Control System Synthesis Problem Research Articles

Problem of synthesis of the control system for a group of unmanned ground vehicles

The substantive and formal formulation of the control system synthesis problem for a group of unmanned ground vehicles (UGV) are considered in the article. The decomposition of this problem into a number of particular scientific problems is carried out, such as the problem of substantiating a structure of the control system, developing a method for determining the emergence of the control system, and developing a method for accessing the quality of a control system and the effectiveness of its application. It is shown that the distinctive features of the problem are the stochastic nature of the performance indicator (a probability of achieving the goal of the mission), the uncertainty of the conditions for applying the UGV’s group, and the large size of the design space of the control system. The problem of design space growth is demonstrated by a methodical example. To reduce the complexity of analyzing the size of the design space, we propose the decomposition approach consisting in substantiating the basic version of the structure of the control system and its initial decomposition. The novelty in the implementation of this approach lies in the joint consideration of the «group control method» and the principle of hierarchical of the group control system. This approach allows us to obtain basic solutions for the structure of the control system, and then carry out a parametric synthesis of the control system and conduct a comparative assessment of solutions according to the «Quality-Costs» concept.

МЕТОДИКА СИНТЕЗА СТАНЦИОННЫХ СИСТЕМ ЖЕЛЕЗНОДОРОЖНОЙ АВТОМАТИКИ И ТЕЛЕМЕХАНИКИ С ПРОГРАММИРУЕМОЙ ЛОГИКОЙ С ПРИМЕНЕНИЕМ МОДЕЛИ КОНЕЧНЫХ АВТОМАТОВ

The main advantages of microprocessor systems of railway automation and remote control in relation to relay systems, as well as the advantages of using field-programmable gate array (FPGAs) in comparison with microprocessors for solving control system synthesis problems are presented. Examples of the possibility of using FPGAs in devices and systems of railway automation and remote control are given. The possibility of synthesizing a finite state machine on an FPGA that implements route dependencies at an arbitrary station is considered. For this purpose, the logic of the operation of railway automation and remote control devices is described, all possible states of the designed device are identified and the conditions of transitions between them are recorded. A method of synthesis of a finite state machine implementing route dependencies based on building up graphs of typical devices has been formed. The advantage of this approach is the possibility of synthesizing railway automation and remote control devices according to specified logical algorithms, using a modern element base.

Machine-Made Synthesis of Stabilization System by Modified Cartesian Genetic Programming

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.

Synthesis of sliding control system for automotive suspension under kinematic constraints

This article is about the problem of control system synthesis for an active suspension system with not-ideal actuator under kinematic constrains. This paper investigates the influence of hysteresis and the dead zone in an actuator on efficiency of an active suspension system. To reduce the influence of hysteresis and the dead zone a method of synthesis of discontinuous control systems is proposed. The proposed discontinuous control system reduces the sensitivity of the system to disturbances caused by a non-ideal actuator. It enables a fourfold expansion of the distribution range where an active suspension is more effective than a passive suspension. This system also takes into account the nonlinear structure of the control object. The efficiency of the closed system is studied on a dynamic model constructed using the Simulink package.

Autonomous wheeled mobile robot maneuvering in constraint environment. Trajectory tracking quality criteria

In this article the problem of control system synthesis for differential drive wheeled mobile robots operating within constraint environment is considered. The proposed approaches of solving trajectory tracking problem take into account the geometric features of both the robot and the transported cargo. The collision avoidance problem is solved at the controller level, without any changes to the planned trajectory. Three approaches are proposed: minimizing the distance to the trajectory, minimizing the distance to the reference position, and maximizing the distance to obstacles. In these approaches the constant analysis of position of each point of robot’s body outline contour is used. Negative influence of the position of these points on qualitative trajectory pass is represented in vector form. For each of the approaches formalized tracking quality criteria are determined, methods of implementation of control systems and controllers taking into account these criteria are proposed. The part of the control signal responsible for taking into account geometry of the robot and avoiding collisions is defined via the force-moment vector representation. Results of simulation modeling prove the efficiency of the proposed approaches. A comparison of the proposed approaches is presented. Potential ways of more efficient use of these approaches are given.

A new two-step approach for solving a control system synthesis problem by symbolic regression methods

The problem of synthesizing a control system using symbolic regression methods is considered. A new approach suggested in this work considers the control system synthesis problem as the set of optimal control problems and suggests a two-step algorithm to solve it. At the first step evolutionary algorithms are used to solve the optimal control problem numerically for each initial state from a given domain. As a result of the first step a set of optimal trajectories is obtained. At the second step symbolic regression methods are considered to solve the problem of approximating the found in the first step set of trajectories optimally. The result of the second step is a solution of the control system synthesis problem as a multidimensional control function of object’s state vector. Compared to the known approach to solve the control system synthesis problem using symbolic regression methods, the suggested approach provides betters results since the search of control function is carried out based on the set of optimal trajectories. Computational experiment presents the solution of the applied problem of synthesizing the optimal control system for the spacecraft landing on the Moon. It is experimentally demonstrated that the synthesized control system provides a close to optimal landing trajectory for any initial state from a given domain.

