Terminal Set Research Articles

Distributed MPC based on robustly controllable sets for PWA systems

The optimization problem in model predictive control (MPC) algorithm for piecewise affine (PWA) systems often contains substantial logic variables, which requires extensive computing power for online implementation. This paper proposes a one-step distributed MPC algorithm for spatially interconnected PWA systems with both input and state constraints, where the algorithm is based on a series of r-step robustly controllable sets. Algorithms for offline computing terminal sets and a series of r-step robustly controllable sets are developed using the step-by-step backward approach. The states that lie in the robustly controllable sets are steered into the terminal set in finite steps and ultimately converge into a robustly positively invariant set. The proposed algorithm is demonstrated to significantly reduce the online computational burden. Simulation results are provided to showcase the effectiveness of the algorithm.

Game-theoretical problems for fractional-order nonstationary systems

Nonstationary fractional-order systems represent a new class of dynamic systems characterized by time-varying parameters as well as memory effect and hereditary properties. Differential game described by system of linear nonstationary differential equations of fractional order is treated in the paper. The game involves two players, one of which tries to bring the system’s trajectory to a terminal set, whereas the other strives to prevent it. Using the technique of set-valued maps and their selections, sufficient conditions for reaching the terminal set in a finite time are derived. Theoretical results are supported by a model example.

Computationally Efficient Continuous-Time Model Predictive Control of a 2-DOF Helicopter via B-Spline Parameterization.

This paper investigates one way to reduce the computational burden of continuous-time model predictive control (MPC) laws by representing the input/output signals and related models using B-spline functions. Such an approximation allows to implement the resulting feedback control law more efficiently, requiring less online computational effort. As a result, the proposed controller formulates the control signals as continuous polynomial spline functions. All constraints assumed over the prediction horizon are then expressed as constraints acting on the B-splines control polygon vertices. The performance of the proposed theoretical framework has been demonstrated with several real-time experiments using the well-known 2-DOF laboratory helicopter setup. The aim of the presented experiments was to track given step-like reference trajectories for pitch and yaw angles under notable parameter uncertainties. In order to suppress the influence of uncertainties, the control algorithm is implemented in an adaptive mode, equipped with the recursive least squares (RLS) estimation of model parameters and with the adaptation of stabilizing terminal set and terminal cost calculations. Thanks to the presented framework, it is possible to significantly reduce the computational burden, measured by the number of decision variables and input constrains, indicating the potential of the proposed concept for real-time applications, even when using embedded control hardware.

Host-Dependent Improvement of GFP Expression in Pseudomonas putida KT2440 Using Terminators of Metagenomic Origin.

Transcriptional terminators are key players in the flow of genetic information, but are often overlooked in circuit design. In this work, we used the Standard European Vector Architecture (SEVA) as a scaffold to investigate the effects of different terminators in the output of a reporter construct expressed in two bacterial species, and found that replacing the conventional T1 and T0 transcriptional terminators of the SEVA vector format with a set of broad-host metagenomic terminators resulted in a significant improvement in the signal of a fluorescent device in Pseudomonas putida KT2440 but not in Escherichia coli DH10B. Our results suggest that replacing the default set of terminators present in the SEVA specification may be an useful strategy for fine-tuning circuit expression in P. putida, which can be leveraged for the development of new devices with improved performance in this microbial host.

An Explicit Dual Control Approach for Constrained Reference Tracking of Uncertain Linear Systems

A finite horizon optimal tracking problem is considered for linear dynamical systems subject to parametric uncertainties in the state-space matrices and exogenous disturbances. A suboptimal solution is proposed using a model predictive control (MPC) based explicit dual control approach which enables active uncertainty learning. A novel algorithm for the design of robustly invariant online terminal sets and terminal controllers is presented. Set membership identification is used to update the parameter uncertainty online. A predicted worst-case cost is used in the MPC optimization problem to model the dual effect of the control input. The cost-to-go is estimated using contractivity of the proposed terminal set and the remaining time horizon, so that the optimizer can estimate future benefits of exploration. The proposed dual control algorithm ensures robust constraint satisfaction and recursive feasibility, and navigates the exploration-exploitation trade-off using a robust performance metric.

