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In this study, we consider the extended optimal control problem and search for a control function in the class of feasible functions for a real control object. Unlike the classical optimal control problem, the control function should depend on the state, not time. Therefore, the control synthesis problem for the initial-state domain should be solved, instead of the optimal control problem with one initial state. Alternatively, an optimal trajectory motion stabilisation system may be constructed. Both approaches—control and trajectory motion stabilisation system syntheses—cannot be applied to real-time control, as the task is too complex. The minimum threshold of quality criteria is searched for in the space of mathematical expression codes. Among other problems, the search space is difficult to define and the gradient is hard to determine. Therefore, the advanced control object model is used to obtain a feasible control function. The advanced model is firstly obtained before solving the optimal control problem and it already includes a trajectory motion stabilisation system; in particular, this stabilisation system is synthesised in advance at the control system design stage. When the optimal control problem appears, it is solved in real time in the classical statement, and a control function is searched for as a function of time. The advanced control object model also uses the reference model to generate the optimal trajectory. The search for the optimal control function is performed in real time and considers the synthesised stabilisation system of motion along a determined trajectory. Machine learning control via symbolic regression, namely, the network operator method, is used to directly solve the control synthesis problem. An example solution of the optimal control problem, with an advanced model moving in the environment with obstacles for a group of two mobile robots, is presented. The obtained solution is a control function for a reference model that generates a trajectory from a class of trajectories stabilised with the object's control system. [ABSTRACT FROM AUTHOR]

This paper presents a novel numerical method for solving the control system synthesis problem through the application of machine learning techniques, with a particular focus on symbolic regression. Symbolic regression is used to automate the development of control systems by constructing mathematical expressions that describe control functions based on system data. Unlike traditional methods, which often require manual programming and tuning, this approach leverages machine learning to discover optimal control solutions. The paper introduces a general framework for machine learning in control system design, with an emphasis on the use of evolutionary algorithms to optimize the generated control functions. The key contribution of this research lies in the development of an algorithm based on the principle of small variations in the baseline solution. This approach significantly enhances the efficiency of discovering optimal control functions by systematically exploring the solution space with minimal adjustments. The method allows for the automatic generation of control laws, reducing the need for manual coding, which is especially beneficial in the context of complex control systems, such as robotics. To demonstrate the applicability of the method, the research applies symbolic regression to the control synthesis of a mobile robot. The results of this case study show that symbolic regression can effectively automate the process of generating control functions, significantly reducing development time while improving accuracy. However, the paper also acknowledges certain limitations, including the computational demands required for symbolic regression and the challenges associated with real-time implementation in highly dynamic environments. These issues represent important areas for future research, where further optimization and hybrid approaches may enhance the method's practicality and scalability in real-world applications.

With the publication of this article, the authors continue the research on the development and testing of a methodology for in-flight aircraft rerouting which have begun in previously published articles in the Civil Aviation High Technologies of the Moscow State Technical University of Civil Aviation. This article presents the results of the study in terms of developing the potentials of the methodology from reconfiguring a route of a hypothetical aircraft and obstacles in the horizontal plane, which were previously demonstrated, prior to rerouting in both the horizontal and vertical planes for two different types of obstacles: 1) ground natural or artificial (mountain, power line support, etc.); 2) air (squall line, prohibited flight area, etc.) and their combinations using an example of a Mi-8 helicopter flight on route using a real digital map of the terrain. As mentioned above, a large amount of aviation accidents is associated with the loss of control in-flight, as well as the collision with terrain in a controlled flight (categories LOC-I, CFIT, LALT). As a result of the investigation of the aviation accidents, it was found that these accidents are often caused by the requirement to reroute quickly due to obstacles, for example, a squall line. When determining alternatives to avoid an obstacle, as well as while implementing the selected route for avoiding action, the crew makes errors due to the increased psychophysiological load and lack of time. The methodology and the algorithms, proposed by the authors, make it possible to assess the safety of an original route, estimate options for alternatives to avoid around obstacles detected in-flight, check them for feasibility, taking into account aircraft performance, flight envelope, and also select the optimal route from the view of some criterion, for example, based on minimizing the route length increase, reducing additional fuel consumption, the time required to implement a new route of flight, etc.

