Optimal and robust control of a class of nonlinear systems using dynamically re-optimised single network adaptive critic design

Following the philosophy of adaptive optimal control, a neural network-based state feedback optimal control synthesis approach is presented in this paper. First, accounting for a nominal system model, a single network adaptive critic (SNAC) based multi-layered neural network (called as NN 1 ) is syn...

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Bibliographic Details
Published in:International journal of systems science 2018-01, Vol.49 (2), p.246-263
Main Authors: Tiwari, Shivendra N., Padhi, Radhakant
Format: Article
Language:English
Subjects:
Adaptive control
adaptive optimal control
adaptive systems
Design optimization
Liapunov functions
Mathematical models
Multilayers
Neural networks
neuro-adaptive control
Nonlinear systems
Optimal control
Philosophy
Robust control
single network adaptive critic
Stability analysis
State feedback
Training
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Summary:Following the philosophy of adaptive optimal control, a neural network-based state feedback optimal control synthesis approach is presented in this paper. First, accounting for a nominal system model, a single network adaptive critic (SNAC) based multi-layered neural network (called as NN 1 ) is synthesised offline. However, another linear-in-weight neural network (called as NN 2 ) is trained online and augmented to NN 1 in such a manner that their combined output represent the desired optimal costate for the actual plant. To do this, the nominal model needs to be updated online to adapt to the actual plant, which is done by synthesising yet another linear-in-weight neural network (called as NN 3 ) online. Training of NN 3 is done by utilising the error information between the nominal and actual states and carrying out the necessary Lyapunov stability analysis using a Sobolev norm based Lyapunov function. This helps in training NN 2 successfully to capture the required optimal relationship. The overall architecture is named as 'Dynamically Re-optimised single network adaptive critic (DR-SNAC)'. Numerical results for two motivating illustrative problems are presented, including comparison studies with closed form solution for one problem, which clearly demonstrate the effectiveness and benefit of the proposed approach.
ISSN:0020-7721
1464-5319
DOI:10.1080/00207721.2017.1408871