Terminal Set Research Articles

Genetic Programming-Based Discriminative Feature Learning for Low-Quality Image Classification.

Being able to learn discriminative features from low-quality images has raised much attention recently due to their wide applications ranging from autonomous driving to safety surveillance. However, this task is difficult due to high variations across images, such as scale, rotation, illumination, and viewpoint, and distortions in images, such as blur, low contrast, and noise. Image preprocessing could improve the quality of the images, but it often requires human intervention and domain knowledge. Genetic programming (GP) with a flexible representation can automatically perform image preprocessing and feature extraction without human intervention. Therefore, this study proposes a new evolutionary learning approach using GP (EFLGP) to learn discriminative features from images with blur, low contrast, and noise for classification. In the proposed approach, we develop a new program structure (individual representation), a new function set, and a new terminal set. With these new designs, EFLGP can detect small regions from a large input low-quality image, select image operators to process the regions or detect features from the small regions, and output a flexible number of discriminative features. A set of commonly used image preprocessing operators is employed as functions in EFLGP to allow it to search for solutions that can effectively handle low-quality image data. The performance of EFLGP is comprehensively investigated on eight datasets of varying difficulty under the original (clean), blur, low contrast, and noise scenarios, and compared with a large number of benchmark methods using handcrafted features and deep features. The experimental results show that EFLGP achieves significantly better or similar results in most comparisons. The results also reveal that EFLGP is more invariant than the benchmark methods to blur, low contrast, and noise.

Robust MPC for LPV systems via a novel optimization-based constraint tightening

We propose a novel approach to design a robust Model Predictive Controller (MPC) for constrained uncertain linear systems. The uncertain system is modeled as linear parameter varying with an additive disturbance. Set bounds for the system matrices and the additive uncertainty are assumed to be known. We formulate a novel optimization-based constraint tightening strategy around a predicted nominal trajectory which utilizes these bounds. With an appropriately designed terminal cost function and constraint set, we prove robust satisfaction of the imposed constraints by the resulting MPC in closed-loop with the uncertain system, and Input to State Stability of the origin. We highlight the efficacy of our proposed approach via a numerical example.

Stability of finite horizon optimisation based control without terminal weight

This paper presents a stability analysis tool for model predictive control (MPC) where control action is generated by optimising a cost function over a finite horizon. Stability analysis of MPC with a limited horizon but without terminal weight is a well-known challenging problem. We define a new value function based on an auxiliary one-step optimisation related to stage cost, namely optimal one-step value function (OSVF). It is shown that a finite horizon MPC can be made to be asymptotically stable if OSVF is a (local) control Lyapunov function (CLF). More specifically, by exploiting the CLF property of OSFV to construct a contractive terminal set, a new stabilising MPC algorithm (CMPC) is proposed. We show that CMPC is recursively feasible and guarantees stability under the condition that OSVF is a CLF. Checking this condition and estimation of the maximal terminal set are discussed. Numerical examples are presented to demonstrate the effectiveness of the proposed stability condition and corresponding CMPC algorithm.

Data-Driven Strategies for Hierarchical Predictive Control in Unknown Environments

This article proposes a hierarchical learning architecture for safe data-driven control in unknown environments. We consider a constrained nonlinear dynamical system and assume the availability of state-input trajectories solving control tasks in different environments. In addition to task-invariant system state and input constraints, a parameterized environment model generates task-specific state constraints, which are satisfied by the stored trajectories. Our goal is to use these trajectories to find a safe and high-performing policy for a new task in a new, unknown environment. We propose using the stored data to learn generalizable control strategies. At each time step, based on a local forecast of the new task environment, the learned strategy consists of a target region in the state space and input constraints to guide the system evolution to the target region. These target regions are used as terminal sets by a low-level model predictive controller. We show how to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i)</i> design the target sets from past data and then <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ii)</i> incorporate them into a model predictive control scheme with shifting horizon that ensures safety of the closed-loop system when performing the new task. We prove the feasibility of the resulting control policy, and apply the proposed method to robotic path planning, racing, and computer game applications. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper was motivated by the challenge of designing safe controllers for autonomous systems navigating through new environments. We consider scenarios where trajectory data from control tasks in different environments is available to the control designer. Possible applications include autonomous vehicles racing on new tracks or robotic manipulators performing tasks in the presence of new obstacles. Existing approaches to model-based control design for new environments generally use trajectory libraries, systematically adapting stored trajectories to the constraints of the new environment. This typically requires a priori knowledge of the entire task environment as well as resources to store and maintain the growing library. This paper suggests a new hierarchical control approach, in which stored trajectories are used to learn high-level strategies that can be applied while solving the new task. The strategies are learned offline, and only the parameterized strategy function needs to be stored for online control. Strategies only require knowledge of the nearby task environment, and provide navigation guidelines for the system. In this paper we show how to find such strategies from previous task data and how to integrate them into a low-level controller to safely and efficiently solve the new task. We also show how to adapt the modular framework as needed for a user’s desired application. Simulation experiments in robotic manipulator, autonomous vehicle, and computer game examples suggest that our approach can be used in a wide range of applications. In future research, we will address how to adapt the method for time-varying or stochastic environments.

