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

Abstract

Abstract-This paper presents a Model Predictive Control (MPC) scheme for nonlinear continuous time systems where an extra performance index, which is not a measure of the distance to the set point, is introduced to influence the transient behavior of the controlled system. The scheme is based on the following fact, proven in the paper: Given a stabilizing MPC controller, adding a function, integrable in the interval [t, +∞), to the stage cost does not change the asymptotic convergence property of the closed loop state trajectory. As a numerical example, this result is applied to solve a simple visual servo control problem where an MPC controller drives the state to the origin while penalizing weakly observable trajectories.

A Model predictive control scheme with ultimate bound for economic optimization

“…Moreover, by introducing the stabilizing stage cost, neither the assumption of the dissipativity of the system, e.g, [13], [11], [7], [8], [15], [5], nor constraints on the decrease of the terminal cost, [12], [23], are required. This work is on the same line of [21], [3] where stability and convergence, respectively, are further relaxed to ultimate boundedness for the sake of economic optimization.…”

“…See, e.g., the work [3], where as only difference, the effect of the bounded economic stage cost results in the additive term 2δB of (10). Note that the Lemma 1 applies for any of δ > 0, which is independent from the choice of the sampling instants T in (4).…”

Optimal Control with Limited Sensing via Empirical Gramians and Piecewise Linear Feedback

“…Note that the effect of the terminal cost on the stability of the closed loop system has been studied for linear systems as well as nonlinear systems [24]. By replacing l 1 with l 1 + l 2 in (35), we obtain the well known condition on the final cost for convergence to the origin of the finite-horizon optimal control problem; this step of our analysis has been inspired by the work of Alessandretti et al [25].…”

Augmented state feedback for improving observability of linear systems with nonlinear measurements

“…The observability-based optimal controller design presented in this work is closely related to the analysis discussed in [12] and [13] to avoid unobservable state/output trajectories. In both works, an index of observability is added to the cost functional.…”