Discrete-Time Inverse Optimal Control for Nonlinear Systems

Edgar N. Sanchez, Fernando Ornelas-Tellez

April 8, 2013 by CRC Press
Reference - 268 Pages - 10 Color & 70 B/W Illustrations
ISBN 9781466580879 - CAT# K18856
Series: System of Systems Engineering


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  • Proposes optimal and efficient discrete-time controllers, which minimize a performance index for nonlinear systems, to achieve stabilization and trajectory tracking
  • Provides robust inverse optimal control techniques based on artificial neural networks for uncertain nonlinear systems
  • Explains how proposed controllers can be directly implemented in real-time systems using current technology
  • Examines how the control scheme can be applied to glycemic control in type-1 diabetes mellitus patients
  • Includes 70 figures and an eight-page color insert


Discrete-Time Inverse Optimal Control for Nonlinear Systems proposes a novel inverse optimal control scheme for stabilization and trajectory tracking of discrete-time nonlinear systems. This avoids the need to solve the associated Hamilton-Jacobi-Bellman equation and minimizes a cost functional, resulting in a more efficient controller.

Design More Efficient Controllers for Stabilization and Trajectory Tracking of Discrete-Time Nonlinear Systems

The book presents two approaches for controller synthesis: the first based on passivity theory and the second on a control Lyapunov function (CLF). The synthesized discrete-time optimal controller can be directly implemented in real-time systems. The book also proposes the use of recurrent neural networks to model discrete-time nonlinear systems. Combined with the inverse optimal control approach, such models constitute a powerful tool to deal with uncertainties such as unmodeled dynamics and disturbances.

Learn from Simulations and an In-Depth Case Study

The authors include a variety of simulations to illustrate the effectiveness of the synthesized controllers for stabilization and trajectory tracking of discrete-time nonlinear systems. An in-depth case study applies the control schemes to glycemic control in patients with type 1 diabetes mellitus, to calculate the adequate insulin delivery rate required to prevent hyperglycemia and hypoglycemia levels.

The discrete-time optimal and robust control techniques proposed can be used in a range of industrial applications, from aerospace and energy to biomedical and electromechanical systems. Highlighting optimal and efficient control algorithms, this is a valuable resource for researchers, engineers, and students working in nonlinear system control.

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