Input-to-state stable finite horizon MPC for neutrally stable linear discrete-time systems with input constraints

Jung Su Kim, Tae Woong Yoon, Ali Jadbabaie, Claudio De Persis

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)


MPC or model predictive control is representative of control methods which are able to handle inequality constraints. Closed-loop stability can therefore be ensured only locally in the presence of constraints of this type. However, if the system is neutrally stable, and if the constraints are imposed only on the input, global asymptotic stability can be obtained; until recently, use of infinite horizons was thought to be inevitable in this case. A globally stabilizing finite-horizon MPC has lately been suggested for neutrally stable continuous-time systems using a non-quadratic terminal cost which consists of cubic as well as quadratic functions of the state. The idea originates from the so-called small gain control, where the global stability is proven using a non-quadratic Lyapunov function. The newly developed finite-horizon MPC employs the same form of Lyapunov function as the terminal cost, thereby leading to global asymptotic stability. A discrete-time version of this finite-horizon MPC is presented here. Furthermore, it is proved that the closed-loop system resulting from the proposed MPC is ISS (Input-to-State Stable), provided that the external disturbance is sufficiently small. The proposed MPC algorithm is also coded using an SQP (Sequential Quadratic Programming) algorithm, and simulation results are given to show the effectiveness of the method.

Original languageEnglish
Pages (from-to)293-303
Number of pages11
JournalSystems and Control Letters
Issue number4
Publication statusPublished - 2006 Apr


  • Global stability
  • Input constraints
  • Input-to-state stability (ISS)
  • Model predictive control (MPC)
  • Non-quadratic Lyapunov function

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science(all)
  • Mechanical Engineering
  • Electrical and Electronic Engineering


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