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• Alberto Isidori: Served as the President of the International Federation of Automatic Control (IFAC) from 2008-2011 and as the President of the European Union Control Association (EUCA) from 1995-1997. Affiliated with the Department of Computer, Control, and Management Engineering at the University of Rome, with research interests in nonlinear systems, output regulation, nonlinear control systems, and output feedback.

• Anton A. Pyrkin: Born in 1985 in Zaozerny, Russia, holds degrees in Bachelor, Master, PhD, and Habilitation Thesis in the fields of system analysis, data processing, and control. Since 2016, he has been serving as a Professor and Dean of the School of Control Systems and Robotics at ITMO University in St. Petersburg, with research interests including adaptive and robust control methods, hybrid (switched, iterative) control and estimation methods, disturbance estimation and elimination, and control problems of plants with long input and state delays.

• Islam Bzhikhatlov: Research interests include machine learning, bipedal robots, cancer genome rearrangements, random forests, and hotspots of cancer breakpoints.

• Vladislav S. Gromov: Research interests include finite-time, signals, estimation, and multi-sinusoidal frequency analysis.

Nonlinear Exogenous System and Internal Model Design Research Outline

Abstract

• Study output regulation problem for plants affected by nonlinear exogenous systems
• Propose a new method for controller design with internal model
• Present two implementable controllers: one for known parameters, and an adaptive controller

Introduction

• Introduce a new approach for internal model design targeting output regulation problem in nonlinear systems
• Linear system regulation theory is mature, but no satisfactory solution for nonlinear systems
• Cite related research and present the framework of this study

Problem Formulation

• Describe a simple plant affected by control input u and disturbance δ
• δ is the output of a nonlinear exogenous system with initial conditions and unknown parameters
• Design control u to achieve asymptotic convergence of output y to 0

Internal Model Design

• Motivation for controller design: Seek new methods for internal model design
• Main idea: The controller's internal model repeats the disturbance dynamics
• Add two integrator chains, design saturation functions, and observers
• Define error, calculate its derivative, and ensure matrix A is Hurwitz
• Use small gain theorem to analyze the stability of the closed-loop system

Adaptive Output Regulation

• Propose an adaptive controller, which does not require knowledge of parameters θ
• Control law contains adaptive internal model

Simulation

• Show simulation results using the adaptive internal model control law
• Figure 1: Transient and disturbance signals of output controller for different κ values
• Figure 2: Transient of output controller for different θ values

Conclusion

• Study a new method for internal model design to achieve output regulation problem
• Propose two types of controllers: one with known parameters, and an adaptive one
• Work is ongoing, addressing issues left unresolved in the current presentation

Q: What specific research methods were used in the paper?

• Internal Model Design Method: The paper proposes a new internal model design method to address the output regulation problem of plants affected by nonlinear external systems. The core of this method is to design a controller that includes an internal model capable of replicating the dynamics of the disturbances.
• Control Strategy Proposal: Control strategies are proposed for both known and unknown parameter cases, which are practically implementable.
• Simulation Validation: The effectiveness of the proposed control strategies is verified through simulation experiments.

Q: What are the main research findings and achievements?

• Implementation of Control Strategy: The paper successfully proposes a new control strategy that integrates an internal model within the controller to regulate disturbances from nonlinear external systems.
• Two Controller Designs: Two types of controllers are designed for cases with known and unknown parameters, including conventional and adaptive controllers.
• Simulation Results: The effectiveness of the control strategy is demonstrated through simulation experiments, verifying the achievement of the control objective (output y asymptotically converging to 0).

Q: What are the current limitations of this research?

• Theoretical Limitations: Although the paper studies output regulation problems in nonlinear systems, the authors note that there is not yet a fully satisfactory nonlinear version of the theory.
• Parameter Uncertainty: For cases with uncertain parameters θ, although an adaptive controller is proposed, the effectiveness and stability of this method may depend on the accuracy and speed of parameter estimation.
• Scope Limitation: The control strategy and internal model design method proposed in the paper may only be applicable to specific types of nonlinear systems and external disturbances.
• Unresolved Issues: The authors mention that there are still open questions that need further resolution, but the specific issues are not detailed in the abstract.