Solution of the design problem of nonlinear control systems is accomplished usually using some transformations of mathematical models. In this case, it is convenient to use the mathematical identities of the algebra of polynomials, vectors, and matrices with numerical and functional coefficients, that are proven in this paper. These identities can be used for the transformations of the mathematical models of both the linear systems with constant parameters and studying the nonlinear control systems represented by quasilinear models. These polynomial-matrix identities also have independent significance, as they can be applied to the algebraic transformations of both some vector-matrix expressions and polynomial-matrix expressions with complex arguments. Applying these identities to the state-dependent coefficients models of control systems is problematic, since these models very often describe nonlinear plants and systems approximately. The polynomial-matrix identities presented below are proved by the equivalent transformations of the operator equations in the state variables of the nonlinear feedback control systems represented by the quasilinear models. These models can accurately represent plants and systems defined by nonlinear differential equations in Cauchy form and output equations, it is only important that the nonlinearities of these equations are differentiable with respect to all their arguments. Using some of the proven polynomialmatrix equalities, the following were obtained: the solution of the eigenvalue placement problem for the system matrix of quasilinear models of closed-loop systems; the controllability criterion of the nonlinear plants output; and the controllability criterion of nonlinear closed-loop systems by reference signals. Two examples of nonlinear plants with uncontrollable output are given, as well as numerical examples demonstrating the correctness of the obtained polynomial-matrix identities.

The output feedback controller for the linear multivariable system, developed in the first part of this work, is analyzed. This controller guarantees specified or achievable performance in terms of control errors, stability margins, and response time. The solution to the synthesis problem is based on a standard H∞-optimization procedure, formulated in a special way. This second part provides a physical The output feedback controller for the linear multivariable system, developed in the first part of this work, is analyzed. This controller guarantees specified or achievable performance in terms of control errors, stability margins, and response time. The solution to the synthesis problem is based on a standard H∞-optimization procedure, formulated in a special way. This second part provides a physical interpretation of the stability margin radii for a multivariable system. The interpretation is given in terms of Nyquist plots with breakpoints at individual plant inputs and constitutes the essence of Theorem1. Namely, the Nyquist plot must not touch or enter a circle of radius r_i centered at the critical point (–1, j0), where r_i is the stability margin radius guaranteed by the design procedure for the i-th control input of the plant. This theorem has significant practical value for engineers, as it enables the experimental determination of the stability margin radius for each individual control channel at the physical input of the plant. А direct relationship between the absolute stability of a closed loop multivariable system with sector nonlinearities at the plant input and its stability margin radii is established. This result is formalized in Theorem 2. In particular, by applying the circle criterion of absolute stability, the theorem establishes that the closed loop system remains absolutely stable for time-varying nonlinearities introduced at each control input of the plant. In this case, the sector for each nonlinearity physically representing actuator nonlinearities is uniquely determined by the guaranteed stability margin radius in each channel at the physical input of the plant. The proposed approach is illustrated by a controller design example for a load-coupled electric drive, demonstrating its practical relevance. 

This paper considers the problem of estimating an unmeasured state vector for a class of nonlinear dynamic systems with parametric uncertainties and output delay. Such systems are widely encountered in control problems involving technical objects operating under uncertain external disturbances, limited availability of measurement information, and bounded data transfer rates. The class of systems under consideration is characterized by unit relative degree and the presence of additive nonlinearities that exhibit a nonlinear dependence on the measured output signal and a linear dependence on the vector of unknown parameters and the state vector. The magnitude of the delay is assumed to be known. The proposed approach to solving the estimation problem is based on a multi-stage observer synthesis procedure, which includes three steps. In the first stage, an unknown input observer for delayed state vector is developed, which ensures the formation of auxiliary estimates. Its application provides the complete elimination of the influence of the unknown input signal on the dynamics of the observation error. At the second stage, an algorithm for estimating the vector of unknown system parameters is constructed based on the obtained estimates. This problem is solved by transforming the original system into a linear regression model, followed by parametric identification based on the gradient descent method. At the final stage, a filtering procedure is introduced, which reduces the problem of estimating the state vector of the original nonlinear system to the problem of identifying the parameters of a linear regression, which is also solved using the gradient descent method. The obtained theoretical results confirm the asymptotic convergence of the estimates of the state vector and unknown parameters to their true values. The performance and effectiveness of the developed method were verified through testing using computer simulation. Obtained unknown parameter estimates and the estimation errors of the state variables of a nonlinear system are presented in the article and confirm the correctness and stability of the estimation process. 

Identifying dynamic systems from data is a complex problem, where a key requirement of modern research is not only accuracy but also model interpretability. Although highly effective, the symbolic regression method based on genetic programming has inherent limitations, the most important of which is stochasticity, leading to instability of results. In this paper, a new hybrid method, GP-SINDy, is proposed to overcome these shortcomings. Its core idea is to combine two approaches: genetic programming performs a global search for the model structure, while sparse identification fine-tunes the corresponding parameters. The effectiveness of the proposed method was validated through comprehensive computational experiments. On test data, GP-SINDy demonstrated the ability to find models with an optimal balance of accuracy and complexity, outperforming the baseline genetic programming algorithm. Analysis on noisy data confirmed the increased efficiency of the proposed method. Verification on a real system demonstrated the practical applicability of the approach for constructing adequate analytical models. Thus, the GP-SINDy hybrid method represents a powerful and versatile tool for automatically deriving interpretable system dynamics equations, opening up new possibilities in various fields of science and engineering.

The problem of transporting payloads suspended from a quadcopter is gradually acquiring not only theoretical but also practical importance. If the mass and size of the payload are large enough, control algorithms should take into account its motion relative to the copter and aerodynamic forces acting on the payload. Special attention should be paid to preventing large-amplitude payload oscillations, since such oscillations can lead to emergency situations. This paper considers a mechanical system consisting of a quadcopter and a spherical cargo suspended from its center of mass on a weightless rod using a spherical hinge. The system can perform spatial motion in a wind flow, the speed of which is assumed to be constant and directed horizontally. The drag force acting on the payload is taken into account. The controllability of the system in the vicinity of the uniform rectilinear flight is discussed. It is shown that the system is not completely controllable, with the uncontrolled variables corresponding to payload rotation about the axis coinciding with the rod. The remaining variables are completely controllable (at least if the aerodynamic force is small enough). To stabilize the uniform rectilinear flight, a control is constructed, optimal in the sense of the standard quadratic functional. The problem of the motion of the copter along a target sufficiently smooth trajectory with a given cruising speed, while preventing intense oscillations of the payload, is considered. An algorithm is constructed to control the forces generated by the copter’s rotors, which ensures the motion of the system along the target trajectory and prevents the occurrence of high-amplitude payload oscillations.

The paper formulates the task of controlling a group of drones to deliver goods to the orders of the population in an urban environment, for example, food and medicines. To solve the problem, it is proposed to create an intelligent drone group resource management system (ISUR-Drones), which should operate autonomously (unpopulated) 24/7 and provide the ability to automatically select and distribute orders for drones, build routes and plan drone operations, optimize (while there is time), monitor and control the execution of plans, as well as adaptive realignment of plans for new orders or other events that occur in real time. To implement an ISUR Drone that performs the functions of an autonomous "smart control room", a model of an ontologically configurable multi-agent network of needs and capabilities and a modification of the adaptive resource planning method for a group of drones are proposed. The functions and architecture of ISUR Drones have been developed and a prototype of the system has been implemented using the example of deliveries in the city of Tolyatti. The high adaptability of the developed system is shown, ensuring the maximum possible satisfaction of consumer wishes and high efficiency in using drone resources.