Refining Management of Apple Powdery Mildew in New York State with Weather-Based Fungicide Application Timing Programs.

In the absence of durable host resistance among commercial cultivars, chemical management continues to be an essential component of disease control in apple production. Apple powdery mildew, caused by the ascomycete Podosphaera leucotricha, is largely managed with regular fungicide applications from the host phenological stages of tight cluster to terminal bud growth set, with applications typically being made in a prophylactic manner irrespective of existing disease pressure. Here we evaluated two management programs that aligned fungicide applications to specific weather thresholds conducive to powdery mildew development using a rotation of single-site fungicides and sulfur. In three separate orchards among four cultivars, we compared powdery mildew disease progression over the growing season for each of the weather factor-based programs and a typical calendar-based application program. In each year of the trial, we found that management programs with weather-based fungicide applications provided levels of disease control similar to the calendar program but required 50 to 83.3% fewer mildew-specific fungicide applications throughout the growing season. Our results provide a framework with which to evaluate future weather-based management programs for apple powdery mildew management. This knowledge could be implemented in the creation of a powdery mildew disease management decision support system to better inform and aid fungicide application programs for continued sustainable apple production in the northeast United States.

A Single-Tube Robust Model Predictive Control Method Based on ε-Approximation

This paper aims to solve the problem of the robust model predictive control, the contradiction of the system robustness, and the conservative terminal constraint set range. A robust model predictive control (RMPC) method based on an ε-approximation single-tube set is proposed. We construct a single-tube RMPC structure for linear discrete time invariant systems with additive disturbances. To this structure, we add the state estimation and state feedback to improve the convergence rate. Furthermore, we use the ε-approximation to estimate the terminal constraint set with less conservatism, thus improving the robustness. Then, we conduct a stability analysis of the ε-approximation single-tube RMPC system. The simulation results demonstrate the stability and interference allowance advantages of the proposed method.

Efficient min–max MPC: Achieving a large domain of attraction with short horizon

AbstractThis article considers the regulation problem of a constrained linear system with bounded disturbance. The objective is to overcome the offline and online problems of the standard dual‐mode min–max model predictive control (MPC). The offline problem is related to the construction of a polyhedral terminal set, which is prohibitively complex especially for high order systems. We propose to replace the polyhedral set with the ellipsoidal one, which is much easier to construct. The online problem is related to the computational burden, which grows exponentially with the prediction horizon . We show how to employ a new terminal cost function, that results in a new min–max MPC with a large domain of attraction even with or . Hence the computational complexity is drastically reduced. Two numerical examples with comparison to earlier solutions from the literature illustrate the effectiveness of the proposed approach.

Structural Properties of Minimum Multi-source Multi-Sink Steiner Networks in the Euclidean Plane

Given two finite sets A and B of points in the Euclidean plane, a minimum multi-source multi-sink Steiner network in the plane, or a minimum (A, B)-network, is a directed graph embedded in the plane with a dipath from every node in A to every node in B such that the total length of all arcs in the network is minimised. Such a network may contain Steiner points—nodes appearing in the solution that are neither in A nor B. We show that for any finite point sets A, B in the plane, there exists a minimum (A, B)-network that is constructible by straightedge and compass (this was claimed in a paper by Maxwell and Swanepoel, but their argument is incorrect). We use this property to formulate an algorithmic framework for exactly finding minimum (A, B)-networks in the Euclidean plane. We also present several new structural and geometric properties of minimum (A, B)-networks. In particular, we resolve a conjecture of Alfaro by proving that, for any terminal set A, adding an appropriate orientation to the edges of a minimum 2-edge-connected Steiner network on A yields a minimum (A, A)-network.

