Fuzzy time-optimal controller (FTOC) for second order nonlinear systems

The motivation behind this paper is to seek alternative techniques to achieve a near optimal controller for non-linear systems without solving the analytical problem. In classical optimal control systems, the system states and optimization co-state parameters generate a two-point boundary value prob...

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Bibliographic Details
Published in:ISA transactions 2011-07, Vol.50 (3), p.364-375
Main Authors: Nagi, Farrukh, Ahmed, Syed Khaleel, Zularnain, Abdul Talip, Nagi, Jawad
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Bang–bang control
Computer science
control theory
systems
Computer Simulation
Control system synthesis
Control systems
Control theory. Systems
Dynamical systems
Exact sciences and technology
Feedback
Fuzzy
Fuzzy Logic
Fuzzy logic control
Fuzzy set theory
Mathematical analysis
Models, Theoretical
Nonlinear Dynamics
Optimal control
Optimization
State trajectories
Time-optimal control
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Summary:The motivation behind this paper is to seek alternative techniques to achieve a near optimal controller for non-linear systems without solving the analytical problem. In classical optimal control systems, the system states and optimization co-state parameters generate a two-point boundary value problem (TPBVP) using Pontryagin’s minimum principle (PMP). The paper contributes a new fuzzy time-optimal controller to the existing fuzzy controllers which has two regular inputs and one bang-bang output. The proposed controller closely approximates the output of the classical time-optimal controller. Further, input membership function are tuned on-line to improve the time-optimal output. The new controller exhibits optimal behaviour for second order non-linear systems. The rules are selected to satisfy the stability and optimality conditions of the new fuzzy time-optimal controller. The paper describes a systematic procedure to design the controller and how to achieve the desired result. To benchmark the new controller performance, a sliding mode controller is used for guidance and comparison purpose. Simulation of three non-linear examples shows promising results. The work described here is expected to incite researcher’s interest in fuzzy time-optimal controller design.
ISSN:0019-0578
1879-2022
DOI:10.1016/j.isatra.2011.01.014