Modified Infinite-Time State-Dependent Riccati Equation Method for Nonlinear Affine Systems: Quadrotor Control

Stępień, S.; Superczyńska, Paulina

doi:10.3390/app112210714

Cited by 9 publications

(3 citation statements)

References 33 publications

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“…Note that the use of an online gain scheduling [30] or solutions on the basis of statedependent Riccati equations could be used to enhance the reliability of this approach [31]; however, it comes with the price of a significantly higher implementation and computational effort than the proposed methodology presented in the previous section.…”

Section: Extended Kalman Filter-based Linear Quadratic Regulator Designmentioning

confidence: 99%

Combined Observer-Based State Feedback and Optimized P/PI Control for a Robust Operation of Quadrotors

Benzinane,

Rauh

2024

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This paper deals with a discrete-time observer-based state feedback control design by taking into consideration bounded parameter uncertainty, actuator faults, and stochastic noise in an inner control loop which is extended in a cascaded manner by outer PI- and P-control loops for velocity and position regulation. The aim of the corresponding subdivision of the quadrotor model is the treatment of the control design in a systematic manner. In the inner loop, linear matrix inequality techniques are employed for the placement of poles into a desired area within the complex z-plane. A robustification of the design towards noise is achieved by optimizing both control and observer gains simultaneously guaranteeing stability in a predefined bounded state domain. This procedure helps to reduce the sensitivity of the inner control loop towards changes induced by the outer one. Finally, a model-based optimization process is employed to tune the parameters of the outer P/PI controllers. To allow for the validation of accurate trajectory tracking, a comparison of the novel approach with the use of a standard extended Kalman filter-based linear-quadratic regulator synthesis is presented to demonstrate the superiority of the new design.

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Section: Extended Kalman Filter-based Linear Quadratic Regulator Designmentioning

confidence: 99%

Combined Observer-Based State Feedback and Optimized P/PI Control for a Robust Operation of Quadrotors

Benzinane,

Rauh

2024

Axioms

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“…Our approach uses the dynamic model derived from [55,56], which consists of the following equation system:…”

Section: Application To Quadrotor Controlmentioning

confidence: 99%

Hermitian Solutions of the Quaternion Algebraic Riccati Equations through Zeroing Neural Networks with Application to Quadrotor Control

Jerbi,

Alshammari,

Aoun

et al. 2023

Mathematics

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The stability of nonlinear systems in the control domain has been extensively studied using different versions of the algebraic Riccati equation (ARE). This leads to the focus of this work: the search for the time-varying quaternion ARE (TQARE) Hermitian solution. The zeroing neural network (ZNN) method, which has shown significant success at solving time-varying problems, is used to do this. We present a novel ZNN model called ’ZQ-ARE’ that effectively solves the TQARE by finding only Hermitian solutions. The model works quite effectively, as demonstrated by one application to quadrotor control and three simulation tests. Specifically, in three simulation tests, the ZQ-ARE model finds the TQARE Hermitian solution under various initial conditions, and we also demonstrate that the convergence rate of the solution can be adjusted. Furthermore, we show that adapting the ZQ-ARE solution to the state-dependent Riccati equation (SDRE) technique stabilizes a quadrotor’s flight control system faster than the traditional differential-algebraic Riccati equation solution.

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“…In some cases LQR approach is used as a tuning method for strictly nonlinear controllers, see for instance [10]. Modifications of LQR for nonlinear systems have been considered, such as the state-dependent Riccati equation (SDRE) approach [11] and its various implementations [12][13][14]. In addition, techniques inspired by differential dynamic programming [15,16] lead to iterative LQR (iLQR) [17,18], for which the dynamics are linearized in a sequence and the cost function about a given nominal trajectory is computed to find an LQR control policy.…”

Section: Introductionmentioning

confidence: 99%

Sub-Optimal Stabilizers of the Pendubot Using Various State Space Representations

et al. 2022

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This paper considers the issue of linear-quadratic regulator (LQR) design for nonlinear systems with the use of smooth state and input transformations. The proposed design methodology is considered in the stabilisation task of the Pendubot, which is based on the concept of feedback equivalent control systems. It turns out that it is possible to find a controller that ensures comparable dynamics of the closed-loop system in the vicinity of the set point regardless of the state-space representation adopted. In addition, the synthesis of suboptimal controllers according to the LQR strategy ensuring equal dynamics at the equilibrium point is presented. The properties of the studied controllers were investigated in a simulation environment and using experimental tests. The detailed forms of transformations and linear approximations given can be regarded as ready-made procedures that can be applied to stabilise similar mechanical systems in robotics.

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Modified Infinite-Time State-Dependent Riccati Equation Method for Nonlinear Affine Systems: Quadrotor Control

Cited by 9 publications

References 33 publications

Combined Observer-Based State Feedback and Optimized P/PI Control for a Robust Operation of Quadrotors

Combined Observer-Based State Feedback and Optimized P/PI Control for a Robust Operation of Quadrotors

Hermitian Solutions of the Quaternion Algebraic Riccati Equations through Zeroing Neural Networks with Application to Quadrotor Control

Sub-Optimal Stabilizers of the Pendubot Using Various State Space Representations

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