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• REINFORCEMENT LEARNING METHODS IN ADAPTIVE CONTROL OF NONLINEAR DYNAMIC OBJECTS

  М.Y. Medvedev , V.K., А.R. Gaiduk , I.М. Medvedev , Е.Y. Kosenko

  2026-04-29

  Abstract ▼

  The relevance of the problem of adaptive control of nonlinear dynamic objects is ensured by the ever-increasing demands on the quality and operating conditions of technical systems. Automation and robotics lead to an increase in the complexity of the problems being solved and the need to adapt to structural and parametric uncertainty and external disturbances. In recent years, the use of reinforcement learning methods for the synthesis of adaptive control systems has gained popularity. These methods demonstrate effectiveness in controlling uncertain dynamic objects. However, there are two fundamental problems with the application of machine learning methods to control systems for dynamic objects. First, the need to ensure asymptotic stability of the desired trajectory of a closed-loop system limits the application of deep learning methods. Second, during the learning process, it is necessary that the intelligent controller does not generate controls that lead to state variables exceeding specified limits. The purpose of this article is to review and analyze recent advances in the application of reinforcement learning methods to the synthesis of adaptive control systems for nonlinear dynamic objects. Particular attention is given to Actor-Critic methods, which are structurally similar to adaptive control systems with self-adjusting parameters. Based on the analysis, the structure of an adaptive system with two-component control, including nominal and adaptive controllers, is proposed. An adaptive control algorithm is proposed, distinguished by the use of a modified Actor-Critic algorithm, distinguished by a new form of the delta error and the absence of a singularity in the neighborhood of zero. The proposed algorithm allows for a reduction in the number of adjustable parameters. The article presents conditions for Lyapunov stability of the zero-equilibrium position of a closed-loop system and an example of the synthesis and modeling of the proposed adaptive control algorithm

• TO ESTIMATION OF ATTRACTION AREA OF EQUILIBRIUM IN NONLINEAR CONTROL SYSTEMS

  Almashaal Mohammad Jalal

  6-14

  2025-07-31

  Abstract ▼

  Designing nonlinear control systems is still difficult, so many researchers are trying to find
  some useful ways and methods to solve this problem. As a result of such research, some methods
  have been seen trying to design a good enough control system for nonlinear plants. But a disadvantage
  of these methods is the complexity, so it created a need to compare some methods to determine
  which one is the easiest method to design a control system for nonlinear plants. It was
  found a way to compare two methods, which is comparing the regions of initial conditions of the systems which are designed using these methods. Two analytical nonlinear control systems design
  methods are compared on the example of the design control systems mobile robots. The algebraic
  polynomial-matrix method uses a quasilinear model, and the feedback linearization method uses
  particular feedback. Both considered methods give a bounded domain of equilibrium attraction,
  therefore the obtained control systems can be operated only with bounded initial conditions. The
  numerical example of designing the control systems for one object by these methods and the estimates
  of the attraction areas of the system’s equilibriums in these systems are given in the paper.
  As a result of this paper, it was found that using the algebraic polynomial-matrix method will get a
  bigger section of initial conditions of the plant’s variable than the same section which is given by
  the feedback linearization method.