A robust MPC approach with controller tuning for close following operation of virtually coupled train set

Virtual coupling, as an emerging concept in railways, expects successive trains in a virtually coupled train set (VCTS) to maintain a short following distance. However, this close following operation is still difficult to be achieved given uncertain resistances and nonlinear safety constraints. To solve this problem, this paper proposes a robust model predictive control (RMPC) approach for the close following operation of VCTS while satisfying a nonlinear safety constraint with relative braking principle. First, we construct a robust positively invariant set that bounds the tracking errors caused by uncertain resistances. Further, a semi-definite program-based controller tuning algorithm is proposed to reduce the following distance in the premise of the tightened constraint for robustly satisfying the nonlinear safety constraint. Then, by mathematically examining the future trajectories of successive trains, we create a terminal constraint set to ensure the recursive feasibility of the proposed RMPC. This closed-loop property guarantees the satisfaction of the safety constraint in any situation, even in the case of sudden deceleration of VCTS. Finally, numerical experiments are conducted to evaluate the following distance with respect to heterogeneous trains and verify the effectiveness of our approach. Experimental results demonstrate that the expected close following operation can be achieved while robustly satisfying the nonlinear safety constraint with uncertain resistances. Moreover, our approach further reduces the following distance in a VCTS by over 5%, compared with existing research.

Research on the value orientations of students using information and communication technologies

The current study is an attempt to compare online and offline results of research on students’ value orientations. The main scientific methods and approaches used in the current research are comparative analysis, online and offline comparison and statistical rank correlation. We defined the questionnaire’s content, formed its text and chose homogeneous representative groups. Results obtained both with classical (paper) technology and with information and communication technologies (ICT) are compared. The terminal and instrumental sets of values proposed by Milton Rokeach are compared. Based on the processed data, we draw conclusion about the reliability (validity) of online survey results. ICT is very helpful in conducting scientific research faster with fewer professionals involved but its time-consuming and requires numerous activities. Recommendations are given on the feasibility of using ICT in modern methods of sociological research. Work on the creation of modern research platforms, programs and algorithms that would ensure obtaining valid and informative results is prominent among the aspects of further scientific research.

Lyapunov-Based Impact Time Control Guidance Law with Performance Prediction

This paper proposes an impact time control guidance law based on exact nonlinear kinematics equations. To address the impact time control problem of providing enhanced intercept accuracy, we formulated an error variable whose regulation ensures the fulfillment of the required tasks without time-to-go estimation. Based on the Lyapunov stability theory, a desired line-of-sight rate profile that satisfies the convergence of the error variable was constructed, from which the guidance command was designed using the optimal tracking formulation. The simple structure of the proposed guidance law enables the prediction of interceptor behavior during homing, thereby allowing the interceptor to maneuver along feasible trajectories. In addition, although the structure of the proposed guidance law is simple and similar to that of proportional navigation, it is theoretically guaranteed to execute the required mission precisely at the end of homing. Numerical simulations demonstrated that the proposed guidance law achieved effective target interception under various terminal constraint settings.

Induced Disjoint Paths and Connected Subgraphs for H-Free Graphs

Paths P^1,ldots ,P^k in a graph G=(V,E) are mutually induced if any two distinct P^i and P^j have neither common vertices nor adjacent vertices. The Induced Disjoint Paths problem is to decide if a graph G with k pairs of specified vertices (s_i,t_i) contains k mutually induced paths P^i such that each P^i starts from s_i and ends at t_i. This is a classical graph problem that is NP-complete even for k=2. We introduce a natural generalization, Induced Disjoint Connected Subgraphs: instead of connecting pairs of terminals, we must connect sets of terminals. We give almost-complete dichotomies of the computational complexity of both problems for H-free graphs, that is, graphs that do not contain some fixed graph H as an induced subgraph. Finally, we give a complete classification of the complexity of the second problem if the number k of terminal sets is fixed, that is, not part of the input.