This paper discusses a formal control design of a discrete-time unicycle model using Satisfiability Modulo Theory (SMT). Given a set of possible initial positions, a set of possible target positions, a lane and a time horizon, we develop a method to formally synthesize a controller that drives the unicycle from a starting position to a target position within the given time horizon, while staying in the lane. The method encodes the set of possible initial positions, the set of possible target positions, the lane and the discrete-time unicycle model into linear real arithmetic expressions, and then checking the satisfaction via an SMT solver. If a solution exists, then the solution represents the controller. Finally, the proposed method is applied to a case study.

The problem of a stabilisation system synthesis for the motion of a control object along a given spatial trajectory is considered. The complexity of the problem is that the preset trajectory is defined in the state subspace and not in time. This paper describes a stabilisation system synthesis for motion along a trajectory specified in time and along a trajectory specified in the form of a manifold in a state space. In order to construct a stabilisation system, it is necessary to determine a distance between an object and the given trajectory at each moment in time. For trajectories that are not given in time, the determination of this distance can be ambiguous. An object may be exactly on a trajectory but at a different time. This paper proposes some approaches to solve the problem. One of the approaches is to transform a given trajectory in a state subspace into a trajectory given in time. A description of a universal method to perform this transformation is presented. In order to solve the synthesis problem automatically, without having to analyse the mathematical model of the control object, it is suggested that machine learning control by symbolic regression is used. In computational experiments, examples of stabilisation system syntheses for quadcopter motion along a given spatial trajectory are presented. [ABSTRACT FROM AUTHOR]

This paper presents a new control synthesis methodology for nonholonomic mobile robots subjected to time-varying delays and input saturation constraints. The proposed control method is based on smooth static nonlinear functions, leading to a simpler structure than other available control strategies for this class of systems. In addition, the convergence to a certain target position with guaranteed exponential decay rate can be proved for any orientation error. To this end, a nonlinear Lyapunov-Krasovskii functional has specifically been designed to deal with the inherent discontinuity of the kinematics model as well as the presence of time-varying delays. Thus, the control design can efficiently be addressed by means of Linear Matrix Inequalities (LMIs). Finally, the effectiveness of the proposed control design algorithm is validated through simulation and experimentally using a two-wheeled mobile robot.

A significant number of aviation incidents is related to loss of control in flight and controlled flight into terrain (LOC-I, CFIT, LALT categories). Investigation of these aviation incidents has revealed that these incidents often occur due to the need for rapid changes in flight routes as a result of detecting obstacles, such as thunderstorms, along the aircraft's path. During the determination of alternative routes to circumvent the encountered obstacle, as well as during the implementation process of the chosen rerouted route, the flight crew makes errors due to increased psycho-physiological workload and time constraints. This article presents an approach to the automatic rerouting of the aircraft's flight route to avoid obstacles detected during flight. The algorithm proposed by the authors allows for evaluating the safety of the original route, calculating alternative route options to bypass the obstacles encountered during flight, verifying their feasibility considering the aircraft's flight technical characteristics and control parameter limitations, and selecting the optimal rerouted route based on specific criteria, such as minimizing the increase in the flight route length, reducing additional fuel consumption, time required for implementing the new flight route, etc. Examples of rerouting the flight route of a hypothetical aircraft with detected obstacles along the flight path are provided in the article to demonstrate the algorithm's functionality. It is shown, in particular, that in the considered example, the shortest route for obstacle avoidance is not optimal in terms of time. It is also demonstrated that the safety of flying along the identified alternative rerouted routes depends, among other factors, on the selected flight speed. Therefore, for each calculated rerouted route, the algorithm determines a range of speeds within which the implementation of the obtained rerouted route is possible. This highlights the complexity and non-triviality of the pilot's task of autonomously finding a safe obstacle avoidance route on board the aircraft.

