Discrete-time Linear Model Research Articles

Event-trigger rolling horizon optimization for congestion management considering peer-to-peer energy trading among microgrids

This paper designs an event-trigger rolling horizon optimization framework to alleviate electricity congestion caused by peer-to-peer (P2P) energy transactions among microgrids (MGs) under uncertainty. This framework incorporating abounded time dimensions includes three processes: first, a discrete-time linear programming model for the P2P energy trading among MGs with real-time data updating for reaction to underling uncertainties, are formulated to derive initial schemes in prediction time windows; second, a modified optimal power flow model is used to verify congestion in control time windows, with congestion occurrence defined as an event; third, the power rescheduling of MGs is triggered by this event for reducing periodic calculation burden and executed to generate new trading schemes for congestion alleviation in control time windows. We develop an online distributed optimization algorithm to realize independent decisions of MGs and guarantee rolling updates of system parameters through embedding alternating direction method of multipliers into every time window. Finally, simulations in different cases are implemented to illustrate the reasonability and effectiveness of the proposed optimization framework. Results show that congestion is reasonably managed while ensuring the diversity of P2P energy transactions. Compared with the period-driven rolling horizon optimization framework, the computational time is significantly reduced in the proposed framework.

Interval Observers for Discrete-Time Linear Systems with Uncertainties

In this paper, we consider the problem involved when designing the interval observer for the system described by a linear discrete-time model under external disturbances and measurement noises. To solve this problem, we used the reduced order model of the initial system, which is insensitive or has minimal sensitivity to the disturbances. The relations involved in designing the interval observer, which has minimal dimensions and estimates the prescribed linear function of the original system state vector, were obtained. The theoretical results were illustrated by a practical example.

A discrete-time linear model predictive control for motion planning of an autonomous vehicle with adaptive cruise control and obstacle overtaking

Motion planners for autonomous driving improve traffic safety through collision-free motion generation along the path. However, conventional motion planners render passengers uncomfortable as a result of jerky motion. To overcome this, we propose a model predictive control (MPC) based motion planner that not only ensures safety but also improves driving comfort. The proposed planner generates path tracking and collision-free maneuvers to ensure safety, and improve driving comfort by minimizing acceleration and jerk. Collision-free maneuvers include vehicle following and overtaking. The target speed is determined by comprehensively considering path tracking performance improvement and whether overtaking is possible. The speed of the vehicle is controlled by considering longitudinal acceleration and jerk minimization. The steering command is determined by considering both path tracking error reduction, and lateral acceleration and jerk minimization. In cases where vehicle overtaking is required and during high-speed driving conditions, the consideration of lateral acceleration and jerk minimization increases to improve driving comfort. The proposed planner is formulated as a convex optimization problem. The effectiveness of the proposed planner was evaluated in path tracking and collision avoidance simulations. The simulation results confirm that the proposed planner ensures vehicle safety through lane keeping and collision avoidance, and improves driving comfort.

Linear parameter-varying-based transition flight control design for a tilt-rotor aircraft

This paper presents the development of novel transition flight controllers for a class of urban air mobility aircrafts configured with a fixed-wing and six distributed electric rotor assemblies. Only the two tilt-rotors are utilized for thrust vectoring during transition flight from hovering to steady-level flight, while the four lift-rotors are modulated with aerodynamic lift induced by fixed-wing to maintain stable altitude-hold. Three tractable tilt-rotor articulation profiles are proposed by taking into account of various aircraft and hardware constraints. Given a predefined nominal tilting profile, a family of linear models is obtained by linearizing the nonlinear aircraft model at multiple tilt-rotor angular positions along the tilting profile. Using tilt-rotor angular position as a scheduling parameter, a discrete-time linear parameter-varying model can be constructed, which is then used to develop a novel transition flight control architecture that integrates the adaptive model predictive control law with feedforward effect of the dynamic reference compensation. The simulation results demonstrate the effectiveness of proposed transition flight controllers and its robustness subject to external disturbance.

