Optimal Control of Nonlinear Continuous-Time Systems in Strict-Feedback Form

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...

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Bibliographic Details
Published in:IEEE transaction on neural networks and learning systems Vol. 26; no. 10; pp. 2535 - 2549
Main Authors: Zargarzadeh, Hassan, Dierks, Travis, Jagannathan, Sarangapani
Format: Journal Article
Language:English
Published: United States IEEE 01.10.2015
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Adaptive backstepping
adaptive control
Adaptive systems
Backstepping
Control systems
Control theory
Dynamical systems
Economic models
Feedforward neural networks
neural network (NN)-based dynamic programming
Neural networks
Nonlinear dynamical systems
Nonlinear dynamics
nonlinear strict-feedback systems
Nonlinearity
Optimal control
Optimization
Vehicle dynamics
adaptive control
optimal control
Adaptive backstepping
nonlinear strict-feedback systems
neural network (NN)-based dynamic programming
ISSN:2162-237X, 2162-2388
Online Access:Get full text
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Summary: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.
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ISSN:2162-237X
2162-2388
DOI:10.1109/TNNLS.2015.2441712