mechatronic system is subject to state constraints, external disturbances and norm-bounded parametric uncertainties. The main idea to solve the stabilization problem lies in the use of the S-procedure Lemma. Such problem is then transformed into a solving problem of Bilinear Matrix Inequalities (BMIs). Through the Schur complement Lemma and the Matrix Inversion Lemma, a linearization procedure is employed to transform the BMIs into LMIs. Some improvements and comparisons with other LMI-based design techniques without state constraints are developed and discussed. An extensive portfolio of numerical studies is presented. The effectiveness and robustness of the proposed feedback controller toward uncertainties in the friction parameters and external disturbances are illustrated through simulation results.

Robust feedback control of the underactuated Inertia Wheel Inverted Pendulum under parametric uncertainties and subject to external disturbances: LMI formulation

Summary
This paper proposes an integrated fault estimation and fault-tolerant control (FTC) design for Lipschitz non-linear systems subject to uncertainty, disturbance, and actuator/sensor faults. A non-linear unknown input observer without rank requirement is developed to estimate the system state and fault simultaneously, and based on these estimates an adaptive sliding mode FTC system is constructed. The observer and controller gains are obtained together via H∞ optimization with a single-step linear matrix inequality (LMI) formulation so as to achieve overall optimal FTC system design. A single-link manipulator example is given to illustrate the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.

Integrated fault estimation and fault-tolerant control for uncertain Lipschitz nonlinear systems

This paper presents an observer-based controller design for the class of nonlinear systems with time-varying parametric uncertainties and norm-bounded disturbances. The design methodology, for the less conservative one-sided Lipschitz nonlinear systems, involves astute utilization of Young’s inequality and several matrix decompositions. A sufficient condition for simultaneous extraction of observer and controller gains is stipulated by a numerically tractable set of convex optimization conditions. The constraints are handled by a nonlinear iterative cone-complementary linearization method in obtaining gain matrices. Further, an observer-based control technique for one-sided Lipschitz nonlinear systems, robust against L2-norm-bounded perturbations, is contrived. The proposed methodology ensures robustness against parametric uncertainties and external perturbations. Simulation examples demonstrating the effectiveness of the proposed methodologies are presented.

Observer-based robust control of one-sided Lipschitz nonlinear systems

This paper considers the problem of controlling the position and the orientation of a Coaxial-Rotor Unmanned Aerial Vehicle -CRUAV- despite unknown aerodynamic efforts. A hierarchical flight controller is designed, allowing the trajectory tracking and the stabilization of the vehicle. The designed controller is build through a hierarchical approach yielding two control loops, an inner one to control the attitude and an outer one to control the translational trajectory of the rotorcraft. An Extended State Observer -ESO- is used to estimate the state and the unknown aerodynamic disturbances. The analysis further extends to the design of a control law that takes the disturbance estimation procedure into account. Numerical simulations are carried out to demonstrate the efficiency of the proposed control strategy.

Extended State Observer based control for coaxial-rotor UAV.

This paper presents a new observer-based controller design method for Lipschitz nonlinear systems with uncertain parameters and math formula-bounded disturbance inputs. In the presence of uncertain parameters, the separation principle is not applicable even in the case of linear time invariant systems. A state of the art review for uncertain linear systems is first presented to describe the shortcomings and conservatism of existing results for this problem. Then a new LMI-based design technique is developed to solve the problem for both linear and Lipschitz nonlinear systems. The features of the new technique are the use of a new matrix decomposition, the allowance of additional degrees of freedom in design of the observer and controller feedback gains, the elimination of any need to use equality constraints, the allowance of uncertainty in the input matrix and the encompassing of all previous results under one framework. An extensive portfolio of numerical case studies is presented to illustrate the superiority of the developed design technique to existing results for linear systems from literature and to illustrate application to Lipschitz nonlinear systems.

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Robust observer-based stabilization of Lipschitz nonlinear uncertain systems via LMIs - discussions and new design procedure

Summary

This paper deals with the robust observer-based control design for a class of Lipschitz nonlinear discrete-time systems with parameter uncertainties Based on the use of a reformulated Lipschitz property combined with the slack variable techniques and some mathematical artifacts, it is shown that the solution of the discrete-time output feedback stabilization problem is conditioned by a set of bilinear matrix inequalities, which become linear matrix inequalities by freezing some scalars Furthermore, we show that some existing and elegant results reported in the literature can be regarded as particular cases of the stability conditions presented here Numerical examples are provided to show the validity and superiority of the proposed method Copyright © 2015 John Wiley & Sons, Ltd

A robust ℋ∞ observer‐based stabilization method for systems with uncertain parameters and Lipschitz nonlinearities

In this paper a new finite-time convergent functional dynamical observer design for descriptor systems is presented. The conditions for its existence and stability are given. This observer is then applied to the sensor and actuator faults detection and estimation. This estimation is used in the observer-based fault tolerant control design. All the obtained results are illustrated by numerical examples.

Finite time functional observers for descriptor systems. Application to fault tolerant control

This note focuses on the design of an observer-based controller for a class of Lipschitz nonlinear discrete-time systems with parameter uncertainties. Thanks to the reformulated Lipschitz property [1] that take into account all the properties of the nonlinearities of the system combined with some mathematical tools, it is shown that the solution of the discrete-time output feedback problem, expressed in term of Linear Matrix Inequality (LMI), is conditioned by a set of simple convex optimization conditions that are numerically tractable and free from any equality constraint. This latter leads to a less restrictive synthesis condition than those available in the literature. A numerical example is provided in order to show the validity and superiority of the proposed method.

Robust ℋ ∞ observer-based controller for lipschitz nonlinear discrete-time systems with parameter uncertainties

This paper deals with the problem H ∞ of observer-based stabilization via LMI for nonlinear systems with Lipschitz nonlinearities. Thanks a new variant of the Young's inequality and a reformulation of the Lipschitz property, a new and less conservative LMI condition is proposed. This later contains more degrees of freedom and some existing results in the literature can be viewed as particular cases.

H ∞ observer-based stabilization for Lipschitz nonlinear systems

In this paper, the design process of two robust H∞ control architectures for a Gun Launched Micro Aerial Vehicle - GLMAV - is presented. The process starts with the developement of a nonlinear dynamic model reflecting the important elements of the GLMAV. This model is then linearized around hover and used for the design of static output feedback H∞ controllers for position and orientation control. Unlike the full-order H∞ controller synthesis case, the H∞ optimization problem of static output feedback (SOF) controllers cannot be parameterized as a convex optimization problem. The cone complementarity linearization algorithm is therefore used to overcome the nonconvexity problem due to the constraint on the controller order. Finally, numerical simulations show the efficiency of the designed controllers.

http://ieeexplore.ieee.org/iel7/6589043/6608682/06608719.pdf

Harouna Souley-Ali

Papers

A robust ℋ∞ observer‐based stabilization method for systems with uncertain parameters and Lipschitz nonlinearities

Finite time functional observers for descriptor systems. Application to fault tolerant control

Robust ℋ ∞ observer-based controller for lipschitz nonlinear discrete-time systems with parameter uncertainties

H ∞ observer-based stabilization for Lipschitz nonlinear systems

Two robust static output feedback H ∞ control architectures for a Gun Launched Micro Aerial Vehicle