A robust whiteness test for the identification of discrete-time linear models: Use of orthonormal transfer functions

A novel whiteness test of residuals is proposed, which makes use of generalized bases of orthonormal transfer functions. It can be viewed as a robustified version of the classical whiteness test in the sense that it reduces the risk of type II errors, by introducing a frequency weighting in the assessment of the flatness in the residual power spectrum density. This frequency weighting, which depends on the basis poles, can be employed for the validation of reduced order models, when the flatness of the residual power spectrum density is evaluated over a limited frequency band.

Model Predictive Control for Blending Processes in Cement Plants

In this paper, we discuss model predictive control applied to blending processes. Blending processes are ubiquitous in the chemical process industries since reactants usually need to be mixed before entering a reactor. Many times, the blending is trivial as pure streams of reactants are mixed. We consider non-trivial blending problems in which non-pure streams with the reactants are to be mixed. The motivating example is the blending problem that occurs in cement production. The raw mix for the cement kiln must have a specified chemical composition. This composition is obtained by mixing piles with different chemical compositions and economic value such that the raw mix meets specifications in the cheapest possible way. We formulate the blending problem as a nonlinear optimization problem that can be approximated well as a convex quadratic optimization problem. We implement the corresponding nonlinear and linear model predictive controllers (NMPC, LMPC) using a continuous-time transfer function description that is realized as a discrete-time linear state space model. The controller obtains feedback by combining regularly sampled online measurements and irregularly sampled laboratory measurements using a time variant dynamic Kalman filter with memory. Numerical simulations demonstrate that the NMPC and LMPC have similar performance.

Modeling and Optimization of an Inductive Oven with Continuous Product Flow

A control-oriented mathematical model of a continuous industrial wafer oven with inductive heating is derived. The model utilizes the specific system structure of periodically circulating baking plates. A tailored state transformation allows the formulation of a linear time-invariant discrete-time model. This model is validated based on measurements on a pilot plant. The model serves as a basis to optimize steady-state inputs and inductor positions for minimized temperature variations along the path of the baking plates.

P-020. The relationship of the parameter of ambulatory blood pressure monitoring and bio-marker in women with hypertensive disorders of pregnancy

This paper deals with a sensor fault detection approach using the Optimal Upper Bounded Interval Kalman Filter (OUBIKF) and an adaptive degree of freedom χ2-statistics method. It is devoted to discrete time linear model subjected to mixed uncertainties in terms of observations and noises. Mixed uncertainties mean both bounded and stochastic uncertainties. The degrees of freedom of this χ2 hypothesis test method are adaptively chosen thanks to amplifier coefficients improving the detection of the sensor faults. The proposed approach is an extension of a result developped in Lu et al. (2019). Application on a vehicle bicycle model highlights the efficiency of the proposed approach. Comparisons with other efficient estimation and fault detection strategies are provided to discuss the accuracy of the obtained results.

An improved ellipsoid optimization algorithm in subspace predictive control

PurposeThe purpose of this paper is to derive the output predictor for a stationary normal process with rational spectral density and linear stochastic discrete-time state-space model, respectively, as the output predictor is very important in model predictive control. The derivations are only dependent on matrix operations. Based on the output predictor, one quadratic programming problem is constructed to achieve the goal of subspace predictive control. Then an improved ellipsoid optimization algorithm is proposed to solve the optimal control input and the complexity analysis of this improved ellipsoid optimization algorithm is also given to complete the previous work. Finally, by the example of the helicopter, the efficiency of the proposed control strategy can be easily realized.Design/methodology/approachFirst, a stationary normal process with rational spectral density and one stochastic discrete-time state-space model is described. Second, the output predictors for these two forms are derived, respectively, and the derivation processes are dependent on the Diophantine equation and some basic matrix operations. Third, after inserting these two output predictors into the cost function of predictive control, the control input can be solved by using the improved ellipsoid optimization algorithm and the complexity analysis corresponding to this improved ellipsoid optimization algorithm is also provided.FindingsSubspace predictive control can not only enable automatically tune the parameters in predictive control but also avoids many steps in classical linear Gaussian control. It means that subspace predictive control is independent of any prior knowledge of the controller. An improved ellipsoid optimization algorithm is used to solve the optimal control input and the complexity analysis of this algorithm is also given.Originality/valueTo the best knowledge of the authors, this is the first attempt at deriving the output predictors for stationary normal processes with rational spectral density and one stochastic discrete-time state-space model. Then, the derivation processes are dependent on the Diophantine equation and some basic matrix operations. The complexity analysis corresponding to this improved ellipsoid optimization algorithm is analyzed.

