Quadratic Optimization Criterion Research Articles

NON-ANALYTICAL DESIGN OF THE PI CONTROLLER OPTIMAL PARAMETERS FOR A CONTINUOUS LINE

The multiple motor drives are complex and coupled MIMO nonlinear systems. Due to the complexity of their mathematical models the development of effective control systems is quite complicated task. This paper presents the design of optimal control based on the quadratic optimality criterion for the central section of the continuous production line using soft computer methods when fuzzy model of the controlled system has been used. In this case, the proposed method demonstrates non-analytical design of the optimal parameters of PI controller with emphasis on minimal knowledge on the controlled system. The realized experimental measurements on a continuous line laboratory model confirmed the effectiveness and the good dynamic properties of the optimal continuous line controller and also its applicability to others MIMO nonlinear dynamic systems.

Adaptive optimal sliding-mode fault-tolerant control for nonlinear systems with disturbances and estimation errors

This paper gives a fault-tolerant control scheme concerning with the optimal and near-optimal system performance for a class of nonlinear systems with time-varying actuator faults, time-varying disturbances, and identification errors of the neural network-based identifier. In this paper, the adaptive dynamic programming method is directly used to design the optimal sliding surface, so that the designer can design the target dynamics of the sliding mode in advance. In addition, the barrier function-based sliding-mode control is used to cope with the bounded but boundary-unknown estimation errors of the identifier, and the method ensures that the sliding-mode variable converges to the designer’s predefined neighborhood of zero in finite time and the control gain is not overestimated. Specifically, first, by adaptive dynamic programming, near-optimal sliding surface is designed in the sense of the quadratic optimal criterion. Second, a neural network identifier is designed to model the lumped uncertainties including actuator faults and disturbances. Third, a barrier function-based adaptive sliding-mode control is used to cope with the identification errors of the neural network identifier and has no control gain overestimation, which can guarantee to confine the sliding variable to a predefined vicinity of the proposed sliding surface. For this system with faults and disturbances, it is shown that near-optimal property is achieved by this scheme, the chattering phenomenon is effectively suppressed, and the reconstruction error of the neural network identifier with unknown boundary is effectively handled by the adaptive sliding-mode control based on the barrier function. The proof of stability is given by Lyapunov’s direct method and the effectiveness of this control scheme is verified by applying it to the spacecraft attitude system.

Investigation of secure routing models based on basic vulnerability metrics in SDN networks

The article presents and investigates flow-based models of secure routing under base score metrics of vulnerability criticality in Software-Defined Networks (SDN). The analysis of the routing means functionality against possible attacks confirmed the perspective of their application, taking into account the base score metrics of vulnerability criticality to increase the level of network security of the SDN data plane. It is proposed to improve the existing secure routing model taking into account the base score metrics of vulnerability criticality by modifying the routing metrics so that the resulting model acquires the properties of secure QoS routing. In the improved model, the optimal route was chosen considering base score metrics of vulnerability criticality and the bandwidth of the communication links that make up this route. In addition, the quadratic optimality criterion is used in the model for the balanced distribution of flows transmitted in the data plane of the software-defined network into sub-flows taking into account the multipath routing strategy. The comparative analysis of the existing secure routing model, the QoS-routing model with metrics similar to the OSPF protocol, and the improved secure-QoS-routing model taking into account the base score metrics of vulnerability criticality proved the adequacy and efficiency of the model proposed in work. The comparison of models was based on calculating the compromise probability of the transmitted packet flow.

Comparative Study of Markov Chain Filtering Schemas for Stabilization of Stochastic Systems under Incomplete Information

The object under investigation is a controllable linear stochastic differential system affected by some external statistically uncertain piecewise continuous disturbances. They are directly unobservable but assumed to be a continuous-time Markov chain. The problem is to stabilize the system output concerning a quadratic optimality criterion. As is known, the separation theorem holds for the system. The goal of the paper is performance analysis of various numerical schemes applied to the filtering of the external Markov input for system stabilization purposes. The paper briefly presents the theoretical solution to the considered problem of optimal stabilization for systems with the Markov jump external disturbances: the conditions providing the separation theorem, the equations of optimal control, and the ones defining the Wonham filter. It also contains a complex of the stable numerical approximations of the filter, designed for the time-discretized observations, along with their accuracy characteristics. The approximations of orders 12, 1, and 2 along with the classical Euler–Maruyama scheme are chosen for the comparison of the Wonham filter numerical realization. The filtering estimates are used in the practical stabilization of the various linear systems of the second order. The numerical experiments confirm the significant influence of the filtering precision on the stabilization performance and superiority of the proposed stable schemes of numerical filtering.