Robust MPC for polytopic uncertain systems via a high-rate network with the round-robin scheduling.

This article is concerned with the robust model predictive control (RMPC) problem for polytopic uncertain systems under the round-robin (RR) scheduling in the high-rate communication channel. From a set of sensors to the controller, several sensors transmit the data to the remote controller via a shared high-rate communication network, data collision might happen if these sensors start transmissions at the same time. For the sake of preventing data collision in the high-rate communication channel, a communication scheduling known as RR is used to arrange the data transmission order, where only one node with token is allowed to send data at each transmission instant. In accordance with the token-dependent Lyapunov-like approach, the aim of the problem addressed is to design a set of controllers in the framework of RMPC such that the asymptotical stability of the closed-loop system is guaranteed. By taking the effect of the underlying RR scheduling in the high-rate communication channel into consideration, sufficient conditions are obtained by solving a terminal constraint set of an auxiliary optimization problem. In addition, an algorithm including both off-line and online parts is provided to find a sub-optimal solution. Finally, two simulation examples are used to demonstrate the usefulness and effectiveness of the proposed RMPC strategy.

Economic model predictive control with terminal set dynamic programming for tracking control

AbstractThis paper focuses on vehicle tracking control issues with consideration of energy efficiency, ride comfort and tracking performance. To address this issue, an economic model predictive control (EMPC) framework is proposed by taking average performance into account and introducing a time‐varying terminal set. We integrate an economic model predictive controller and a terminal controller with a feedback gain related to the time‐varying terminal set into the proposed EMPC framework. An acceleration‐dependent average constraint is designed and incorporated into the MPC optimization problem to facilitate the convergence of the actual acceleration to the desired one, which enables the vehicle to implement a smooth driving style that boosts energy economy. A tuning factor in the average constraint has the capacity to balance energy consumption and control performance. Under the premise of invariance constraints, a dynamic terminal set is constructed by solving a dynamic programming problem online, which enables an arbitrary location and scale of the terminal set at each iteration by taking the current and predicted tracking errors into account. This allows a reduction in the conservativeness of an economic model predictive controller in the sense of both the region of attraction and the cost bound. Recursive feasibility of the MPC optimization problem and the terminal set dynamic programming is ensured, and average performance is not worse than the performance with an optimal steady‐state operation. Moreover, the convergence of the closed‐loop tracking error to the optimal steady‐state is guaranteed by using the dissipativity theory. The effectiveness of the proposed algorithm is verified by numerical comparisons with different controller parameters and standard EMPC.

On a group pursuit problem on time scales

In a finite-dimensional Euclidean space $\mathbb R^k$, we consider a linear problem of pursuit of one evader by a group of pursuers, which is described on the given time scale $\mathbb{T}$ by equations of the form \begin{gather*} z_i^{\Delta} = a z_i + u_i - v, \end{gather*} where $z_i^{\Delta}$ is the $\Delta$-derivative of the functions $z_i$ on the time scale $\mathbb{T}$, $a$ is an arbitrary number not equal to zero. The set of admissible controls for each participant is a unit ball centered at the origin, the terminal sets are given convex compact sets in $\mathbb R^k$. The pursuers act according to the counter-strategies based on the information about the initial positions and the evader control history. In terms of initial positions and game parameters, a sufficient capture condition has been obtained. For the case of setting the time scale in the form $\mathbb T = \{ \tau k \mid k \in \mathbb Z,\ \tau \in \mathbb R,\ \tau >0\}$ sufficient pursuit and evasion problems solvability conditions have been found. In the study, in both cases, the resolving function method is used as basic one.

