H ∞ optimal preview tracking control problem with disturbance attenuation

This paper investigates the problem of path following control for an autonomous vehicle subject to the localization errors and the tire slip effects. First, by analyzing the effects of localization errors, a loss‐of‐effectiveness actuator model is formulated, and a new chain form model is constructed for path following system of the vehicle. Then, the polytopic model is proposed to characterize the nonlinearity of the system, and an observer‐based path following controller is designed by satisfying both the H∞$$ {H}_{\infty } $$ criterion and L1$$ {L}_1 $$ criterion. Finally, the path following controller design problem is converted into an optimization problem, which can be solved readily through convex optimization techniques. The effectiveness of the proposed control strategy is verified by simulation results.

“…Based on Theorem 1 and Corollary 1, the following theorem guarantees that the closed-loop system (33) is asymptotically stable and satisfies performances (34), (35), and (36).…”

Section: Observer-based Robust Mixed L1/h∞ Control Synthesismentioning

confidence: 99%

“…Proof. According to [33,34], closed-loop system (19) is asymptotically stable and satisfies H ∞ performance (21) if there exist 𝛾 1 > 0 and P > 0 satisfying the following condition:…”

Section: Robust H∞ Control Analysis Under Localization Errorsmentioning

confidence: 99%

Section: Observer-based Robust Mixed L1/h∞ Control Synthesismentioning

confidence: 99%

“…Proof According to [33, 34], closed‐loop system () is asymptotically stable and satisfies

{H}_{\infty }

performance () if there exist

{\gamma}_1&gt;0

and

P&gt;0

satisfying the following condition:

\left[\begin{array}{ccc}{\bar{A}}&#x0005E;TP&#x0002B;P\bar{A}&amp; P{\overline{B}}_1&amp; {\overline{C}}_1&#x0005E;T\\ {}\ast &amp; -{\gamma}_1I&amp; {\overline{D}}_1&#x0005E;T\\ {}\ast &amp; \ast &amp; -{\gamma}_1I\end{array}\right]&lt;0.

For a given matrix

P&#x0003D;\mathit{\operatorname{diag}}\left\{{P}_1,{P}_2\right\}

, substituting () into inequality () gives

([], \begin{matrix} center center center center center \\ array S_{1} & array S_{3} & array P_{1} B & array 0 & array 0 \\ array * & array S_{2} & array - P_{2} B & array - P_{2} L D_{1} & array C_{1}^{T} \\ array * \end{matrix})

…”

Section: Robust H∞$$ {H}_{\infty } $$ Control Analysis Under Localiz...mentioning

confidence: 99%

See 2 more Smart Citations

Observer‐based path following control for autonomous vehicles with localization errors and tire slip effects

Wang

Zhang

Quan

et al. 2022

“…Yu et al revisited the observer‐based robust preview tracking control problem for discrete‐time Lipschitz nonlinear systems and analyzed the robustness of the system to external disturbances by means of the

{H}_{\infty }

performance criterion [23]. Liu et al [24] combined optimal PC with

{H}_{\infty }

control to solve the disturbance attenuation problem in a zero‐sum game framework. In recent research progress, a novel method was proposed to track a previewable reference signal in the polytopic time‐varying system with input saturation [25].…”

Section: Introductionmentioning

confidence: 99%

Estimation and rejection of periodic disturbance in a preview repetitive control system

Lan,

Liu

2023

This paper deals with the problem of two‐dimensional (2D) system‐based preview repetitive control (PRC) with external periodic disturbance for a class of continuous‐time linear systems. First, a repetitive learning‐based estimator (RLE) is incorporated into the controller block to compensate for the periodic disturbance. Next, the PRC law with repetitive learning compensation disturbance is obtained by combining the observer and RLE. Then, we combine the 2D system theory with the linear matrix inequality (LMI) method to derive sufficient conditions to ensure the robustness and stability of the closed‐loop system. Finally, numerical simulations verify the superiority of the proposed method.

Yawing stability and manipulative approach design for maglev car based on active disturbance rejection control

Zhang,

Ke,

et al. 2023

In the present work, to realize the stable static suspension of a new type of electrodynamic wheel (EDW) magnetic levitation (maglev) car without track constraints on the conductor plate. Design and analysis of the active disturbance rejection control and explicit complementary filter (ADRC‐ECF) have been presented to solve the maglev car's yaw angle disturbance rejection under low lateral damping characteristics. Simple and efficient ECF helps to filter the high and low frequency noise generated by EDWs when rotating at high speed, to obtain accurate data in real‐time. Design and build the hardware control system for maglev car, and conduct experimental comparisons with PID controller to verify the effectiveness of suppressing yaw angle disturbances. Based on simulation and experimental results, it is shown that both PID and ADRC‐ECF can improve the stable yaw angle convergence of maglev car under external disturbances. However, ADRC performs better in resisting disturbances than PID and can achieve more accurate fixed angle steering. This paper is the first attempt to control maglev car on a trackless conductor plate for precise steering and anti‐disturbance, which is anticipated to have some reference significance in this field.