Advanced Tensor Solution to the Problem of Inter-Domain Routing with Normalized Quality of Service

The advanced tensor solution to the problem of inter-domain routing with normalized Quality of Service under hierarchical coordination in a communication network is proposed in the paper. The novelty of the method based on the tensor model lies in the more flexible load balancing over the network due to the presence of requirements to average end-to-end delay of packets. The framework of the method comprises a decomposed flow-based routing model that includes the inter-domain routing interaction conditions and ensures the normalized Quality of Service derived from the tensor model. Considering the mentioned above, the advanced inter-domain Quality of Service routing task was formulated in the optimization form, using the quadratic optimality criterion. The conducted analysis of the numerical research results confirmed the efficiency and adequacy of the proposed method when the desired solutions were obtained during the finite number of iterations under a provision of the normalized Quality of Service. It should be noted that the reduced number of such iterations during the operation of the method will decrease the amount of service traffic transmitted over the network needed for obtaining the final solution in the process of inter-domain routing with normalized Quality of Service.

Research and Development of the Secure Routing Flow-Based Model with Load Balancing

The article is devoted to developing and researching the model of secure routing with load balancing in SD-WAN-based networks. In addition, an analysis of numerical research results using Python, GEKKO Optimization Suite, and NumPy has been carried out. The technical task of secure routing with load balancing was formulated as an optimization problem with quadratic optimality criterion. Such a criterion form allows for balancing the flow shares transmitting in the network. The simulation results showed that the link load (namely, the transmitted part of the flow) under study decreases with an increased probability of the link compromise. The analysis of the calculated results revealed the value of the security and performance ratio metric when the model is most sensitive to the network link compromise probability deterioration. That is, the best sensitivity of the model to the network security indicator (compromise probability) appears when the ratio between performance and security metric takes values of 100 to 300. Therefore, the presented model of secure routing with load balancing with an additive metric that accounts for network performance and security allows using network resources more efficiently but also considers the link compromise probability in making routing decisions.

Stability Analysis of Following Vehicles on a Highway for Safety of Automated Transportation Systems

The development and integration of advanced control technologies in vehicles and infrastructure can make intelligent (or automated) transportation systems much more safe and efficient. This paper focuses on a proper approach to stability and control of two adjacent vehicles following each other on the same traffic lane of a highway to ensure the functional safety of their automated driving systems. These vehicles are as entirely automated as they have the ability to follow a line path at a high speed and reduce the distance that separates them while adjusting their dynamic responses automatically without intervention from humans (i.e. drivers). To meet requirements for driving safety and stability, this paper explores a new approach to string stability of (any) two adjacent vehicles traveling in the same direction based on using optimal control and Lyapunov stability theories. Therefore, sufficient conditions for string stability of a vehicle traffic using continuous-time Lyapunov function and matrix Riccati equation are presented. The search for a quadratic Lyapunov function is formulated as a convex optimization problem in terms of a linear invariant system towards a quadratic optimal criterion. The analysis of these methods for minimizing the desired performance criteria is also given. Finally, the paper ends with a conclusion and perspective for future work.

Design of a High Gain Observer Optimization Method for the State Synchronization of Nonlinear Perturbed Chaotic Systems

This paper propounds addressing the design of a high gain observer optimization method in order to ensure a reliable state synchronization of nonlinear perturbed chaotic systems. The salient feature of the developed approach lies in the optimization of the high gain observer by using the optimal control theory associated with a proposed numerical algorithm. Thereby, an innovative quadratic optimization criterion is proposed to calculate the required optimal value of the observer setting parameter θ, characterizing the observation gain and corresponding to the minimal value of the cost function, by achieving a compromise between the correction term of the state observer and its observation error. Moreover, the exponential stability of the high gain observer is demonstrated within the Lyapunov framework. The efficacy of the designed approach is highlighted by numerical simulation on two prominent examples of nonlinear perturbed chaotic systems.

Lyapunov stability-based optimal control of following vehicles on a highway

The application of modern control methods to automated driving of following vehicles on a highway can make the advanced transportation systems much more safe and efficient. This paper focuses on a computational approach to optimal control and stability analysis of the adjacent vehicles following in a single traffic lane of a highway in order to ensure the functional safety and assistance of automated driving systems. These vehicles are entirely automated as they have the ability to follow a line path at a high speed and reduce the distance that separates them while adjusting their responses automatically without intervention from humans (i.e. drivers). To meet such requirements for driving safety, this paper explores a new approach to string stability of following vehicles that travel in a straight line of a highway, using optimal control and Lyapunov stability theories. Consequently, sufficient conditions for string stability of a vehicle traffic using continuous-time Lyapunov function and matrix Riccati equation are presented. The search for a quadratic Lyapunov function is then formulated as a convex optimisation problem in terms of a linear invariant system towards a quadratic optimal criterion. The analysis of these methods for minimising the performance criterion is also given. Finally, the paper ends with a conclusion and perspective for future work.

