Abstract Quadratic Programming (QP) has been used to combine Control Lyapunov and Control Barrier Functions (CLF and CBF) to design controllers for nonlinear systems with constraints. It has been successfully applied to robotic and automotive systems. The approach could be considered an extension of the CLF-based point-wise minimum norm controller. In this paper we modify the original QP problem in a way that guarantees that V 0 , if the barrier constraint is inactive, as well as local asymptotic stability under the standard (minimal) assumptions on the CLF and CBF. We also remove the assumption that the CBF has uniform relative degree one. The two design parameters of the new QP setup allow us to control how aggressive the resulting control law is when trying to satisfy the two control objectives. The paper presents the controller in a closed form making it unnecessary to solve the QP problem on line and facilitating the analysis. Next, we introduce the concept of Robust-CBF that, when combined with existing ISS-CLFs, produces controllers for constrained nonlinear systems with disturbances. In an example, a nonlinear system is used to illustrate the ease with which the proposed design method handles non-convex constraints and disturbances and to illuminate some tradeoffs.
[1]
Eduardo Sontag.
A universal construction of Artstein's theorem on nonlinear stabilization
,
1989
.
[2]
Stephen P. Boyd,et al.
Convex Optimization
,
2004,
Algorithms and Theory of Computation Handbook.
[3]
Randy A. Freeman,et al.
Robust Nonlinear Control Design
,
1996
.
[4]
Eduardo Sontag.
Smooth stabilization implies coprime factorization
,
1989,
IEEE Transactions on Automatic Control.
[5]
Miroslav Krstic,et al.
Stabilization of Nonlinear Uncertain Systems
,
1998
.
[6]
Z. Artstein.
Stabilization with relaxed controls
,
1983
.
[7]
W. Hager.
Lipschitz Continuity for Constrained Processes
,
1979
.
[8]
Paulo Tabuada,et al.
Control Barrier Function Based Quadratic Programs for Safety Critical Systems
,
2016,
IEEE Transactions on Automatic Control.
[9]
Mrdjan J. Jankovic,et al.
Constructive Nonlinear Control
,
2011
.