title: Suboptimal control construction for the model predictive controller
metadata.name: dc.contributor.author
metadata.value: Ponomarev, Anton A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2017-07-19T11:26:36Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2017-07-19T11:26:36Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2017-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Ponomarev A. A. Suboptimal control construction for the model predictive controller. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2017, vol. 13, iss. 2, pp. 193–208.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu10.2017.206
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/6972
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Model predictive control (MPC) is a well-known and widely used control algorithm. The
  problem of real-time MPC implementation for complex systems is of particular practical interest
  due to the complexity of the associated optimization problem which is generally intractable in
  real time. The paper presented deals with this issue making use of the famous dynamical
  programming idea and reducing the dimensionality of the original optimization problem. The
  outline of the paper is as follows. The MPC problem is considered for a nonlinear discrete-time
  system with state and control constraint sets and a quadratic cost functional. The assumptions
  worth noting are, firstly, the Lipschitz continuity of the right hand side of the system and,
  secondly, continuity in some sense of the admissible control set with respect to the current
  state of the system. Employing these properties we are able to prove the Lipschitz continuity
  of the optimal cost value as a function of the initial state of the system. This result provides
  us with the opportunity to approximate the minimal value of the last several summands of the
  cost functional as a function of the intermediate system state by means of precalculating it for
  a set of state values before the controller is launched. The summands mentioned may be then
  excluded from the optimization reducing the dimensionality of the problem. The results are followed by a discussion of their limitations and an example of application. It is shown that the
  simpler the resulting problem, the less smooth it becomes, thus making it necessary to use more
  data points for the approximation. Another observation is that the smoothness of the problem
  decreasing far from the set point. The theorems proven in the paper give the reasoning behind
  these facts but the means of dealing with them are due to further research. Refs 18. Figs 2.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при финансовой поддержке Российского фонда фундаментальных исследований (грант № 16-38-00789 мол_а).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Applied Mathematics. Computer Science. Control Processes;Volume 13; Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: optimal control
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: suboptimal control
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: optimal cost value continuity
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: numerical optimization
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: approximate optimization
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: real-time control
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: model predictive control
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: MPC
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Suboptimal control construction for the model predictive controller
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 06-Ponomarev.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/6972/1/06-Ponomarev.pdf
resources.format: Adobe PDF
resources.size: 401,25 kB