A general dissipativity constraint for feedback system design, with emphasis on MPC

Summary A “general dissipativity constraint” (GDC) is introduced to facilitate the design of stable feedback systems. A primary application is to MPC controllers when it is preferred to avoid the use of “stabilising ingredients” such as terminal constraint sets or long prediction horizons. Some very...

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Bibliographic Details
Published inInternational journal of robust and nonlinear control Vol. 29; no. 14; pp. 4775 - 4796
Main Authors Tran, Tri, Maciejowski, Jan, Ling, K‐V.
Format Journal Article
LanguageEnglish
Published Bognor Regis Wiley Subscription Services, Inc 25.09.2019
Subjects
Control stability
Control theory
Convergence
dissipativity
feedback design
Helicopters
Linear matrix inequalities
linear matrix inequality
Mathematical analysis
Matrix methods
model predictive control
quadratic dissipativity constraint
Quadratic equations
State feedback
Systems design
Terminal constraints
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Summary:Summary A “general dissipativity constraint” (GDC) is introduced to facilitate the design of stable feedback systems. A primary application is to MPC controllers when it is preferred to avoid the use of “stabilising ingredients” such as terminal constraint sets or long prediction horizons. Some very general convergence results are proved under mild conditions. The use of quadratic functions, replacing GDC by “quadratic dissipativity constraint” (QDC), is introduced to allow implementation using linear matrix inequalities. The use of QDC is illustrated for several scenarios: state feedback for a linear time‐invariant system, MPC of a linear system, MPC of an input‐affine system, and MPC with persistent disturbances. The stability that is guaranteed by GDC is weaker than Lyapunov stability, being “Lagrange stability plus convergence.” Input‐to‐state stability is obtained if the control law is continuous in the state. An example involving an open‐loop unstable helicopter illustrates the efficacy of the approach in practice.
ISSN:1049-8923
1099-1239
DOI:10.1002/rnc.4651