Model predictive control with implicit terminal ingredients

This paper proposes a new formulation of model predictive control for linear discrete time systems under state and control constraints. The main novelty of the proposed formulation is the introduction, and a computationally adequate utilization, of the implicit terminal constraint set and the implicit terminal cost function. From a numerical point of view, the deployment of the implicit terminal ingredients enables a computationally tractable use of model predictive control for higher dimensional control problems. From a practical point of view, the design of the proposed model predictive control algorithm is very constructive for a class of linear systems with polyhedral constraints. From a structural point of view, the proposed model predictive control retains a priori guarantees of the highly desirable positive invariance and exponential stability properties.

A Three-Phase Dual-Output T-Type Three-Level Converter

A novel three-phase dual-output T-type three-level converter (DO-T-TLC) topology is proposed in this article. The proposed topology has the dc-link and two sets of three-phase ac voltage output terminals. The topology of DO-T-TLC is introduced. Then, the operating principle of multiplexing switches and the available switching states of converter are analyzed, including current path, output phase voltage level, and blocking voltage of different switching states. The phase disposition pulsewidth modulation scheme with dc offsets is discussed in detail, and the key problems of the modulation scheme under both the common frequency and different frequency operation modes, such as voltage level selection, displacement angle constraint, and modulation index range, are studied. For the imbalance of two series capacitors in the dc-link, the mechanism is first revealed, and then a dc-link capacitor voltage balance method to control the average neutral point current is proposed. When DO-T-TLC is used in different operation modes, the ability and effect of this method to balance capacitor voltages are summarized. A low-power three-phase prototype is built, and the experimental results are given to verify the feasibility of the proposed topology and the effectiveness of the modulation scheme to control the voltage balance.

Maximal Quasi-Cliques Mining in Uncertain Graphs

Cohesive subgraph mining is a fundamental problem in the field of graph data analysis. Many existing cohesive graph mining algorithms are mainly tailored to deterministic graphs. Real-world graphs, however, are often not deterministic, but uncertain in nature. Applications of such uncertain graphs include protein-protein interactions networks with experimentally inferred links and sensor networks with uncertain connectivity links. In this article, we study the problem of mining cohesive subgraphs from an uncertain graph. Specifically, we introduce a new <inline-formula><tex-math notation="LaTeX">$(\alpha,\gamma)$</tex-math></inline-formula> -quasi-clique model to model the cohesive subgraphs in an uncertain graph, and propose a basic enumeration algorithm to find all maximal <inline-formula><tex-math notation="LaTeX">$(\alpha,\gamma)$</tex-math></inline-formula> -quasi-cliques. We also develop an advanced enumeration algorithm based on several novel pruning rules, including early termination and candidate set reduction. To further improve the efficiency, we propose several optimization techniques. Extensive experiments on five real-world datasets demonstrate that our solutions are almost three times faster than the baseline approach.

A vertex-separator-based integer linear programming formulation for the partitioned Steiner tree problem

Given an undirected graph G with a cost function on vertices, a collection of subgraphs of G such that in each subgraph, there are some distinguished vertices called terminals, the Partitioned Steiner Tree Problem (PSTP) asks for a minimum cost vertex set such that, in each of the given subgraph Gi, the graph induced by the vertex set spans the terminal set in Gi. The PSTP generalizes the well-known Steiner tree problem and has important applications in computational sustainability, network design, and social network analysis. However, for solving the PSTP, conventional integer programming approaches based on single-commodity flow, multi-commodity flow and subtour elimination integer linear programs, suffer from low computational efficiency due to a substantial number of variables. In this paper, we propose a compact vertex-separator-based integer linear programming formulation with much fewer variables. Enhancing inequalities are also studied for tightening the formulation. We further investigate a branch-and-cut algorithm, a local-branching heuristic algorithm, and a hybrid algorithm combining them. In experiments where both public real-world and synthetic graphs are used, our hybrid algorithm outperforms all conventional approaches, especially for large graphs with more than ten thousand vertices. Further tests also validate the effectiveness of the proposed formulation and enhancing inequalities.