Abstract
A control Lyapunov function (CLF)-based optimal control method is proposed to solve an affine nonlinear system with input limitation for the wheeled robot. Motivated by Lyapunov stability theory, viability theory, and exact linearization and sliding mode control, the construction of the CLF uses the information of the multi-order derivatives of the system outputs. The result shows the stability depends on the controller coefficients and the input limitation. Thus, the sufficient conditions are given and proved for stable controller design. The proposed control method provides a new robust regulation map to an affine nonlinear system for high-dimensional trajectory tracking. A simulation of multi-agent wheeled robot formation is designed to illustrate the application of the proposed controller. Meanwhile, the validation and feasibility of the controller are also verified by the simulation.
Highlights
Affine nonlinear is a common character in mobile robot systems, such as differential wheeled mobile robots
In this paper, we proposed a new robot tracking optimal controller based on control Lyapunov function (CLF) cost function
Compared with traditional CLF method, our method use the technology of viability, such as the set value analysis method, to guarantee the stability with the limitation of the input
Summary
Affine nonlinear is a common character in mobile robot systems, such as differential wheeled mobile robots. Exact linearization aims to find a coordinate transformation of the control input via the Lie derivative [2] of the system output [3] This method can transfer the original nonlinear system into a new linear system without any errors. With a linear control input constraint, this study can transform a control problem into a linear programming problem, instead of a common quadratic or other nonlinear functions This will benefit online application, because our optimization problem can be solved in real time. The contribution of this work is we design a new control method for affine nonlinear systems as an optimization problem by treating the CLF function as the cost function rather than constraints. The notations of the paper is listed as Table 1
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