Lyapunov stability-based optimal control of following vehicles on a highway

The application of modern control methods to automated driving of following vehicles on a highway can make the advanced transportation systems much more safe and efficient. This paper focuses on a computational approach to optimal control and stability analysis of the adjacent vehicles following in a single traffic lane of a highway in order to ensure the functional safety and assistance of automated driving systems. These vehicles are entirely automated as they have the ability to follow a line path at a high speed and reduce the distance that separates them while adjusting their responses automatically without intervention from humans (i.e. drivers). To meet such requirements for driving safety, this paper explores a new approach to string stability of following vehicles that travel in a straight line of a highway, using optimal control and Lyapunov stability theories. Consequently, sufficient conditions for string stability of a vehicle traffic using continuous-time Lyapunov function and matrix Riccati equation are presented. The search for a quadratic Lyapunov function is then formulated as a convex optimisation problem in terms of a linear invariant system towards a quadratic optimal criterion. The analysis of these methods for minimising the performance criterion is also given. Finally, the paper ends with a conclusion and perspective for future work.

Study on Exchange Rate Forecasting Using Recurrent Neural Networks

It focuses on the problems of forecasting exchange rate that is a nonlinear time series. A dynamics systems approach and the recurrent neural networks (RNN) were employed to modeling this nonlinear time series. The delay time was calculated using mutual information method and embedding dimension was confirmed by false nearest neighbors. The dataset was reconstructed form source time series for trained and verified the neural networks model. The quadratic optimization criterion was considered which the neural networks weights update algorithm were derived using gradient descent method for hidden layer; recurrent layer and output layer. The calculation flow chart was designed for neural networks learning and emulation. The reliability and stability of neural networks was confirmed by testing dataset. The results of simulation showed that the recurrent neural networks were preferably performance for prediction the change of exchange rate.

Integral Sliding Manifold Design for Linear Systems With Additive Unmatched Disturbances

This note offers an integral sliding manifold design method for linear systems that minimizes the impact of unmatched constant external disturbances. System sensitivity upon an unmatched disturbance vector is assessed by the steady-state dependent criterion function. The derived procedure easily finds a unique integral sliding manifold that minimizes a quadratic optimization criterion. Applicability of this method in case of slowly-varying disturbances is supported by determining disturbance frequency limit that guarantees satisfactory performance. The proposed approach has been demonstrated on a numerical example and verified by simulations.

Optimal stabilization of small spacecraft angular motion in the process of deployment of an orbital tether system

The problem of stabilizing the motion of small spacecraft relative to the center of mass in the process of deploying an orbital tether system is presented in the paper. Stabilization is carried out with respect to the direction of the tether and is characterized by the classical Euler angles (precession, nutation and proper rotation). The proposed method of suboptimal control is based on the joint application of the principle of Bellman's dynamic programming and the averaging method. The integral quadratic optimality criterion that depends on operating deviations and low control inputs is used. Control synthesis is accomplished using the model of angular motion recorded for small angles of nutation. An example of calculating optimal control of an orbital tether system deployed for the purpose of de-orbiting small satellites to the Earth is given. The efficiency of the optimal control arrived at is confirmed by numerical calculations for the basic nonlinear model of motion of an orbital tether system.

Методи керування імпульсними процесами когнітивних карт із запізненнями

Background. The paper deals with the problem of cognitive modelling, namely control of complex systems with dynamics in impulse process presented by cognitive maps. It is assumed that the systems operate with delays that may occur either between vertices coordinates of a cognitive map or during transmission of control signals.Objective. Build models of cognitive maps with different delays and to apply these models to control impulse processes in cognitive maps.Methods. The article discusses two approaches for delays – control delays and delays during interaction between the vertices of a cognitive map. For the first case, a control algorithm based on reference model of a closed system was proposed, for the second case it is based on quadratic optimality criterion. Obtained results were verified using cognitive maps of commercial bank and health care system. Different delays were included into these systems and control laws were developed.Results. Simulation results have confirmed that proposed methods reach the objective, i.e. they allow stabilising system with delays in impulse mode.Conclusions. Research provided in the paper extended the class of controlled cognitive maps by systems with delays.

