Nonlinear stabilization for a class of time delay systems via inverse optimality approach

Patricio Ordaz; Omar-Jacobo Santos-Sánchez; Liliam Rodríguez-Guerrero; Alberto González-Facundo

doi:10.1016/j.isatra.2016.11.015

Nonlinear stabilization for a class of time delay systems via inverse optimality approach

ISA Trans. 2017 Mar:67:1-8. doi: 10.1016/j.isatra.2016.11.015. Epub 2016 Dec 7.

Authors

Patricio Ordaz¹, Omar-Jacobo Santos-Sánchez², Liliam Rodríguez-Guerrero³, Alberto González-Facundo⁴

Affiliations

¹ Research Center on Technology of Information and Systems (CITIS) of the Autonomous University of Hidalgo State (UAEH), Mexico.
² Research Center on Technology of Information and Systems (CITIS) of the Autonomous University of Hidalgo State (UAEH), Mexico. Electronic address: omarj@uaeh.edu.mx.
³ Automatic Control Department of the Center for Research and Advanced Studies of the National Polytechnic Institute (CINVESTAV-IPN), Mexico.
⁴ Electric and Electronic Engineering Department, Minatitlan Institute of Technology, Mexico.

PMID: 27939564
DOI: 10.1016/j.isatra.2016.11.015

Abstract

This paper is devoted to obtain a stabilizing optimal nonlinear controller based on the well known Control Lyapunov-Krasovskii Functional (CLKF) approach, aimed to solve the inverse optimality problem for a class of nonlinear time delay systems. To determine sufficient conditions for the Bellman's equation solution of the system under consideration, the CLKF and the inverse optimality approach are considered in this paper. In comparison with previous results, this scheme allows us to obtain less conservative controllers, implying energy saving (in terms of average power consumption for a specific thermo-electrical process). Sufficient delay-independent criteria in terms of CLKF is obtained such that the closed-loop nonlinear time-delay system is guaranteed to be local Asymptotically Stable. To illustrate the effectiveness of the theoretical results, a comparative study with an industrial PID controller tuned by the Ziegler-Nichols methodology (Z-N) and a Robust-PID tuned by using the D-partition method is presented by online experimental tests for an atmospheric drying process with time delay in its dynamics.

Keywords: Atmospheric tomatoes drying process; Control Lyapunov-Krasovskii functional; Inverse optimality; Time delay control system.