In this study, we consider the extended optimal control problem and search for a control function in the class of feasible functions for a real control object. Unlike the classical optimal control problem, the control function should depend on the state, not time. Therefore, the control synthesis problem for the initial-state domain should be solved, instead of the optimal control problem with one initial state. Alternatively, an optimal trajectory motion stabilisation system may be constructed. Both approaches—control and trajectory motion stabilisation system syntheses—cannot be applied to real-time control, as the task is too complex. The minimum threshold of quality criteria is searched for in the space of mathematical expression codes. Among other problems, the search space is difficult to define and the gradient is hard to determine. Therefore, the advanced control object model is used to obtain a feasible control function. The advanced model is firstly obtained before solving the optimal control problem and it already includes a trajectory motion stabilisation system; in particular, this stabilisation system is synthesised in advance at the control system design stage. When the optimal control problem appears, it is solved in real time in the classical statement, and a control function is searched for as a function of time. The advanced control object model also uses the reference model to generate the optimal trajectory. The search for the optimal control function is performed in real time and considers the synthesised stabilisation system of motion along a determined trajectory. Machine learning control via symbolic regression, namely, the network operator method, is used to directly solve the control synthesis problem. An example solution of the optimal control problem, with an advanced model moving in the environment with obstacles for a group of two mobile robots, is presented. The obtained solution is a control function for a reference model that generates a trajectory from a class of trajectories stabilised with the object’s control system.

The main steps of the synthesis of the control of DC-DC converters based on Matlab are discussed in the manuscript. Shown is the implementation and setup of 3 types of controllers used in a specific example Boost DC-DC converter: classic PID, neural network, and Fuzzy. For some of the cases, the source code is also given, thus the examples presented are useful both for the purposes of training in power electronics and for the specialists-designers of power electronic devices. [ABSTRACT FROM AUTHOR]

Background. The paper contains a refined statement of the optimal control problem, the solution of which, in contrast to the classical formulation, can be implemented directly in a real object. For this purpose, the optimal control problem includes the problem of synthesis of the stabilisation system of the object motion along the optimal trajectory, which is obtained as a result of solving the classical optimal control problem. Materials and methods. To solve the problem of stabilisation system synthesis the method of symbolic regression, method of network operator, was applied. The real control object contains a reference model of the control object for generating the program trajectory. An example of the solution of the refined optimal control problem of the spatial motion of a quadrocopter with phase constraints is presented. In the first step, the optimal control problem was solved in the classical formulation and the control function was found in the form of a piecewise linear approximation as a time function. The problem was solved using a direct approach in which the accuracy of reaching the final state and the penalties for violating the phase constraints were included in a single function together with a given quality criterion. An evolutionary algorithm was used for the solution, which found sixty-eight parameters. To confirm the poor feasibility of the solution found, a simulation of the solution obtained with a small perturbation of the initial conditions was carried out. As a result, the solution did not reach the final state and the phase constraints were significantly violated. In the second stage, a refined optimal control problem was solved, in which the synthesis problem of motion stabilisation along this trajectory was solved for the obtained program trajectory. When solving the synthesis problem, the initial state was changed to a set of initial states, and the target function was the sum of values of a given criterion for all initial states. To verify the feasibility of the obtained solution, a simulation of the control system with perturbed initial values was carried out. Results and conclusions. The simulation results showed that all perturbed trajectories reached the final state practically without violating the phase constraints. In this paper, it is assumed that the obtained stabilisation system works for trajectories of a certain class. To confirm this assumption, another optimal control problem was solved with the same phase constraints but with a different trajectory of their circumvention. The same stabilisation system was used for the obtained optimal control. Modelling of the perturbed solution confirmed the assumption.

An attempt to construct a universal stabilisation system that ensures the object motion along specified trajectory from certain class is presented. If such a stabilisation system is constructed, then only the problem of optimal control is solved, but for a model of the object, which includes a stabilisation system and a subsystem with a reference model for generating a specified trajectory. In this case, the desired control is the control in the reference model. Statement of complete optimal control problem includes two problems, optimal control problem and stabilisation system synthesis problem for motion along given trajectory in the state space. Numerical methods for solving these problems based on evolutionary computation and symbolic regression are described. It is shown that when solving the stabilisation system synthesis problem, it is possible to obtain a universal system that provides stabilisation of the object motion relative to any trajectory from a certain class. Therefore, it is advisable to formulate an optimal control problem for an object with a motion stabilisation system. A computational example of solving the problem for the spatial motion of a quadrocopter is given. [ABSTRACT FROM AUTHOR]