Population Encoding With Hodgkin–Huxley Neurons

The recovery of (weak) stimuli encoded with a population of Hodgkin-Huxley neurons is investigated. In the absence of a stimulus, the Hodgkin-Huxley neurons are assumed to be tonically spiking. The methodology employed calls for 1) finding an input-output (I/O) equivalent description of the Hodgkin-Huxley neuron and 2) devising a recovery algorithm for stimuli encoded with the I/O equivalent neuron(s). A Hodgkin-Huxley neuron with multiplicative coupling is I/O equivalent with an Integrate-and-Fire neuron with a variable threshold sequence. For bandlimited stimuli a perfect recovery of the stimulus can be achieved provided that a Nyquist-type rate condition is satisfied. A Hodgkin-Huxley neuron with additive coupling and deterministic conductances is first-order I/O equivalent with a Project-Integrate-and-Fire neuron that integrates a projection of the stimulus on the phase response curve. The stimulus recovery is formulated as a spline interpolation problem in the space of finite length bounded energy signals. A Hodgkin-Huxley neuron with additive coupling and stochastic conductances is shown to be first-order I/O equivalent with a Project-Integrate-and-Fire neuron with random thresholds. For stimuli modeled as elements of Sobolev spaces the reconstruction algorithm minimizes a regularized quadratic optimality criterion. Finally, all previous recovery results of stimuli encoded with Hodgkin-Huxley neurons with multiplicative and additive coupling, and deterministic and stochastic conductances are extended to stimuli encoded with a population of Hodgkin-Huxley neurons.

Consistent recovery of sensory stimuli encoded with MIMO neural circuits.

We consider the problem of reconstructing finite energy stimuli encoded with a population of spiking leaky integrate-and-fire neurons. The reconstructed signal satisfies a consistency condition: when passed through the same neuron, it triggers the same spike train as the original stimulus. The recovered stimulus has to also minimize a quadratic smoothness optimality criterion. We formulate the reconstruction as a spline interpolation problem for scalar as well as vector valued stimuli and show that the recovery has a unique solution. We provide explicit reconstruction algorithms for stimuli encoded with single as well as a population of integrate-and-fire neurons. We demonstrate how our reconstruction algorithms can be applied to stimuli encoded with ON-OFF neural circuits with feedback. Finally, we extend the formalism to multi-input multi-output neural circuits and demonstrate that vector-valued finite energy signals can be efficiently encoded by a neural population provided that its size is beyond a threshold value. Examples are given that demonstrate the potential applications of our methodology to systems neuroscience and neuromorphic engineering.

Reconstruction of Sensory Stimuli Encoded with Integrate-and-Fire Neurons with Random Thresholds

We present a general approach to the reconstruction of sensory stimuli encoded with leaky integrate-and-fire neurons with random thresholds. The stimuli are modeled as elements of a Reproducing Kernel Hilbert Space. The reconstruction is based on finding a stimulus that minimizes a regularized quadratic optimality criterion. We discuss in detail the reconstruction of sensory stimuli modeled as absolutely continuous functions as well as stimuli with absolutely continuous first-order derivatives. Reconstruction results are presented for stimuli encoded with single as well as a population of neurons. Examples are given that demonstrate the performance of the reconstruction algorithms as a function of threshold variability.

Suboptimal Regulation of a Class of Bilinear Interconnected Systems with Finite-Time Sliding Planning Horizons

This paper focuses on the suboptimization of a class of multivariable discrete-time bilinear systems consisting of interconnected bilinear subsystems with respect to a linear quadratic optimal regulation criterion which involves the use of state weighting terms only. Conditions which ensure the controllability of the overall system are given as a previous requirement for optimization. Three transformations of variables are made on the system equations in order to implement the scheme on an equivalent linear system. This leads to an equivalent representation of the used quadratic performance index that involves the appearance of quadratic weighting terms related to both transformed input and state variables. In this way, a Riccati-matrix sequence, allowing the synthesis of a standard feedback control law, is obtained. Finally, the proposed control scheme is tested on realistic examples.

OPTIMAL ITERATIVE LEARNING CONTROL OF WAFER TEMPERATURE UNIFORMITY IN RAPID THERMAL PROCESSING

An optimal iterative learning control (ILC) technique based on a quadratic optimal criterion has been implemented and evaluated in an experimental rapid thermal processing (RTP) system fabricating 8-inch silicon wafers. The control technique is based on a time-varying linear state space model which approximates a nonlinear system along a reference trajectory. This ILC control technique is capable of making improvements in the control performance from one run to next and eventually converges to a minimum achievable tracking error despite model error. Through a series of experiments with wafers on which thermocouples are glued, it was observed that the wafer temperatures are steered to the reference trajectory reducing the differences overcoming various disturbances.

Control of Wafer Temperature Uniformity in Rapid Thermal Processing Using an Optimal Iterative Learning Control Technique

An iterative learning control (ILC) technique based on a quadratic optimal criterion is proposed for temperature uniformity control of a wafer under rapid thermal processing (RTP). The proposed tec...