We propose a new controller parameter adaptive law that guarantees the exponentialstability of the classical dynamic model of the tracking error without using its coordinates in theadaptive law and relaxes some classical assumptions and requirements of adaptive control theory(the need to know the sign/value of the control input gain, the need for an experimental choice ofthe adaptive law gain, and the requirement to the tracking error transfer function to be strictlypositive real considering the output feedback control). The applicability of the proposed law toadaptive state and output feedback control problems is shown. The advantages of developedapproach over the existing ones are demonstrated mathematically and experimentally.

In this paper, for a continuous function defined on a closed subset of a Banach space and differentiable on the interior of the domain, the infimum of the norm of the first derivative is estimated through the variation of the function on the boundary of the domain. A similar result is obtained for locally Lipschitz functions. These results generalize the previously known estimates of the infimum of the norm of the derivative in terms of the variation of the function on the entire domain. Under the assumption that the considered function is twice differentiable on the interior of the domain, similar estimates for the infimum of the norm of the first-order derivative and the estimates of the values of the second-order derivative are obtained. The proof of these results is based on the application of the modifications of the Bishop-Phelps variational principle and the Borwein-Preiss smooth variational principle. As applications of these results, we obtain second-order necessary optimality conditions for minimizing sequences. This proposition is proved under an additional assumption on the norm of the Banach space valid for a wide class of function spaces. In addition, some of the described results are generalized for mappings, acting in Banach spaces ordered by pointed closed convex cones.

A new approach is proposed for solving the problem of suppressing nonrandom bounded exogenous disturbances in linear control systems using dynamic output feedback. The approach is based on reducing the problem to a matrix optimization problem with the feedback matrix and the observer matrix as the variables. A gradient method for finding dynamic output feedback is written out and justified. A number of examples are considered.

We propose an approach to the normalization of the excitation of the identification loop regressor constructed based on the dynamic extension and mixing procedure. With a constant estimation loop gain, applying this approach allows one to have the same upper bound on the parametric identification error for scalar regressors with various degrees of excitation, a feature that is a significant advantage for practice. The approach developed is compared with the well-known regressor amplitude normalization method, and it is shown that the classical normalization method does not have the above-mentioned property. As a validation of our theoretical conclusions, the results of comparative mathematical modeling are presented for the classical gradient estimation loop, loops with amplitude regressor normalization, and loops with the proposed regressor excitation normalization.

A simple, universal approach to solving the sparse filtering problem - problem using a reduced number of outputs - with arbitrary bounded exogenous disturbances by employing an observer is presented. The approach is based on the invariant ellipsoid method and the technique of linear matrix inequalities. An application of this concept has made it possible to reduce the original problem to a semidefinite programming problem that is easy to solve numerically. The approach is distinguished by its simplicity and ease of implementation and covers both continuous- and discrete-time statements of the problem. The efficiency of the procedure proposed is demonstrated by a test example.