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Robust optimal control of uncertain nonaffine MIMO nonlinear discrete‐time systems with application to HCCI engines
Author(s) -
Zargarzadeh H.,
Jagannathan S.,
Drallmeier J.
Publication year - 2012
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.2294
Subject(s) - control theory (sociology) , nonlinear system , discrete time and continuous time , mimo , lyapunov function , optimal control , robustness (evolution) , computer science , affine transformation , mathematics , mathematical optimization , control (management) , channel (broadcasting) , computer network , statistics , physics , biochemistry , chemistry , quantum mechanics , artificial intelligence , gene , pure mathematics
SUMMARY 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.