Stable algorithms of adaptive control, estimation of controller parameters, synthesis of adaptive control of dynamic objects by the criterion of minimum dispersion, and synthesis of suboptimal adaptive-local control of dynamic objects based on predictive models are presented. Algorithms for the stable identification of dynamic control objects based on regularization and pseudoinversion methods based on a singular decomposition are presented. Based on the use of approximations in the form of a finite sum of Gaussian distributions, recurrent identification algorithms have been developed using multiple models and adapting their parameters. Stable algorithms are proposed for identifying the parameters of an object and a controller in a closed-loop control system based on the principle of iterative regularization using the method of variational inequalities, ensuring the convergence of the desired estimates of the parameters of the object and the controller almost certainly to true values. Stable algorithms for generating control actions in locally optimal adaptive control systems for dynamic objects based on non-orthogonal factorizations and pseudoinversions of ill-conditioned or degenerate square matrices are proposed that enhance the accuracy of forming control actions in a closed control loop.

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