Structural Differences Between Healthy Subjects and Patients With Schizophrenia or Schizoaffective Disorder: A Graph and Control Theoretical Perspective.

The coordinated dynamic interactions of large-scale brain circuits and networks have been associated with cognitive functions and behavior. Recent advances in network neuroscience have suggested that the anatomical organization of such networks puts fundamental constraints on the dynamical landscape of brain activity, i.e., the different states, or patterns of regional activation, and transition between states the brain can display. Specifically, it has been shown that densely connected, central regions control the transition between states that are “easily” reachable (in terms of expended energy), whereas weakly connected areas control transitions to states that are hard-to-reach. Changes in large-scale brain activity have been hypothesized to underlie many neurological and psychiatric disorders. Evidence has emerged that large-scale dysconnectivity might play a crucial role in the pathophysiology of schizophrenia, especially regarding cognitive symptoms. Therefore, an analysis of graph and control theoretic measures of large-scale brain connectivity in patients offers to give insight into the emergence of cognitive disturbances in the disorder. To investigate these potential differences between patients with schizophrenia (SCZ), patients with schizoaffective disorder (SCZaff) and matched healthy controls (HC), we used structural MRI data to assess the microstructural organization of white matter. We first calculate seven graph measures of integration, segregation, centrality and resilience and test for group differences. Second, we extend our analysis beyond these traditional measures and employ a simplified noise-free linear discrete-time and time-invariant network model to calculate two complementary measures of controllability. Average controllability, which identifies brain areas that can guide brain activity into different, easily reachable states with little input energy and modal controllability, which characterizes regions that can push the brain into difficult-to-reach states, i.e., states that require substantial input energy. We identified differences in standard network and controllability measures for both patient groups compared to HCs. We found a strong reduction of betweenness centrality for both patient groups and a strong reduction in average controllability for the SCZ group again in comparison to the HC group. Our findings of network level deficits might help to explain the many cognitive deficits associated with these disorders.

Integration of maintenance scheduling and planning for large-scale asset fleets

Large fleets of engineering assets that are subject to ongoing degradation are posing the challenge of how and when to perform maintenance. For a given case study, this paper proposes a formulation for combined scheduling and planning of maintenance actions. A hierarchical approach and a two-stage approach (with either uniform or non-uniform time grid) are considered and compared to each other. The resulting discrete-time linear programming model follows the Resource Task Network framework. Asset deterioration is considered linearly and tackled with an enumerator-based formulation. Advantages of the model are its computational efficiency, scalability, extendability and adaptability. The results indicate that combined maintenance planning and scheduling can be solved in appropriate time and with appropriate accuracy. The decision-support that is delivered helps the choice of the specific maintenance action to perform and proposes when to conduct it. The paper makes a case for the benefits of optimally combining long-term planning and short-term scheduling in industrial-sized problems into one system.

One step ahead adaptive control technique featured by fuzzy-based least square estimator for wind systems