Direct ethanol fuel cells (DEFCs) technology as a promising clean-energy, is obstructed by unsatisfactory activity of ethanol oxidation reaction (EOR) nanocatalysts. Traditional shape-controllers usually lead to regular nanoparticles. Three-dimensional dendrimers, like hyperbranched polyamide (HBPA), however, have superiorities to form irregular morphologies, due to their multitudinous terminal functional groups and irregular interior cavities. Considering the lack of researches, herein, a novel HBPA was utilized to facilely and controllably synthesize irregular gravel-like PtPd nanoparticles (g-PtPd-NPs) with rich active sites. The synthetic mechanism was studied by both experiments and density functional theory calculations. N atoms of HBPA were proven essential. In EOR tests, the activity of g-PtPd-NPs was 2.05-fold of commercial Pt/C, and higher than PtPd catalysts of control sets and reports. The durability was excellent, too. This study is promotive for DEFCs into practice, and may enlighten more nanomaterials' synthesis. [Display omitted] • Irregular gravel-like PtPd nanoparticles were prepared facilely and controllably. • A novel 3D hyperbranched polyamide was adopted for shape-controlling. • The synthetic mechanism was studied by combining experiments and DFT calculations. • The product exhibited excellent catalytic properties in ethanol oxidation reaction. [ABSTRACT FROM AUTHOR]

We consider the problem of automatically synthesizing a hybrid controller for non-linear dynamical systems which ensures that the closed-loop fulfills an arbitrary Linear Temporal Logic specification. Moreover, the specification may take into account logical context switches induced by an external environment or the system itself. Finally, we want to avoid classical brute-force time- and space-discretization for scalability. We achieve these goals by a novel two-layer strategy synthesis approach, where the controller generated in the lower layer provides invariant sets and basins of attraction, which are exploited at the upper logical layer in an abstract way. In order to achieve this, we provide new techniques for both the upper- and lower-level synthesis. Our new methodology allows to leverage both the computing power of state space control techniques and the intelligence of finite game solving for complex specifications, in a scalable way.

The essential step of abstraction-based control synthesis for nonlinear systems to satisfy a given specification is to obtain a finite-state abstraction of the original systems. The complexity of the abstraction is usually the dominating factor that determines the efficiency of the algorithm. For the control synthesis of discrete-time nonlinear stochastic systems modelled by nonlinear stochastic difference equations, recent literature has demonstrated the soundness of abstractions in preserving robust probabilistic satisfaction of $\omega$-regular linear-time properties. However, unnecessary transitions exist within the abstractions, which are difficult to quantify, and the completeness of abstraction-based control synthesis in the stochastic setting remains an open theoretical question. In this article, we address this fundamental question from the topological view of metrizable space of probability measures, and propose constructive finite-state abstractions for control synthesis of probabilistic linear temporal specifications. Such abstractions are both sound and approximately complete. That is, given a concrete discrete-time stochastic system and an arbitrarily small $\mathcal{L}^{1}$-perturbation of this system, there exists a family of finite-state controlled Markov chains that both abstracts the concrete system and is abstracted by the slightly perturbed system. In other words, given an arbitrarily small prescribed precision, an abstraction always exists to decide whether a control strategy exists for the concrete system to satisfy the probabilistic specification.

This paper develops a novel control synthesis approach for a wide class of practical systems. The control action is derived by inserting a compensator device in the forward path of the system that is to be controlled. The compensator design method is based on a state space system that is embedded in the frequency domain of the plant. It uses a nonlinear subspace that is the image of the compensator being used to determine the parameters of the compensator and modify system behavior. The coordinates of the state space system are taken as the compensator’s parameters. The method is capable of designing a compensator of arbitrary order to make the system comply with given stability/performance requirements provided that these requirements can be geometrically-interpreted in the frequency domain. The approach is developed and a proof of its ability to converge, if a solution exists, to the compensator’s tuning parameter set that satisfy the desired performance conditions is provided. A set of design examples are supplied to demonstrate the applicability of the approach to different types of linear, nonlinear, SISO and MIMO systems and system with delays.