Collision Avoidance System Synthesis for a Group of Robots in Unsupervised Learning Paradigm

Collision avoidance is very important problem in the domain of multi-robot interaction. In this paper we propose a new approach of collision avoidance in the context of the optimal control system synthesis problem definition with minimal information available. It is assumed that robots have a certain scope within which they can interact with static and dynamic phase constraints. A group of robots is considered to be homogeneous, and control system unit for reaching terminal states already available to robots. The control system which is responsible for collision avoidance is only activated when the nearest neighbor is located in the scope of the considered robot. The first important feature of this work is the fact that the collision avoidance between two robots is reciprocal with joint control system, without assigning priorities. Another key feature of this work is the complete absence of information about the environment and the current state of other robots at given time. Robots only share information with nearest neighbors if they locate in the scope of each other. We also present a computational experiment with mobile robots as control objects. A multilayer perceptron was used to approximate the control function. Weights of the perceptron were optimized in unsupervised paradigm by an algorithm belonging to the evolutionary strategies class. At the beginning of each epoch we generate a sample of collision scenarios for optimization, while the quality criterion of the achieved weights at the end of epoch is evaluated on a fixed test sample. Experimental results demonstrate strong ability of the optimized multilayer perceptron to map the relative state of two mobile robots to controls in order to avoid collisions.

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The problem of adaptive control system synthesis using the local criterion is considered. The criterion selection allows you to take into account ship course errors and desired small deviations of rudder. The theoretical basis for solving this problem is the velocity gradient method. To obtain laws (algorithms) for adjusting the regulator parameters, a local quadratic quality criterion that is oriented on ensuring small deviations from the set course and keeping the ship’s heading has been chosen. Adaptive course control systems, obtained on the basis of theoretical research, are modeled in the MATLAB environment. It is shown that the originally obtained adaptation laws can be modified by coarsening due to introducing a negative feedback on the tunable parameter. The results of modeling the ship course control system under the influence of an external disturbance are also presented in the paper. The algorithm developed in the paper for setting the regulator parameters allows controlling the ship movement along the course under wind-wave action with wave amplitude of 6 degrees and the constant wave component of 6 degrees. The results of modeling the ship course control system without setting the regulator and with the setting enabled confirm the effectiveness of the proposed approach.

Resilient Event-Triggered Controller Synthesis of Networked Control Systems Under Periodic DoS Jamming Attacks.

In this paper, the event-based controller synthesis problem for networked control systems under the resilient event-triggering communication scheme (RETCS) and periodic denial-of-service (DoS) jamming attacks is studied. First, a new periodic RETCS is designed under the assumption that the DoS attacks imposed by power-constrained pulsewidth-modulated jammers are partially identified, that is, the period of the jammer and a uniform lower bound on the jammer's sleeping periods are known. Second, a new state error-dependent switched system model is constructed, including the impacts of the RETCS and DoS attacks. According to this new model, the exponential stability criteria are derived by using the piecewise Lyapunov functional. In these criteria, the relationship among DoS parameters, the triggering parameters, the sampling period, and the decay rate is quantitatively characterized. Then, a criterion is also proposed to obtain the explicit expressions of the triggering parameter and event-based state feedback controller gain simultaneously. Finally, the obtained theoretical results are verified by a satellite yaw-angles control system.

Python Package for the Network Operator Implementation and its Application for Group Control System Synthesis Problem

One of the main problems of symbolic regression methods is how to encode mathematical expressions to make the structure concise and readable. Here we address to the problem of network operator’s matrix scarcity, which we resolve using python’s standard types. Our approach allows to get rid of zero elements bellow the main diagonal. Moreover, we introduce new parametric variation, which helps us to tune parameters during structural evolving.We provide a description of the network operator and algorithms for finding the optimal solution using the principle of small variations of the basis solution. Our new encoding scheme and the complex functional for the group control task then described.In the experimental part we introduce a new way to apply network operator with a variable number of arguments to the group control system synthesis problem. Along with this we use for the first time individual network operators for each robot. From the experiment we can see that provided tricks lead to results that are not inferior in the case of usual network operator shared by all robots.

