×
Chen, Qiu-Xia; He, De-Feng; Yu, Li

Input-to-state stability of min-max MPC scheme for nonlinear time-varying delay systems. (English) Zbl 1286.93155

Asian J. Control 14, No. 2, 489-501 (2012).
Summary: This paper studies the robustness problem of the min-max Model Predictive Control (MPC) scheme for constrained nonlinear time-varying delay systems subject to bounded disturbances. The notion of the Input-to-State Stability (ISS) of nonlinear time-delay systems is introduced. Then, by using the Lyapunov-Krasovskii method, a delay-dependent sufficient condition is derived to guarantee Input-to-State practical Stability (ISpS) of the closed-loop system by way of NonLinear Matrix Inequalities (NLMIs). In order to lessen the online computational demand, the non-convex min-max optimization problem is then converted to a minimization problem with Linear Matrix Inequality (LMI) constraints and a suboptimal MPC algorithm is provided. Finally, an example of a truck-trailer is used to illustrate the effectiveness of the proposed results.

Cited in 10 Documents

MSC:

93D25 Input-output approaches in control theory
93B40 Computational methods in systems theory (MSC2010)
93C10 Nonlinear systems in control theory

Keywords:

model predictive control; input-to-state stability; nonlinear time-delay systems; delay-dependent criteria; linear matrix inequality
Cite Review PDF
Full Text: DOI

References:

[1] Camacho, Model Predictive Control (2004) · Zbl 1080.93001
[2] Magni, On robust tracking with non-linear model predictive control, Int. J. Control 75 (6) pp 399– (2002) · Zbl 1010.93047 · doi:10.1080/00207170110115626
[3] Limon, Robust MPC of constrained nonlinear systems based on interval arithmetic, IET Control Theory Appl. 152 (3) pp 325– (2005) · doi:10.1049/ip-cta:20040480
[4] Ulbig, Explicit nonlinear predictive control for a magnetic levitation system, Asian J. Control 12 (3) pp 434– (2010) · doi:10.1002/asjc.191
[5] Coutinho, Delay-dependent robust stability and L2-gain analysis of a catclass of nonlinear time-delay systems, Automatica 44 (8) pp 2006– (2008) · Zbl 1283.93219 · doi:10.1016/j.automatica.2008.01.003
[6] Liu, Robust H filtering for discrete nonlinear stochastic systems with time-varying delay, J. Math. Anal. Appl. 341 (1) pp 318– (2008) · Zbl 1245.93131 · doi:10.1016/j.jmaa.2007.10.019
[7] Hua, Robust controller design of a class of nonlinear time delay systems via backstepping method, Automatica 44 (2) pp 567– (2008) · Zbl 1283.93099 · doi:10.1016/j.automatica.2007.06.008
[8] Zhang, Robust stabilization of uncertain T-S fuzzy time-delay systems with exponential estimates, Fuzzy Sets Syst. 160 (12) pp 1720– (2009) · Zbl 1175.93200 · doi:10.1016/j.fss.2008.10.015
[9] Liu, Distributed model predictive control of nonlinear systems subject to asynchronous and delayed measurements, Automatica 46 (1) pp 52– (2010) · Zbl 1213.93081 · doi:10.1016/j.automatica.2009.10.033
[10] Wang , D. Q. S. H. Xu Parallel model predictive control of nonlinear time-delay systems based on recurrent neural network 677 680
[11] Su, Robust model predictive control for discrete uncertain nonlinear systems with time-delay via fuzzy model, J. Zhejiang Univ. Sci. 7 (10) pp 1723– (2006) · Zbl 1106.93037 · doi:10.1631/jzus.2006.A1723
[12] Sontag, Smooth stabilization implies coprime factorization, IEEE Trans. Autom. Control 34 (4) pp 435– (1989) · Zbl 0682.93045 · doi:10.1109/9.28018
[13] Ye, Stabilization for a class of complex interlaced systems using asymptotical gain, Asian J. Control 12 (2) pp 223– (2010) · doi:10.1002/asjc.168
[14] Limon, Input to state stability of min-max MPC controllers for nonlinear systems with bounded uncertainties, Automatica 42 (5) pp 797– (2006) · Zbl 1137.93407 · doi:10.1016/j.automatica.2006.01.001
[15] Magni, Regional input-to-state stability for nonlinear model predictive control, IEEE Trans. Autom. Control 51 (9) pp 1548– (2006) · Zbl 1366.93608 · doi:10.1109/TAC.2006.880808
[16] Lazar, On input-to-state stability of min-max nonlinear model predictive control, Syst. Control Lett. 57 (1) pp 39– (2008) · Zbl 1129.93433 · doi:10.1016/j.sysconle.2007.06.013
[17] Pepe, A lyapunov-krasovskii methodology for ISS and iISS of time-delay systems, Syst. Control Lett. 55 (12) pp 1006– (2006) · Zbl 1120.93361 · doi:10.1016/j.sysconle.2006.06.013
[18] Sherman, Adjustment of an inverse matrix corresponding to changes in the elements of a given column or a given row of the original matrix, Ann. Math. Stat. 20 (4) pp 621– (1949)
[19] He, On robustness of constrained non-linear H predictive controllers with disturbances, Int. J. Syst. Sci. 41 (2) pp 203– (2010) · Zbl 1292.93054 · doi:10.1080/00207720903045742
[20] Cao, Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi-Sugeno fuzzy models, Fuzzy Sets Syst. 124 (2) pp 213– (2001) · Zbl 1002.93051 · doi:10.1016/S0165-0114(00)00120-2
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.