The extended optimal control problem is considered. It is necessary to find an optimal control function, that not only provides the achievement of terminal state with optimal value of the given quality criterion, but also is implemented in the control system of a real object. It means, that the control function should depend on the state space vector, and the optimal solution should keep optimality property at small perturbations of the found solution. To solve this problem machine learning control by symbolic regression is used. In the extended optimal control problem, the problem statement of stabilization system synthesis for movement along the optimal trajectory is included. Synthesis problem is solved by the network operator method. In the synthesis problem a domain of initial conditions is considered instead of one point of initial state. It provides less sensitivity of found solution to perturbations of initial states. An example of solving the extended optimal control problem with complex phase constraints in the form of bottleneck for four quadcopters is presented. [ABSTRACT FROM AUTHOR]

This paper considers the difficulties that arise in the implementation of solutions to the optimal control problem. When implemented in real systems, as a rule, the object is subject to some perturbations, and the control obtained as a function of time as a result of solving the optimal control problem does not take into account these factors, which leads to a significant change in the trajectory and deviation of the object from the terminal goal. This paper proposes to supplement the formulation of the optimal control problem. Additional requirements are introduced for the optimal trajectory. The fulfillment of these requirements ensures that the trajectory remains close to the optimal one under perturbations and reaches the vicinity of the terminal state. To solve the problem, it is proposed to use numerical methods of machine learning based on symbolic regression. A computational experiment is presented in which the solutions of the optimal control problem in the classical formulation and with the introduced additional requirement are compared. [ABSTRACT FROM AUTHOR]

The article presents an approach based on machine learning with symbolic regression for the synthesis of a stabilization system for a mobile robot. This approach is universal and allows you to numerically solve the synthesis problem in a general setting without the need to form a training sample, instead relying only on the value of the functional. The synthesis is implemented to stabilize the mobile robot Rosbot in the Gazebo simulation environment. The feedback stabilization system is received by the network operator method. The advantage of the method is that it can be applied to a control object of any complexity and linearity. [ABSTRACT FROM AUTHOR]

This paper studies the synthesis of controllers for cyber-physical systems (CPSs) that are required to carry out complex time-sensitive tasks in the presence of an adversary. The time-sensitive task is specified as a formula in the metric interval temporal logic (MITL). CPSs that operate in adversarial environments have typically been abstracted as stochastic games (SGs); however, because traditional SG models do not incorporate a notion of time, they cannot be used in a setting where the objective is time-sensitive. To address this, we introduce durational stochastic games (DSGs). DSGs generalize SGs to incorporate a notion of time and model the adversary's abilities to tamper with the control input (actuator attack) and manipulate the timing information that is perceived by the CPS (timing attack). We define notions of spatial, temporal, and spatio-temporal robustness to quantify the amounts by which system trajectories under the synthesized policy can be perturbed in space and time without affecting satisfaction of the MITL objective. In the case of an actuator attack, we design computational procedures to synthesize controllers that will satisfy the MITL task along with a guarantee of its robustness. In the presence of a timing attack, we relax the robustness constraint to develop a value iteration-based procedure to compute the CPS policy as a finite-state controller to maximize the probability of satisfying the MITL task. A numerical evaluation of our approach is presented on a signalized traffic network to illustrate our results. [ABSTRACT FROM AUTHOR]

In this article, an upper bound on the settling time is provided for exponentially stable systems by the Lyapunov theory. In order to obtain a more accurate estimate on the upper bound of settling time, an optimization problem with a nonlinear objective function needs to be solved. Since this is a complex problem, a linear matrix inequality–based algorithm is proposed to solve it. Then, we address the stability analysis problem of linear systems with the aim to derive the upper bound on the settling time. This problem is extended to design a static feedback controller for linear systems under input saturation. By solving the optimization problem, the upper bound of the settling time for the closed-loop system is minimized. Finally, the validity and effectiveness of the proposed method are verified by the simulation results and comparisons. [ABSTRACT FROM AUTHOR]

The problem of a stabilisation system synthesis for the motion of a control object along a given spatial trajectory is considered. The complexity of the problem is that the preset trajectory is defined in the state subspace and not in time. This paper describes a stabilisation system synthesis for motion along a trajectory specified in time and along a trajectory specified in the form of a manifold in a state space. In order to construct a stabilisation system, it is necessary to determine a distance between an object and the given trajectory at each moment in time. For trajectories that are not given in time, the determination of this distance can be ambiguous. An object may be exactly on a trajectory but at a different time. This paper proposes some approaches to solve the problem. One of the approaches is to transform a given trajectory in a state subspace into a trajectory given in time. A description of a universal method to perform this transformation is presented. In order to solve the synthesis problem automatically, without having to analyse the mathematical model of the control object, it is suggested that machine learning control by symbolic regression is used. In computational experiments, examples of stabilisation system syntheses for quadcopter motion along a given spatial trajectory are presented.