Estimation of proximity of controls synthesized on basis of maximum principle and ADAR method

Introduction. A special case of synthesizing the same electromechanical control system by the Pontryagin maximum principle and by the synergetic synthesis method is considered. The task was to solve the synthesis problem of the time optimal electromechanical position control system; herewith the travel resistance modulus linearly depended on the output coordinate of the system. This approach to the selection of the synthesis problem was because the synthesis of time optimal systems is one of the most widespread problems, and it is solved by increasing the efficiency of the existing control systems.Materials and Methods. Synthesis of the time optimal linear control system based on the maximum principle is a widely accepted problem in the modern control theory. However, the procedure of synergistic synthesis does not have such formalization. This being the case, the paper suggests an approach that brings together these two methods, which, in our opinion, will increase the efficiency of the synergistic synthesis method through adding some features of the synthesis methodology for optimal systems.Research Results. The paper formulates two key concepts. The first one is as follows: the application of the maximum principle for an object of the DC motor class when synthesizing the positioning algorithm under the conditions of linear loading functionally dependent on the engine rotation angle allows the time optimal system to be optimized. The second concept states that synthesis of a control system based on the synergistic approach enables to obtain a system close to optimal (quasioptimal), but after modifying the synergetic synthesis method itself. A hypothesis is formulated on the possible connection between the introduced (when implementing the procedure of state space extension in the synergetic synthesis method) time constants with the optimal switching time of control defined in the maximum method.Discussion and Conclusions. The synthesis through the maximum control technique and the ADAR method is performed. In virtue of the comparison of efficiency of these methods, a hypothesis is put forward on the possible compatibility of the studied methods.

ALGORITHM FOR SYNTHESIZING PARAMETERS OF CONTROL LAWS OF TECHNICAL SYSTEMS UNDER POLYNOMIAL APPROXIMATION OF NONLINEARITIES

The paper considers the algorithm for solving the problem of synthesis of automatic control systems (ACS) with nonlinear characteristics for polynomial approximation. As a mathematical apparatus, the inversion of the direct variational method of analysis, Galerkin generalized method, is applied to the solution of the problem. Recurrence relations are obtained that make it possible to extend this method to a new class of dynamical systems with nonlinear elements whose characteristics are approximated polynomially. The advantages and disadvantages of various methods of approximation of automatic control systems with nonlinear characteristics are analyzed. The presented algorithm of the software complex is universal and allows solving the synthesis problem for control systems of different classes and structures from unified mathematical, methodological and algorithmic positions.

The Comparison of Genetic Programming and Variational Genetic Programming for a Control Synthesis Problem on the Model “Predator-victim”

The work is devoted to the comparison of two methods of symbolic regression, a method of genetic programming and a variational method of genetic programming. The comparison is made on the basis of the computing experiment, which solved a problem of control system synthesis for a model of nonlinear control object, describing the interaction of the two systems of “predator” and “victim”. For the purity of the experiment the genetic algorithms parameters in the both methods were Identical. For variational genetic programming there was selected a trivial basic solution in the form of the sum of input variable products for custom settings. This basic solution is always chosen in the case of the absence of meaningful task analysis. The comparison of methods for the speed of solving the problem and for the quality of the achieved control is made.

Grammatical Evolution for Neural Network Optimization in the Control System Synthesis Problem

Grammatical evolution is a perspective branch of the genetic programming. It uses evolutionary algorithm based search engine and Backus – Naur form of domain-specific language grammar specifications to find symbolic expressions. This paper describes an application of this method to the control function synthesis problem. Feed-forward neural network was used as an approximation of the control function, that depends on the object state variables. Two-stage algorithm is presented: grammatical evolution optimizes neural network structure and genetic algorithm tunes weights. Computational experiments were performed on the simple kinematic model of a two-wheel driving mobile robot. Training was performed on a set of initial conditions. Results show that the proposed algorithm is able to successfully synthesize a control function.

Control System Synthesis by Means of Cartesian Genetic Programming

Cartesian Genetic Programming (CGP) is a type of Genetic Programming based on a program in a form of a directed graph. It also belongs to the methods of Symbolic Regression allowing to receive the optimal mathematical expression for a problem. Nowadays it becomes possible to use computers very effectively for symbolic regression calculations. CGP was developed by Julian Miller in 1999-2000. It represents a program for decoding a genotype (string of integers) into the phenotype (graph). The nodes of that graph contain references to functions from a function table, which could contain arithmetic, logical operations and/or user-defined functions. The inputs of those functions are connected to the node inputs, which itself could be connected to a node output or a graph input. As a result, it's possible to construct several mathematical expressions for the outputs and calculate them for the given inputs. This CGP implementation use point mutation to form new mathematical expressions. Steady-state genetic algorithm is chosen as a search engine. Solution solving the control system synthesis problem is presented in a form of the Pareto set, which contains a set of satisfactory control functions. Nonlinear Duffing oscillator is taken as a dynamic object.

