This paper proposes a new method to provide the exponential convergence of both the parameter and tracking errors of the composite adaptive control system without the persistent excitation (PE) requirement. Instead, the derived composite adaptive law ensures the above-mentioned properties under the strictly weaker finite excitation (FE) condition. Unlike known solutions, in addition to the PE requirement relaxation, it provides better transient response under jump change of the plant uncertainty parameters. To derive such an adaptive law, a novel scheme of uncertainty filtration with resetting is proposed, which provides the required properties of the control system. A rigorous proof of all mentioned properties of the developed adaptive law is presented. Such law is compared with the known composite ones, which also relax the PE requirement, using the wing-rock problem to conduct numerical experiments. The obtained results fully support the theoretical analysis and demonstrate the advantages of the proposed method.

We propose a new controller parameter adaptive law that guarantees the exponential stability of the classical dynamic model of the tracking error without using its coordinates in the adaptive 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 of the adaptive law gain, and the requirement to the tracking error transfer function to be strictly positive real considering the output feedback control). The applicability of the proposed law to adaptive state and output feedback control problems is shown. The advantages of developed approach over the existing ones are demonstrated mathematically and experimentally.

This study deals with relaxing the regressor square integrability condition \(\omega (t)\notin \mathrm {L}_{2} \) in the DREM procedure so as to ensure the monotone asymptotic convergence of the parametric error in the problem of estimating constant parameters of a linear regression dependence.

The main objective of this research is to develop a method to construct a neural tuner of PI-controller parameters. Such tuning is necessary to improve energy efficiency of nonlinear industrial plants since the PI-controller is linear, and its parameters certain values are optimal only for a certain plant functioning mode. The tuner consists of a neural network calculating the controller parameters values and a rule base scheduling moments of the network training and learning rates values. Methods to select both the neural tuner structure and an appropriate neural network structure are proposed. The general network structure is defined by Cybenko, Horknick and Gorban theorems. The number of input layer neurons is chosen in accordance with a PI-controller difference equation. The number of neurons in a hidden layer calculation method is based on the number of input layer neurons, delayed setpoint and plant output signals used in the input layer and the number of points, which are used to average network input signals. Such methods do not use the plant model. Stability of a control system with the tuner is estimated for each transient using technical sustainability criteria. Proposed methods are applied to control empty and loaded electroheating furnace. Obtained results show that the tuner usage allows to achieve up to 6% plant energy efficiency improvement in comparison with the conventional PI-controller with constant parameters usage.

A new method of direct adaptive pole placement control (APPC) is developed for plants with unmatched uncertainty, which linearly depends on a state vector. It guarantees the exponential stability of a control system and exponential convergence of control law adjustable parameters to their true values when the regressor is finitely exciting. Considering the known classical APPC schemes and adaptive methods with exponential regulation, the advantages of the proposed one are that it does not require a priori information on a control input matrix and ensures the monotonic transient behavior of each adjustable parameter of the control law. The theoretical results are supported by the numerical experiments.