The present paper proposes the application to a wind system of the One Step Ahead control scheme featured by a Fuzzy-based Least Square Estimator. The considered wind system power generation supplies an electrical load disconnected from the power supply grid. It is composed of a three bladed horizontal-axis wind turbine which drives a synchronous generator by means of gearbox: the mathematical model for both the horizontal-axis wind-turbine and the synchronous generator will be briefly outlined. The adaptive nature of the One-Step-Ahead control algorithm relies on providing consistent estimation of the controlled system. This is achieved by means of a Least Square Algorithm that is able to provide a good estimation of a linear discrete time model of the controlled system, nevertheless its convergence rate reduces very quickly. For this reason, Least Square Algorithm needs a resetting strategy, which allows the achievement of a compromise between estimation accuracy and convergence rate. This not only represents a very problem-dependent issue but also introduces weaknesses in term of control tracking errors, which in turns needs an extra control contribution (integral correction). The proposed Least Square Algorithm enhancement overcomes these issues managing differently the estimation accuracy and the convergence rate. In the Results section, the achievements of the application of the One-Step-Ahead algorithm to the wind system will prove the reliability of the suggested enhanced control technique.

Robust cascade control of electrical drives using discrete-time chattering-free sliding mode controllers with output saturation

The paper considers electrical drives control having a hierarchical cascaded structure. This structure has an inner current control loop and outer loops for speed and position control. The design of the control is performed using a discrete-time model of electrical drive. In all the loops, the discrete-time quasi sliding mode control is used for controller design because of its robustness to external and parametric matched disturbances (inherent to electrical drives) and the capability to ensure the desired dynamics. To enhance the robustness to disturbances, a nonlinear disturbance compensator is also implemented. The chattering in sliding mode is eliminated by using a new modified discrete-time super twisting control. The current and the speed controllers are designed for linear discrete-time first-order models, while the position controller is designed for a linear second-order discrete-time model. The axis position is measured by a mechanical sensor (encoder). The speed is estimated from the position measurements using Euler derivative approximation. Alternatively, it can be obtained by an observer. The proposed design is straightforward and results in high-performance, robust control with strong disturbance rejection capability and negligible overshoots. All theoretically obtained claims are demonstrated by experiments on an induction motor drive with a rotor field-oriented control structure.

State and Unknown Input Simultaneous Estimation for a Class of Discrete-Time Linear Implicit Models : A Heat Exchanger Pilot Process Application

In this paper, the design problem of simultaneous estimation of unmeasurable states and unknown inputs (UIs) is investigated for a class of discrete-time linear implicit models (DLIMs). The UIs affect both state and output of the system. The approach is based on the separation between dynamic and static relations in the considered DLDM. First, the method permitting to separate dynamic equations from static equations is exposed. Next, an augmented explicit model which contains the dynamic equations and the UIs is constructed. Then an unknown inputs observer (UIO) design in explicit structure is developed. The exponential convergence of the state estimation error is studied by using the Lyapunov theory and the stability condition is given in term of linear matrix inequality (LMI). Finally, an illustrative application of a heat exchanger pilot process is given to show the good performances of the proposed method.

Maximum Likelihood Estimation of Stochastic Fractional Singular Models

Using the non-causal nature of a fractional-order singular (FOS) model, this paper deals with the modification of an estimation algorithm developed by Nosrati and Shafiee, and demonstrates how the derived estimation procedure can be adjusted by additional information related to the future dynamics. The procedure adopts the maximum likelihood (ML) method leading to a 3-block fractional singular Kalman filter (FSKF). In addition to some conditions on existence and uniqueness of solutions for discrete-time linear stochastic FOS models, the estimability analyses are given and an optimal filter is presented. Finally, the performance of the derived filter is verified and validated via numerical simulation on a three machine infinite bus system.

Robust State Estimation for Time-Delay Linear Systems With External Inputs

Robust state estimation problem is investigated for discrete-time linear state space models with uncertain parameters, deterministic control input and d-step state delay. Firstly, the original system is transformed into a non-time-delay system based on the method of state augmentation. Then a robust state estimation algorithm is proposed based on the sensitivity penalty method and the derivation is given. Moreover, compared with the standard Kalman filter, this algorithm has similar iterative form and considerable computational complexity. Finally, numerical simulations are utilized to show the effectiveness of this algorithm.

