Optimal Control of Nonlinear Continuous-Time Systems in Strict-Feedback Form
Abstract
This paper proposes a novel optimal tracking control scheme for nonlinear continuous-time systems in strict-feedback form with uncertain dynamics. The optimal tracking problem is transformed into an equivalent optimal regulation problem through a feedforward adaptive control input that is generated by modifying the standard backstepping technique. Subsequently, a neural network-based optimal control scheme is introduced to estimate the cost, or value function, over an infinite horizon for the resulting nonlinear continuous-time systems in affine form when the internal dynamics are unknown. The estimated cost function is then used to obtain the optimal feedback control input; therefore, the overall optimal control input for the nonlinear continuous-time system in strict-feedback form includes the feedforward plus the optimal feedback terms. It is shown that the estimated cost function minimizes the Hamilton-Jacobi-Bellman estimation error in a forward-in-time manner without using any value or policy iterations. Finally, optimal output feedback control is introduced through the design of a suitable observer. Lyapunov theory is utilized to show the overall stability of the proposed schemes without requiring an initial admissible controller. Simulation examples are provided to validate the theoretical results.
Recommended Citation
H. Zargarzadeh et al., "Optimal Control of Nonlinear Continuous-Time Systems in Strict-Feedback Form," IEEE Transactions on Neural Networks and Learning Systems, vol. 26, no. 10, pp. 2535 - 2549, Institute of Electrical and Electronics Engineers (IEEE), Oct 2015.
The definitive version is available at https://doi.org/10.1109/TNNLS.2015.2441712
Department(s)
Electrical and Computer Engineering
Keywords and Phrases
Adaptive control systems; Backstepping; Cost benefit analysis; Cost estimating; Cost functions; Costs; Dynamic programming; Feedback control; Nonlinear control systems; Nonlinear feedback; Nonlinear systems; Adaptive back-stepping; Adaptive Control; Neural network (nn); Optimal controls; Strict feedback systems; Continuous time systems; Adaptive backstepping; Neural network (NN)-based dynamic programming; Nonlinear strict-feedback systems
International Standard Serial Number (ISSN)
2162-237X; 2162-2388
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2015 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.
Publication Date
01 Oct 2015
Comments
This work was supported by the National Science Foundation under Grant ECCS 0901562.