Inverse optimal control for strict‐feedforward nonlinear systems with input delays

Cai, Xiushan; Lin, Cong; Liu, Leipo; Zhan, Xisheng

doi:10.1002/rnc.4062

Cited by 17 publications

(5 citation statements)

References 21 publications

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“…Combined with the characteristics of the quadrotor and the dynamic model of the pendulum angle of the payload, a compound control scheme is designed to suppress the swing of the payload as shown in Figure 2. In this control scheme, the pendulum angle can be measured by binocular vision detection device, and the detected value is fed back to the attitude loop feedback control channel of the quadrotor through the feedforward controller (Cai et al, 2018). Meanwhile, the position adjustment of the quadrotor suspension system is realized by position control of the outer loop.…”

Section: Modeling Of Quadrotor Suspension System and Design Of Anti-s...mentioning

confidence: 99%

Binocular visual pendulum angle detection and anti-swing control of quadrotor suspension system

Zhang

Yang

Han

et al. 2022

Transactions of the Institute of Measurement and Control

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Different from the pendulum angle detection by the optical capture system in the indoor environment, it is difficult to detect the pendulum angle of quadrotor suspension system in the outdoor environment. This paper presents a pendulum angle vision measurement scheme based on the model of the quadrotor suspension system, and applied to the quadrotor anti-swing control scheme with feedforward controller. The theoretical expression of the coordinate relationship between the pendulum angle and the spherical symbol is obtained by establishing the mathematical model of the quadrotor suspension system. The coordinates of spherical symbol fixed to the payload are detected by the visual algorithm. Simulations and experiments show that proposed method can accurately identify spherical symbol in sufficient light, and the maximum measurement error of [Formula: see text] angle is −0.024 rad and [Formula: see text] angle is −0.068 rad in the Gazebo simulation. Meanwhile, the results in MATLAB simulation indicate the anti-swing control scheme with feedforward controller can effectively restrain the payload’s swing.

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Section: Modeling Of Quadrotor Suspension System and Design Of Anti-s...mentioning

confidence: 99%

Binocular visual pendulum angle detection and anti-swing control of quadrotor suspension system

Zhang

Yang

Han

et al. 2022

Transactions of the Institute of Measurement and Control

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“…IOC is based on the fact that every control Lyapunov function (CLF) solves the HJB equation corresponding to a meaningful performance measure 16–20 . In the past two decades especially, IOC has found widespread application in diverse control problems including attitude control of satellite, speed control of motors and so forth 21–25 . The fundamental concept of IOC lies in the determination of a stabilizing state‐feedback control based on a CLF.…”

Section: Introductionmentioning

confidence: 99%

“…[16][17][18][19][20] In the past two decades especially, IOC has found widespread application in diverse control problems including attitude control of satellite, speed control of motors and so forth. [21][22][23][24][25] The fundamental concept of IOC lies in the determination of a stabilizing state-feedback control based on a CLF. Further, this CLF based IOC feedback analytically solves the HJB equation corresponding to a meaningful performance measure, which is deduced posteriori.…”

Section: Introductionmentioning

confidence: 99%

A novel domain of attraction based synthesis of inverse optimal control

Prasanna

Jacob

Nandakumar

2021

Intl J Robust & Nonlinear

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This article proposes a novel and systematic methodology for the inverse optimal control (IOC) of a class of input affine nonlinear systems. First, the system is represented in the pseudo-linear state-dependent coefficient (SDC) form so as to facilitate the use of matrix algebraic concepts in the design, while preserving the nonlinear system dynamics. Second, the IOC problem which seeks the solution to the Hamilton-Jacobi-Bellman equation is translated to a diagonal stability (D-stability) problem. Therefore, the general notion of D-stability, which deals with the characterization of a matrix A ∈ ℜ n×n for the existence of a diagonal matrix Γ ∈ ℜ n×n such that A T Γ + ΓA < 0, is redefined with respect to SDC factored matrices in this work. Consequently, the criteria for the existence (necessary condition) and determination of a diagonal solution (sufficient condition) are formulated in terms of the SDC matrices. It is shown in this work that these criteria can be readily met by the closed-loop system matrix Â(x) = A(x) − D, for any arbitrary domain S 𝛿 in state-space, by manipulating only the diagonal elements using the diagonal matrix D constituted by the IOC feedback. In short, the IOC feedback is designed such that the criteria for D-stability by the closed-loop system matrix Â(x) is fulfilled. Hence this novel design methodology is meaningfully named as "Inverse optimal control via diagonal stabilization" (IOC-D).The main advantages of IOC-D include: (i) guaranteed estimate of the domain of attraction (DOA), (ii) Immense flexibility of design, and (iii) guaranteed closed form solution which makes the design procedure analytic and computationally efficient. Numerical simulations validate the theoretical developments and the overall efficiency of the proposed approach.

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“…The method in [5] is extended to multi-input linear systems [6]. Inverse optimal control for strictfeedforward nonlinear systems with input delays also exists [11].…”

Section: Introductionmentioning

confidence: 99%