The solution of the optimal control problem in the classical formulation is control in the form of a function of time. The implementation of such a solution leads to an open-loop control system and, therefore, cannot be applied directly in practice. It is believed that solving the classical optimal control problem leads to an optimal control program and a program trajectory in state space. To implement the motion of the control object along the program trajectory, it is necessary to build an additional motion stabilization system. The problem of synthesizing a system for stabilizing motion along a program trajectory and the requirements that this system should meet do not arise from the classical setting of the optimal control problem. A refined statement of the optimal control problem is given that includes an additional requirement for an optimal trajectory and the solution of which can be directly applied in practice in a real control object. [ABSTRACT FROM AUTHOR]

We consider a method for the approximate solution of solvability and control synthesis problems for a nonlinear autonomous system of ordinary differential equations on a fixed time interval. The proposed method is based on the hybridization of equations and passage to equivalent problems for a piecewise linear system. Next, the value function is constructed as an approximate solution of the Hamilton–Jacobi–Bellman equation, and the comparison principle is applied. The solution is chosen from the class of piecewise quadratic functions. To improve the accuracy of the method, the value function is assumed to have discontinuities on certain sets in the state space. We propose a numerical algorithm for feedback control computation and obtain an a priori estimate for the error of reaching the target set for the original nonlinear system. [ABSTRACT FROM AUTHOR]

A control system of an autonomous robot produces a control signal based on feedback. This type of control implies the control of an object according to its state that is mathematically the control synthesis problem. Today there are no universal analytical methods for solving the general synthesis problem, and it is solved by certain particular approaches depending on the type of control object. In this paper, we propose a universal numerical approach to solving the problem of optimal control with feedback using machine learning methods based on symbolic regression. The approach is universal and can be applied to various objects. However, the use of machine learning methods imposes two aspects. First, when using them, it is necessary to reduce the requirements for optimality. In machine learning, optimization algorithms are used, but strictly optimal solutions are not sought. Secondly, in machine learning, analytical proofs of the received properties of solutions are not required. In machine methods, a set of tests is carried out and it is shown that this is sufficient to achieve the required properties. Thus, in this article, we initially introduce the fundamentals of machine learning control, introduce the basic concepts, properties and machine criteria for application of this technique. Then, with regard to the introduced notations, the feedback optimal control problem is considered and reformulated in order to add to the problem statement that such a property adjusts both the requirements of stability and optimality. Next, a description of the proposed approach is presented, theoretical formulations are given, and its efficiency is demonstrated on the computational examples in mobile robot control tasks. [ABSTRACT FROM AUTHOR]

Convolutional and recurrent neural networks (RNNs) have been widely used to achieve state-of-the-art performance on classification tasks. However, it has also been noted that these networks can be manipulated adversarially with relative ease, by carefully crafted additive perturbations to the input. Though several experimentally established prior works exist on crafting and defending against attacks, it is also desirable to have rigorous theoretical analyses to illuminate conditions under which such adversarial inputs exist. This article provides both the theory and supporting experiments for real-time attacks. The focus is specifically on recurrent architectures and inspiration is drawn from dynamical systems’ theory to naturally cast this as a control problem, allowing dynamic computation of adversarial perturbations at each timestep of the input sequence, thus resembling a feedback controller. Illustrative examples are provided to supplement the theoretical discussions. [ABSTRACT FROM AUTHOR]

An attempt to construct a universal stabilisation system that ensures the object motion along specified trajectory from certain class is presented. If such a stabilisation system is constructed, then only the problem of optimal control is solved, but for a model of the object, which includes a stabilisation system and a subsystem with a reference model for generating a specified trajectory. In this case, the desired control is the control in the reference model. Statement of complete optimal control problem includes two problems, optimal control problem and stabilisation system synthesis problem for motion along given trajectory in the state space. Numerical methods for solving these problems based on evolutionary computation and symbolic regression are described. It is shown that when solving the stabilisation system synthesis problem, it is possible to obtain a universal system that provides stabilisation of the object motion relative to any trajectory from a certain class. Therefore, it is advisable to formulate an optimal control problem for an object with a motion stabilisation system. A computational example of solving the problem for the spatial motion of a quadrocopter is given.

