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 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.


Electrical and Computer Engineering


This work was supported by the National Science Foundation under Grant ECCS 0901562.

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


File Type





© 2015 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Oct 2015