A new approach to stability analysis for constrained finite receding horizon control without end constraints

Abstract

We present a new approach to the stability analysis of nite receding horizon control applied to constrained linear systems. By relating the nal predicted state to the current state through a bound on the terminal cost, it is shown that knowledge of upper and lower bounds for the nite horizon costs are su cient to determine the stability of a receding horizon controller. This analysis is valid for receding horizon schemes with arbitrary positive-de nite terminal weights, and does not rely on the use of stabilizing constraints. The result is a computable test for stability, and two simple examples are used to illustrate its application.

On-Line Trajectory Planning for Aerial Vehicles: A Safe Approach with Guaranteed Task Completion

“…Finally, the occasionally occurring case when the optimization routine used in a vehicle fails to satisfy the hard equality constraint (11) may result in a deviating η d . This latter case may occur even though η d has passed the outlier detection rule (12) and has been observed in the simulations, as can be seen in Figure 10. The simulations indicate that, in most cases, the trajectory planner manages to fulfill the will of the consensus planner in one single time step.…”

“…In the literature (see e.g. [11]), several approaches to ensure stability of RHC/MPC schemes can be found, one of the most appealing approaches being that of utilizing a constrained control Lyapunov function (CLF) as terminal cost [12,13]. As a matter of fact, it has been shown in [14], that OCP, RHC as well as the set of CLF-based continuous control designs (such as Sontag's universal formula [15], Freeman and Kokotović's min-norm formula [16], but also the satisficing control methods [9,10]) can be viewed in a unified manner; namely that OCP and CLF-based methods are the two limiting cases of RHC when the planning horizon goes to infinity and zero respectively (see Figure 1).…”

Analysis and Design of Softly Switched Model Predictive Control

“…A common approach to stability analysis for receding horizon control is to consider the optimal value of ( ( ), ( | )) N J x k u k ⋅ as a candidate Lyapunov function (Primbs and Nevistic, 2000). That is,…”

“…A real life application can be found in (Grochowski, et al, 2004b). Although the issues of stability of constrained model predictive control for linear time-invariant (LTI) systems have been deeply investigated (Zheng and Morari, 1995;Mayne, et al, 2000;Primbs and Nevistic, 2000), the research on the stability of switching among multiple constrained predictive controllers is still an open area which incorporates fundamental problems both in the MPC area and in the switched system field (Grochowski, 2003). In (Zheng, 1997), the issue of time-varying weights in model predictive control has been discussed, but it was limited to varying weights only inside the prediction horizon and the weights between each new iterate time step remain the same.…”

A Model Predictive Control scheme with additional performance index for transient behavior

“…From the class of quasi-infinite horizon schemes, where both terminal cost and a terminal set are employed, we refer to [3], [7] and [12] (where the terminal constraint is implicitly satisfied). In [16], [9], [11] the terminal set is dropped. In that case, for these unconstrained MPC schemes, the emphasis is on the computation of a "sufficiently long" horizon length that ensures stability.…”