Function Approximation Technique Based Immersion and Invariance Control for Unknown Nonlinear Systems

2020 ◽  
Vol 4 (4) ◽  
pp. 934-939 ◽  
Author(s):  
Yang Bai ◽  
Yujie Wang ◽  
Mikhail Svinin ◽  
Evgeni Magid ◽  
Ruisheng Sun
Keyword(s):  
Nonlinear Systems ◽  
Function Approximation ◽  
Approximation Technique ◽  
Immersion And Invariance ◽  
Function Approximation Technique ◽  
Invariance Control

Position and Attitude Control of Underactuated Drones Using the Adaptive Function Approximation Technique

2020 ◽  
Author(s):  
Azin Shamshirgaran ◽  
Donald Ebeigbe ◽  
Dan Simon
Keyword(s):  
Disturbance Rejection ◽  
Function Approximation ◽  
Control Method ◽  
System Stability ◽  
Linear Feedback ◽  
Approximation Technique ◽  
Adaptive Function ◽  
Edge Tracking ◽  
Highly Nonlinear ◽  
Function Approximation Technique

Abstract Despite the popularity of drones and their relatively simple operation, the underlying control algorithms can be difficult to design due to the drones’ underactuation and highly nonlinear properties. This paper focuses on position and orientation control of drones to address challenges such as path and edge tracking, and disturbance rejection. The adaptive function approximation technique control method is used to control an underactuated and nonlinear drone. The controller utilizes reference attitude signals, that are derived from a proportional derivative (PD) linear feedback control methodology. To avoid analytic expressions for the reference attitude velocities, we employ a continuous-time Kalman filter based on a model of the measurement signal — which is derived by passing the reference attitude position through a low-pass signal differentiator — as a second-order Newtonian system. Stability of the closed loop system is proven using a Lyapunov function. Our design methodology simplifies the control process by requiring only a few tuning variables, while being robust to time-varying and time-invariant uncertainties with unknown variation bounds, and avoids the requirement for the knowledge of the dynamic equation that governs the attitude of the drone. Three different scenarios are simulated and our control method shows better accuracy than the proportional-derivative controller in terms of edge tracking and disturbance rejection.

Adaptive Multiple-surface Sliding Control of Hydraulic Active Suspension Systems Based on the Function Approximation Technique

2005 ◽  
Vol 11 (5) ◽  
pp. 685-706 ◽  
Author(s):  
P. C. Chen ◽  
A. C. Huang
Keyword(s):  
Function Approximation ◽  
Ride Quality ◽  
Approximation Technique ◽  
Hydraulic Actuator ◽  
Tracking Errors ◽  
Suspension Systems ◽  
Car Suspension ◽  
Mismatched Uncertainties ◽  
Adaptive Laws ◽  
Function Approximation Technique

In this paper we propose an adaptive multiple-surface sliding controller (AMSSC) to control a non-autonomous quarter-car suspension system with hydraulic actuator. Due to the spring nonlinearities, the system property becomes asymmetric under the system’s own weight. Besides, because precise parameters of practical systems are hard to obtain, the system uncertainties should be dealt with. In this paper, these uncertainties are assumed to be lumped into three unknown functions such that the system model has both matched and mismatched uncertainties. Because the bounds of some of time-varying uncertainties are unavailable, traditional adaptive schemes or robust strategies are infeasible. To deal with this problem, a function approximation based adaptive multiple-surface sliding controller (AMSSC) is proposed in this paper. The multiple-surface sliding controller (MSSC) is used to cope with mismatched uncertainties while the function approximation technique is used to represent those uncertainties as finite combinations of basis functions. Adaptive laws for the approximating series can thus be derived based on the Lyapunov-like approach to ensure the closed-loop stability. Convergent performance of tracking errors can be obtained to improve the ride quality. Because the state measurements of the unsprung mass are lumped into the uncertainties, there is no need to feed back these signals with the proposed method. Therefore, the hardware structure can be simplified in the actual implementation. Computer simulations are performed to verify the effectiveness of the proposed strategy.

Forwarding-based immersion and invariance control for $$\varvec{n}$$ n -dimensional strict-feedback nonlinear systems

2015 ◽  
Vol 83 (1-2) ◽  
pp. 483-496 ◽  
Author(s):  
Xu Zhang ◽  
Xianlin Huang ◽  
Hongqian Lu ◽  
Hongyang Zhang
Keyword(s):  
Nonlinear Systems ◽  
Immersion And Invariance ◽  
Invariance Control ◽  
Strict Feedback

A fuzzy-based function approximation technique for reinforcement learning1

2017 ◽  
Vol 32 (6) ◽  
pp. 3909-3920 ◽  
Author(s):  
Cheng Wu ◽  
Huichun Song ◽  
Changsheng Yan ◽  
Yiming Wang
Keyword(s):  
Function Approximation ◽  
Approximation Technique ◽  
Function Approximation Technique
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