СИНТЕЗ УПРАВЛЕНИЯ ДЛЯ АВТОНОМНОЙ ГРУППЫ РОБОТОВ С ФАЗОВЫМИ ОГРАНИЧЕНИЯМИ МЕТОДОМ МНОГОСЛОЙНОГО СЕТЕВОГО ОПЕРАТОРА С РАССТАНОВКОЙ ПРИОРИТЕТОВ

We consider a control system synthesis problem for the small group of autonomous robots with state constraints and several possible initial conditions. The main control task for team of robots is to move the robots out of some current position to the specified terminal position without colliding with each other. Typically, the control synthesis for the group of robots consists of two phases: stabilization of the robot with respect to some point of the state space and the design of optimal trajectories. The trajectories must ensure that the robots move from the initial states to certain states of the terminal set without collisions. To avoid collision, the control system uses priorities based, for example, on a distance between the robot and its end position. Since there are phase constraints, ordinary stabilization of robots cannot ensure the safe movement of robots from different initial conditions to the terminal positions. The paper presents our new approach to solving the stabilization problem with phase constraints by multi-layer network operator. We show an example of synthesis of control for the group of four robots.

Variational Genetic Programming for Optimal Control System Synthesis of Mobile Robots

The paper focuses on the problem of autonomous control system synthesis for the mobile robot. The proposed numerical solution is based on a new method of symbolic regression called variational genetic programming. This method uses the principle of variations of the basic solution. An optimal solution is searched over the set of small variations of the given basic solution. Such approach allows to generate automatically a control function that describes the feedback controller. In the given example the control system is synthesized using variational genetic programming for the unmanned mobile robot that has to move to some terminal position from the different initial states avoiding obstacles.

Control synthesis problem for networked linear sampled-data control systems with band-limited channels

This paper addresses the control synthesis problem of networked linear sampled-data control systems (NLSCSs) with band-limited channels. First, since there exist packet dropouts when the information is transmitted through the band-limited channels, a novel compression compensation (C–C) method is proposed to ensure the integrity of transmission. Based on this method, a compound control strategy is established to deal with the data transmission synchronization problem under the band-limited channels. Then, a nonlinear switched system model with uncertainty is constructed, in which both the inter-sampler behavior and the packet dropouts behavior are considered. Furthermore, some more general stability results of the NLSCSs with band-limited channels are obtained by using a packet dropouts dependent Lyapunov functional method, and then the compound state feedback controller can be designed. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed results.

Riccati equations for generalized singular estimate control systems

We consider the Bolza problem associated with boundary/point control systems governed by strongly continuous semigroups. In continuation of our work in Lasiecka and Tuffaha [I. Lasiecka and A. Tuffaha, Riccati equations for the Bolza problem arising in boundary/point control problems governed by C 0–semigroups satisfying a singular estimate, J. Optim. Theory Appl. 136 (2008), pp. 229–246; I. Lasiecka and A. Tuffaha, A Bolza optimal synthesis problem for singular estimate control systems, Control Cybernet 38(4B) (2009), pp. 1429–1460], we yet extend the theory to a more general class of control problems that are not analytic providing sharp blow-up rates for the regularity. Solvability of the associated Riccati equations and an optimal feedback synthesis are established. The presence of unbounded control actions, such as boundary/point controls, naturally lead to a singularity at the terminal point t = T of the optimal control and of the corresponding feedback operator as before. The class of control systems considered in this article is a generalization to the class usually referred to in the literature as ‘Singular Estimate Control Systems’. The prototype is still that of a PDE system consisting of coupled hyperbolic parabolic dynamics interacting on an interface with point/boundary control. The distinct feature of the class considered in this article is that the degree of unboundedness in the control is stronger than that allowed in the usual singular estimate control system configuration, giving rise to less regular optimal state trajectories.

H∞ Control Synthesis for Lurie Networked Control Systems with Multiple Delays Based on the Non‐Uniform Characteristic

AbstractThis paper investigates the H ∞ control synthesis problem for Lurie networked control systems (NCSs) with multiple time‐varying delays. With the consideration of both network‐induced delays and data packet dropout, Lurie NCSs discussed in this work can effectively be transformed into Lurie control systems with multiple time‐varying delays. In addition, with the non‐uniform distribution characteristics of network delays, based on the delay probability distribution, the stable controller design, and H ∞ synthesis, approaches are derived in the form of linear matrix inequalities (LMIs). Finally, a set of numerical examples are studied, and the results demonstrate the applicability and effectiveness of the suggested approaches.