Observer Design for Simultaneous State and Fault Estimation for a Class of Discrete-time Descriptor Linear Models

This paper investigates the problem of observer design for simultaneous states and faults estimation for a class of discrete-time descriptor linear models in presence of actuator and sensor faults. The idea of the present result is based on the second equivalent form of implicit model [1] which permits to separate the differential and algebraic equations in the considered singular model, and the use of an explicit augmented model structure. At that stage, an observer is built to estimate simultaneously the unknown states, the actuator faults, and the sensor faults. Next, the explicit structure of the augmented model is established. Then, an observer is built to estimate simultaneously the unknown states, the actuator faults, and the sensor faults. By using the Lyapunov approach, the convergence of the state estimation error of the augmented system is analyzed, and the observer’s gain matrix is achieved by solving only one linear matrix inequality (LMI). At long last, an illustrative model is given to show the performance and capability of the proposed strategy.

Joint Vertex-Time Filtering on Graphs With Random Node-Asynchronous Updates

In graph signal processing signals are defined over a graph, and filters are designed to manipulate the variation of signals over the graph. On the other hand, time domain signal processing treats signals as time series, and digital filters are designed to manipulate the variation of signals in time. This study focuses on the notion of vertex-time filters, which manipulates the variation of a time-dependent graph signal both in the time domain and graph domain simultaneously. The key aspects of the proposed filtering operations are due to the random and asynchronous behavior of the nodes, in which they follow a collect-compute-broadcast scheme. For the analysis of the randomized vertex-time filtering operations, this study first considers the random asynchronous variant of linear discrete-time state-space models, in which each state variable gets updated randomly and independently (and asynchronously) in every iteration. Unlike previous studies that analyzed similar models under certain assumptions on the input signal, this study considers the model in the most general setting with arbitrary time-dependent input signals, which lay the foundations for the vertex-time graph filtering operations. This analysis shows that exponentials continue to be eigenfunctions in a statistical sense in spite of the random asynchronous nature of the model. This study also presents the necessary and sufficient condition for the mean-squared stability and shows that stability of the underlying state transition matrix is neither necessary nor sufficient for the mean-squared stability of the randomized asynchronous recursions. Then, the proposed filtering operations are proven to be mean-square stable if and only if the filter, the graph operator and the update probabilities satisfy a certain condition. The results show that some unstable vertex-time graph filters (in the synchronous case) can be implemented in a stable manner in the presence of randomized asynchronicity, which is also demonstrated by numerical examples.

A new scheme for fault detection based on Optimal Upper Bounded Interval Kalman Filter

This paper deals with a sensor fault detection approach using the Optimal Upper Bounded Interval Kalman Filter (OUBIKF) and an adaptive degree of freedom χ 2-statistics method. It is devoted to discrete time linear model subjected to mixed uncertainties in terms of observations and noises. Mixed uncertainties mean both bounded and stochastic uncertainties. The degrees of freedom of this χ 2 hypothesis test method are adaptively chosen thanks to amplifier coefficients improving the detection of the sensor faults. The proposed approach is an extension of a result developped in Lu et al. (2019). Application on a vehicle bicycle model highlights the efficiency of the proposed approach. Comparisons with other efficient estimation and fault detection strategies are provided to discuss the accuracy of the obtained results.

ОБ АЛГОРИТМЕ ОБНАРУЖЕНИЯ ИЗМЕНЕНИЯ РЕЖИМА ДВИЖЕНИЯ ОБЪЕКТА

The article deals with the solution to the problem of determining the motion mode of an object along a complex trajectory. A hybrid stochastic model is used to describe a complex trajectory. The solution of the problem is based on the application of a sequential decision rule about the choice at an unknown time of the hypothesis about the current mode of motion, with a limited size of the bank of competing Kalman filters. An algorithm is constructed for calculating the average size of the Kalman filter bank in the case of M-possible motion modes. The algorithm is developed in a general form, therefore, it can be used not only for the four types of object motion models considered in this paper, but also for any linear discrete-time models with Gaussian noise presented by equations in the state space. The algorithm for a priori estimation of the average size of a bank of competing Kalman filters for M-possible modes of motion is implemented in MATLAB, the results of computer simulation are presented.