Robust Control of Relative Degree Two Systems Subject to Output Constraints with Time-Varying Bounds

In this paper robust constrained control of nonlinear systems that have relative degree two with respect to the control variable is considered. The first time derivative of the control variable is assumed to be the constrained variable. The developed control approach is based on sliding mode control design. It places sliding manifolds below the bounds of the constraints so that the constrained variable will be forced to stay in the admissible region if it approaches a bound. For the proposed control method it is analytically shown that the constrained control problem can be solved. This includes consideration of time-varying behavior of the bounds. Velocity-constrained control of a two-link robot is considered as a numerical example.