Direct heuristic dynamic programming based on an improved PID neural network

Jian Sun, Feng Liu, Jennie Si, Shengwei Mei

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


In this paper, an improved PID-neural network (IPIDNN) structure is proposed and applied to the critic and action networks of direct heuristic dynamic programming (DHDP). As one of online learning algorithm of approximate dynamic programming (ADP), DHDP has demonstrated its applicability to large state and control problems. Theoretically, the DHDP algorithm requires access to full state feedback in order to obtain solutions to the Bellman optimality equation. Unfortunately, it is not always possible to access all the states in a real system. This paper proposes a solution by suggesting an IPIDNN configuration to construct the critic and action networks to achieve an output feedback control. Since this structure can estimate the integrals and derivatives of measurable outputs, more system states are utilized and thus better control performance are expected. Compared with traditional PIDNN, this configuration is flexible and easy to expand. Based on this structure, a gradient decent algorithm for this IPIDNN-based DHDP is presented. Convergence issues are addressed within a single learning time step and for the entire learning process. Some important insights are provided to guide the implementation of the algorithm. The proposed learning controller has been applied to a cart-pole system to validate the effectiveness of the structure and the algorithm.

Original languageEnglish (US)
Pages (from-to)497-503
Number of pages7
JournalJournal of Control Theory and Applications
Issue number4
StatePublished - Nov 2012


  • Approximate dynamic programming (ADP)
  • Direct heuristic dynamic programming (DHDP)
  • Improved PID neural network (IPIDNN)

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Hardware and Architecture
  • Computer Science Applications


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