The extended optimal control problem is considered. It is necessary to find an optimal control function, that not only provides the achievement of terminal state with optimal value of the given quality criterion, but also is implemented in the control system of a real object. It means, that the control function should depend on the state space vector, and the optimal solution should keep optimality property at small perturbations of the found solution. To solve this problem machine learning control by symbolic regression is used. In the extended optimal control problem, the problem statement of stabilization system synthesis for movement along the optimal trajectory is included. Synthesis problem is solved by the network operator method. In the synthesis problem a domain of initial conditions is considered instead of one point of initial state. It provides less sensitivity of found solution to perturbations of initial states. An example of solving the extended optimal control problem with complex phase constraints in the form of bottleneck for four quadcopters is presented.

This article studies the problem of synthesis with guaranteed cost and less human intervention for linear human-in-the-loop (HiTL) control systems. Initially, the human behaviors are modeled via a hidden controlled Markov process, which not only considers the inference’s stochasticity and observation’s uncertainty of the human internal state but also takes the control input to human into account. Then, to integrate both models of human and machine as well as their interaction, a hidden controlled Markov jump system (HCMJS) is constructed. With the aid of the stochastic Lyapunov functional together with the bilinear matrix inequality technique, a sufficient condition for the existence of human-assistance controllers is derived on the basis of the HCMJS model, which not only guarantees the stochastic stability of the closed-loop HiTL system but also provides a prescribed upper bound for the quadratic cost function. Moreover, to achieve less human intervention while meeting the desired cost level, an algorithm that mixes the particle swarm optimization and linear matrix inequality technique is proposed to seek a suitable feedback control law to the human and a human-assistance control law to the machine. Finally, the proposed method is applied to a driver-assistance system to verify its effectiveness. [ABSTRACT FROM AUTHOR]

A numerical solution of the problem of the general synthesis of a stabilization system by a symbolic regression method is considered. The goal is to automatically find a feedback control function using a computer so that the control object can reach a given terminal position from anywhere in a given region of the initial conditions with an optimal value of the quality criterion. Usually, the control synthesis problem is solved analytically or technically taking into account the specific properties of the mathematical model. We suppose that modern numerical approaches of symbolic regression can be applied to find a solution without reference to specific model equations. It is proposed to use the numerical method of Cartesian genetic programming (CGP). It was developed for automatic writing of programs but has never been used to solve the synthesis problem. In the present work, the method was modified with the principle of small variations in order to reduce the search area and increase the rate of convergence. To apply the general principle of small variations to CGP, we developed special types of variations and coding. The modified CGP searches for the mathematical expression of the feedback control function in the form of a code and, at the same time, the optimal value of the parametric vector which is also a new feature—simultaneous tuning of the parameters inside the search process. This approach enables working with objects and functions of any type, which is not always possible with analytical methods. The need to use the received solution on the onboard processor of the control object imposes certain restrictions on the used basic set of elementary functions. This article proposes the theoretical foundations of the study of these functions, and the concept of the space of machine-made functions is introduced. The capabilities of the approach are demonstrated on the numerical solution of the control system synthesis problems for a mobile robot and a Duffing model. [ABSTRACT FROM AUTHOR]

The article presents an approach based on machine learning with symbolic regression for the synthesis of a stabilization system for a mobile robot. This approach is universal and allows you to numerically solve the synthesis problem in a general setting without the need to form a training sample, instead relying only on the value of the functional. The synthesis is implemented to stabilize the mobile robot Rosbot in the Gazebo simulation environment. The feedback stabilization system is received by the network operator method. The advantage of the method is that it can be applied to a control object of any complexity and linearity.

