Robust Optimal Control of Uncertain Nonaffine MIMO Nonlinear Discrete-Time Systems with Application to HCCI Engines


MIMO optimal control of unknown nonaffine nonlinear discrete-time systems is a challenging problem owing to the presence of control inputs inside the unknown nonlinearity. in this paper, the nonaffine nonlinear discrete-time system is transformed to an affine-like equivalent nonlinear discrete-time system in the input-output form. Next, a forward-in-time Hamilton-Jacobi-Bellman equation-based optimal approach, without using value and policy iterations, is developed to control the affine-like nonlinear discrete-time system by using both NN as an online approximator and output measurements alone. to overcome the need to know the control gain matrix in the optimal controller, a new online discrete-time NN identifier is introduced. the robustness of the overall closed-loop system is shown via singular perturbation analysis by using an additional auxiliary term to mitigate the higher-order terms. Lyapunov stability of the overall system, which includes the online identifier and robust control term, demonstrates that the closed-loop signals are bounded and the approximate control input approaches the optimal control signal with a bounded error. the proposed optimal control approach is applied to a cycle-by-cycle discrete-time representation of an experimentally validated homogeneous charge compression ignition fuel-flexible engine whose dynamics are modeled as uncertain nonlinear, nonaffine, and MIMO discrete-time system. Simulation results are included to demonstrate the efficacy of the approach in presence of actuator disturbances. Copyright © 2012 John Wiley & Sons, Ltd.


Mechanical and Aerospace Engineering

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Article - Journal

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© 2012 Wiley-Blackwell, All rights reserved.

Publication Date

01 Jan 2012