A predictive control scheme for systems with variable time-delay

Abstract

This article deals with the robust control design problem for linear time invariant systems affected by variable feedback delay. Constraints on the system state are considered in the system description. The starting point is the construction of a predictive control law which guarantees the existence of a nonempty robust positive invariant (RPI) set with respect to the closed-loop dynamics. Subsequently, an iterative algorithm is proposed in order to obtain an approximation of the maximal RPI set. The problem can be treated in the framework of piecewise affine systems due to the explicit formulations of the control law obtained via multiparametric programming.

Keywords:

• variable delay
• polytopic embedding
• invariant sets
• predictive control

Notes

Notes

1. For some non-negative scalars α₀, α₁, α₂, … , α _n summing to one,

2. The interested reader can consult the comparison study presented in Heemels et al. (2010) for a deeper analysis of different embedding methodologies.

3. The same notation applies for the rest of this article. The time-varying characteristic of the discrete delays are omitted for the sake of compactness, d ₁(k) = d ₁ and d ₂(k) = d ₂.

4. A common Lyapunov function for the extreme dynamics exists under the form: