Disturbance Attenuation for Constrained Discrete-Time Systems via Receding Horizon Controls

Abstract

Abstract-In this note, we propose new receding horizon control (RHHC) schemes for linear input-constrained discrete time-invariant systems with disturbances. The proposed control schemes are based on the dynamic game problem of a finite-horizon cost function with a fixed finite terminal weighting matrix and a one-horizon cost function with timevarying finite terminal weighting matrices, respectively. We show that the resulting RHHCs guarantee closed-loop stability in the absence of disturbances and norm bound for 2-norm bounded disturbances. We also show that the proposed schemes can easily be implemented via linear matrix inequality optimization. We illustrate the effectiveness of the proposed schemes through simulations.

Reduced order model predictive control with disturbance attenuation

“…For a small γ > 0, this problem aims to attenuate the disturbance effect. The worst disturbance sequence w ( k ) ,…,w ( k + N − 1) maximizing J can be obtained by using the completing square 3 if γ satisfies the following condition: …”

“…A decomposition method for reducing the size of an optimization problem arising in MPC has been proposed 1,2. Taking into account the effect of a disturbance is also an important issue and an MPC with disturbance attenuation property has been considered 3.…”

Model Predictive Control for Space Teleoperation Systems Based on a Mixed-H2/H∞ Approach

“…Tadmor (1992) applied the linear-system H ∞ control theory to moving-horizon control and proposed zero-terminal-constraint H ∞ control for continuous linear time-varying systems with outside disturbances. Since Kothare et al (1996) first proposed using LMI to solve robust-constraint MPC problems, researchers have presented various moving-horizon H ∞ control schemes (Kim and Kwon 2002;Chen and Scherer 2004;Kim 2003) and MPC methods based on mixed H 2 ∕H ∞ for different systems. Orukpe et al (2007) extended the method proposed by Kothare et al (1996) to constrained linear discrete-time-invariant systems by introducing a mixed-H 2 ∕H ∞ approach that guarantees robustness.…”

One-step receding horizon control for networked control systems with random delay and packet disordering

“…Its essential feature renders the MPC approach very appropriate to incorporate the input/output constraints into the on-line optimization as well as to compensate time delays (see [11]), which increases the possibility of its application in the synthesis and analysis of NCSs [8][9][10][11]. However, in most of practical control systems, disturbances may appear and often adversely affect system performance and stability (see [17][18][19][20]). In [17], a one-horizon RHHC strategy that was proposed based on the min-max problem of a one-horizon cost function with time-varying finite terminal weighting matrices.…”

“…However, in most of practical control systems, disturbances may appear and often adversely affect system performance and stability (see [17][18][19][20]). In [17], a one-horizon RHHC strategy that was proposed based on the min-max problem of a one-horizon cost function with time-varying finite terminal weighting matrices. The RHHC strategy was studied in [18,19] for both linear continuous and discrete time-varying systems.…”