This paper considers the difficulties that arise in the implementation of solutions to the optimal control problem. When implemented in real systems, as a rule, the object is subject to some perturbations, and the control obtained as a function of time as a result of solving the optimal control problem does not take into account these factors, which leads to a significant change in the trajectory and deviation of the object from the terminal goal. This paper proposes to supplement the formulation of the optimal control problem. Additional requirements are introduced for the optimal trajectory. The fulfillment of these requirements ensures that the trajectory remains close to the optimal one under perturbations and reaches the vicinity of the terminal state. To solve the problem, it is proposed to use numerical methods of machine learning based on symbolic regression. A computational experiment is presented in which the solutions of the optimal control problem in the classical formulation and with the introduced additional requirement are compared.

This paper studies the synthesis of controllers for cyber-physical systems (CPSs) that are required to carry out complex time-sensitive tasks in the presence of an adversary. The time-sensitive task is specified as a formula in the metric interval temporal logic (MITL). CPSs that operate in adversarial environments have typically been abstracted as stochastic games (SGs); however, because traditional SG models do not incorporate a notion of time, they cannot be used in a setting where the objective is time-sensitive. To address this, we introduce durational stochastic games (DSGs). DSGs generalize SGs to incorporate a notion of time and model the adversary’s abilities to tamper with the control input (actuator attack) and manipulate the timing information that is perceived by the CPS (timing attack). We define notions of spatial, temporal, and spatio-temporal robustness to quantify the amounts by which system trajectories under the synthesized policy can be perturbed in space and time without affecting satisfaction of the MITL objective. In the case of an actuator attack, we design computational procedures to synthesize controllers that will satisfy the MITL task along with a guarantee of its robustness. In the presence of a timing attack, we relax the robustness constraint to develop a value iteration-based procedure to compute the CPS policy as a finite-state controller to maximize the probability of satisfying the MITL task. A numerical evaluation of our approach is presented on a signalized traffic network to illustrate our results.

This paper proposes an innovative automatic carrier landing control law for carrier-based aircraft considering complex ship motion and wind environment. Specifically, a strategy is proposed to synthesize preview control with an adaptive nonlinear control scheme. Firstly, incremental nonlinear backstepping control law is adopted in the attitude control loop to enhance the anti-disturbance capability of the aircraft. Secondly, to enhance the glide slope tracking performance under severe sea conditions, the carrier motion is predicted, and the forecasted motion is adopted in an optimal preview control guidance law to compensate influences induced by carrier motion. However, synthesizing the inner-loop and outer-loop control is not that straightforward since the preview control is naturally an optimal control law which requires a state-space model. Therefore, low-order equivalent fitting of the attitude-to-altitude high-order system model needs to be performed; furthermore, a state observer needs to be designed for the low-order equivalent system to supply required states to the landing controller. Finally, to validate the proposed methodology, an unmanned tailless aircraft model is used to perform the automatic landing tasks under variant sea conditions. Results show that the automatic carrier landing system can lead to satisfactory landing precision and success rate even under severe sea conditions.

In this paper, WO3 nanowires were successfully synthesized via a one-step water bath method at an appropriate temperature. The XRD (Energy Dispersive Spectrometer), SEM (Scanning electron microscope), TEM (Transmission Electron Microscope) and other characterization methods proved that the synthesized product was WO3, and the product of water bath reaction for 9 h showed the nanowires' structure. The nanowires were evenly distributed, and the length ranged from 2 μm to 4 μm. The results showed that the nanowires had excellent light transmittance (66%), a very short response time (1.2 s, 2 s) and excellent color rendering efficiency (115.2 cm2 C−1) at 650 nm. The electrochemical performance test showed that the specific capacity of the WO3 nanowires was up to 565 F/g at 1 A/g. Change the different current densities and cycle 100 times, then return to the initial current density, accounting for 99% of the initial specific capacity of 565 F/g. We used this method for the first time to prepare tungsten oxide nanowires and investigated the bifunctional properties of the material, namely the electrochromic and capacitive properties. All of these data indicate that WO3 nanorods have excellent electrochromic and electrochromic properties and have potential market prospects in the fields of electrochromic glass, variable glasses, advertising, and supercapacitors. [ABSTRACT FROM AUTHOR]