Doctoral Dissertations

Keywords and Phrases

Adaptive Critics; Approximate Dynamic Programming; Finite Horizon Control; Fixed-Final-Time Optimal Control; Neural Networks; Optimal Switching


"Optimal solutions with neural networks (NN) based on an approximate dynamic programming (ADP) framework for new classes of engineering and non-engineering problems and associated difficulties and challenges are investigated in this dissertation. In the enclosed eight papers, the ADP framework is utilized for solving fixed-final-time problems (also called terminal control problems) and problems with switching nature. An ADP based algorithm is proposed in Paper 1 for solving fixed-final-time problems with soft terminal constraint, in which, a single neural network with a single set of weights is utilized. Paper 2 investigates fixed-final-time problems with hard terminal constraints. The optimality analysis of the ADP based algorithm for fixed-final-time problems is the subject of Paper 3, in which, it is shown that the proposed algorithm leads to the global optimal solution providing certain conditions hold. Afterwards, the developments in Papers 1 to 3 are used to tackle a more challenging class of problems, namely, optimal control of switching systems. This class of problems is divided into problems with fixed mode sequence (Papers 4 and 5) and problems with free mode sequence (Papers 6 and 7). Each of these two classes is further divided into problems with autonomous subsystems (Papers 4 and 6) and problems with controlled subsystems (Papers 5 and 7). Different ADP-based algorithms are developed and proofs of convergence of the proposed iterative algorithms are presented. Moreover, an extension to the developments is provided for online learning of the optimal switching solution for problems with modeling uncertainty in Paper 8. Each of the theoretical developments is numerically analyzed using different real-world or benchmark problems"--Abstract, page v.


Balakrishnan, S. N.

Committee Member(s)

Sarangapani, Jagannathan, 1965-
Landers, Robert G.
Bristow, Douglas A.
Madria, Sanjay Kumar


Mechanical and Aerospace Engineering

Degree Name

Ph. D. in Mechanical Engineering


National Science Foundation (U.S.)


Missouri University of Science and Technology

Publication Date


Journal article titles appearing in thesis/dissertation

  • Finite-Horizon Control-Constrained Nonlinear Optimal Control Using Single Network Adaptive Critics
  • Fixed-final-time Optimal Control of Nonlinear Systems with Terminal Constraints
  • Global Optimality of Approximate Dynamic Programming and its use in Non-convex Function Minimization
  • Optimal Multi-therapeutic HIV Treatment Using a Global Optimal Switching Scheme
  • Optimal Switching and Control of Nonlinear Switched Systems Using Approximate Dynamic Programming
  • Optimal Switching between Autonomous Subsystems
  • Optimal Switching between Controlled Subsystems with Free Mode Sequence
  • Optimal Switching of Nonlinear Systems with Modeling Uncertainty


vii, 239 pages

Note about bibliography

Includes bibliographic references.


© 2013 Ali Heydari, All rights reserved.

Document Type

Dissertation - Open Access

File Type




Library of Congress Subject Headings

Neural networks (Computer science) -- Design
Dynamic programming
Mathematical optimization
Optimal stopping (Mathematical statistics)
Automatic programming (Computer science)
Stochastic control theory

Thesis Number

T 10854

Electronic OCLC #