4.6 Article

Optimal Steady-State Regulator Design for a Class of Nonlinear Systems With Arbitrary Relative Degree

Journal

IEEE TRANSACTIONS ON CYBERNETICS
Volume 52, Issue 6, Pages 4728-4740

Publisher

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCYB.2020.3034930

Keywords

Optimization; Regulators; Steady-state; Nonlinear systems; Uncertainty; Power system dynamics; Stability analysis; Distributed optimization; multi-input-multioutput (MIMO) nonlinear system; online optimization; optimal steady state; singular perturbation

Funding

  1. National Natural Science Foundation of China [61603084, 61621004, U1908213]
  2. Fundamental Research Funds for the Central Universities of China [N2004008, N170404017, N2004010]
  3. Research Fund of State Key Laboratory of Synthetical Automation for Process Industries [2018ZCX03]

Ask authors/readers for more resources

This article considers the regulator design problem for a class of uncertain multi-input-multioutput (MIMO) nonlinear systems with arbitrary relative degree. State and output-feedback-based regulators are proposed, and the exponential stability of the resulting closed-loop systems is established through singular perturbation analysis. The effectiveness of the proposed methods is validated through numerical simulations.
In this article, we consider the regulator design problem for a class of uncertain multi-input-multioutput (MIMO) nonlinear systems with arbitrary relative degree. The objective is to regulate the output of the nonlinear system to an optimal steady state that solves a constrained optimization problem, without computing the optimal solution in advance. By embedding saddle-point dynamics, both state and output-feedback-based regulators are proposed and the resulting closed-loop systems are modeled in standard singularly perturbed forms. By invoking the singular perturbation analysis, exponential stability is established under some regularity condition. Compared with the existing methods, the proposed regulators can deal with a class of nonlinear systems with uncertainties and arbitrary relative degree. Furthermore, the current results can include some recent works on the distributed optimization problem as special cases. Finally, the effectiveness of the proposed methods is validated through numerical simulations.

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