Online policy iterations for optimal control of input-saturated systems

Simone Baldi, Giorgio Valmorbida, Antonis Papachristodoulou, Elias B. Kosmatopoulos

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

1 Citation (Scopus)
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This work proposes an online policy iteration procedure for the synthesis of sub-optimal control laws for uncertain Linear Time Invariant (LTI) Asymptotically Null-Controllable with Bounded Inputs (ANCBI) systems. The proposed policy iteration method relies on: a policy evaluation step with a piecewise quadratic Lyapunov function in both the state and the deadzone functions of the input signals; a policy improvement step which guarantees at the same time close to optimality (exploitation) and persistence of excitation (exploration). The proposed approach guarantees convergence of the trajectory to a neighborhood around the origin. Besides, the trajectories can be made arbitrarily close to the optimal one provided that the rate at which the the value function and the control policy are updated is fast enough. The solution to the inequalities required to hold at each policy evaluation step can be efficiently implemented with semidefinite programming (SDP) solvers. A numerical example illustrates the results.

Original languageEnglish
Title of host publicationProceedings of the 2016 American Control Conference (ACC 2016)
EditorsGeorge Chiu, Katie Johnson, Danny Abramovitch
Place of PublicationPiscataway, NJ, USA
ISBN (Electronic)978-1-4673-8682-1
Publication statusPublished - 2016
EventAmerican Control Conference (ACC), 2016 - Boston, MA, United States
Duration: 6 Jul 20168 Jul 2016


ConferenceAmerican Control Conference (ACC), 2016
Abbreviated titleACC 2016
CountryUnited States
CityBoston, MA

Bibliographical note

Accepted Author Manuscript


  • Optimal control
  • Linear systems
  • Convergence
  • Asymptotic stability
  • Lyapunov methods
  • Estimation
  • Trajectory


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