Synthesis H∞ of an observers of the state of a nonlinear continuous dynamical systems, linear in control and disturbance

<p><strong>Context and relevance.</strong> In the context of the increasingly widespread use and distribution of aircraft and complex aerospace systems, the development of joint estimation and control systems is of great importance, in which the control algorithm uses an estimation of the state vector based on the results of accumulated measurement information instead of the state vector. In modern control theory, one of the effective approaches to solving this problem is the methods of synthesizing H∞ - controllers and H∞-state observers. The use of these methods enables building a robust controllers or observers. Some of the most popular ways to solve such problems are associated with the use of linear matrix inequalities, as well as the frequency method associated with the Fourier transform. However, when considering complex engineering problems, their application often complicates the solution. Therefore, this paper proposes an approximate method for solving the problem of finding an observer for nonlinear continuous dynamical systems that are linear in control and disturbance. <strong>Objective.</strong> The first goal is to formulate and prove a sufficient condition for an H∞-observer for nonlinear continuous dynamical systems that are linear in control and disturbance, in the presence of uncertainty in the initial conditions, limited external influences and measurement errors over a semi-infinite time interval of system operation. The second goal is to formulate an approximate method for synthesis of an H∞-observer and test the proposed approach on a model example. <strong>Hypothesis.</strong> The paper proposes an approximate method for solving the problem of finding an observer for dynamic systems that are nonlinear in state, similar to the methods used for linear systems. The hypothesis arose as a result of analyzing the solution of applied synthesis problems in nonlinear systems in the absence of limited external influences. Its implementation is associated with the extension of the methodology for applying Riccati equations with coefficients depending on the state vector to the problems of synthesis of an observer for a class of nonlinear systems that are linear in control and disturbance. <strong>Methods and materials.</strong> The sufficient conditions for synthesis of an observer for nonlinear continuous dynamical systems that are linear in control and disturbance, in the presence of uncertainty in the initial conditions, limited external influences, and measurement errors over a semi-infinite time interval of system operation are proven. When solving the observer synthesis problem, it is proposed to look for an approximate solution by analogy with the theory of linear systems, that is, the original nonlinear dynamical system is transformed by factorization to a structure similar to a linear one, with matrices depending on the state vector. To implement the developed method and solve model examples, the MATLAB mathematical package was used. <strong>Results.</strong> A model example was solved to test the proposed approach. The graphs of the state vector change and its estimate demonstrate the desired quality of transient processes under conditions of incomplete information about the object's state vector. <strong>Conclusions. </strong>As a result, the sufficient conditions of the observer for nonlinear continuous dynamical systems that are linear in control and disturbance were formulated and proven. An approximate approach to solving the observer synthesis problem and a step-by-step solution algorithm were proposed. A model example was solved and graphs of transient processes and their estimates are presented, demonstrating the results of numerical modeling. Analysis of the error behavior confirms the operability of the proposed method.</p>