ε-Positional Strategies in Theory of Differential Pursuit Games and Invariance of Constant Multivalued Mappings in Heat-Conductivity Problems

In this paper, we consider two problems. In the first problem, we prove that if the assumption from [1] and one additional condition on the parameters of the game hold, then the pursuit can be completed in any neighborhood of the terminal set. To complete the game, an ε-positional pursuit strategy is constructed.In the second problem, we study the invariance of a given multivalued mapping with respect to the system with distributed parameters. The system is described by the heat-conductivity equation containing additive control terms at the right-hand side.

Limit sets in global multiobjective optimization

ABSTRACT Inspired by the recently introduced branch-and-bound method for continuous multiobjective optimization problems from G. Eichfelder, P. Kirst, L. Meng, O. Stein [A general branch-and-bound framework for continuous global multiobjective optimization. J Glob Optim. 2021;80:195–227], we study for a general class of branch-and-bound methods in which sense the generated terminal enclosure and the terminal provisional nondominated set approximate the nondominated set when the termination accuracy is driven to zero. Our convergence analysis of the enclosures relies on constructions from the above paper, but is self-contained and also covers the mixed-integer case. The analysis for the provisional nondominated set is based on general convergence properties of the epsilon-nondominated set, and hence it is also applicable to other algorithms which generate such points. Furthermore, we discuss post-processing steps for the terminal enclosure and provide numerical illustrations for the cases of two and three objective functions.

A new artificial intelligent approach to buoy detection for mussel farming

ABSTRACT Aquaculture is an important industry in New Zealand (NZ). Mussel farmers often manually check the state of the buoys that are required to support the crop, which is labour-intensive. Artificial intelligence (AI) can provide automatic and intelligent solutions to many problems but has seldom been applied to mussel farming. In this paper, a new AI-based approach is developed to automatically detect buoys from mussel farm images taken from a farm in the South Island of NZ. The overall approach consists of four steps, i.e. data collection and preprocessing, image segmentation, keypoint detection and feature extraction, and classification. A convolutional neural network (CNN) method is applied to perform image segmentation. A new genetic programming (GP) method with a new representation, a new function set and a new terminal set is developed to automatically evolve descriptors for extracting features from keypoints. The new approach is applied to seven subsets and one full dataset containing images of buoys over different backgrounds and compared to three baseline methods. The new approach achieves better performance than the compared methods. Further analysis of the parameters and the evolved solutions provides more insights into the performance of the new approach to buoy detection.

Detailed Proof of Existence of Value Function in Time-Optimal Games with Lifeline

The paper discusses the existence of the value function of a time-optimal differential game with lifeline in a quite general formulation. In such a game, the first player tries to lead the trajectory of the system to a terminal set as soon as possible avoiding the lifeline. The aim of the second player is to lead the trajectory to the lifeline or, if it is not possible, to keep it outside the terminal set, or, if the latter is impossible too, to postpone maximally reaching the terminal set.

System level disturbance reachable sets and their application to tube-based MPC

Tube-based model predictive control (MPC) methods leverage tubes to bound deviations from a nominal trajectory due to uncertainties in order to ensure constraint satisfaction. This paper presents a novel tube‑based MPC formulation based on system level disturbance reachable sets (SL‑DRS), which leverage the affine system level parameterization (SLP). We show that imposing a finite impulse response (FIR) constraint on the affine SLP guarantees containment of all future deviations in a finite sequence of SL‑DRS. This allows us to formulate a system level tube‑MPC (SLTMPC) method using the SL‑DRS as tubes, which enables concurrent optimization of the nominal trajectory and the tubes, while using a positively invariant terminal set. Finally, we show that the SL‑DRS tubes can also be computed offline.

Robust Output Feedback MPC for LPV Systems Using Interval Observers

This article addresses the problem of robust output feedback model predictive control for discrete-time, constrained, linear parameter-varying systems subject to (bounded) state and measurement disturbances. The vector of scheduling parameters is assumed to be an unmeasurable signal taking values in a given compact set. The proposed controller incorporates an interval observer, that uses the available measurement to update the set-membership estimation of the states, and an interval predictor, used in the prediction step of the model predictive control (MPC) algorithm. The resulting MPC scheme offers guarantees on recursive feasibility, constraint satisfaction, and input-to-state stability in the terminal set. Furthermore, this novel algorithm shows low computation complexity and ease of implementation (similar to conventional MPC schemes).

Dual Self-Triggered Model-Predictive Control for Nonlinear Cyber-Physical Systems

This article is concerned with the event-based model-predictive control (MPC) problem of nonlinear cyber-physical systems with control constraints. A novel dual self-triggered MPC strategy is proposed to significantly reduce communication loads. In particular, two triggering mechanisms with two different optimal control problems are appropriately designed by considering whether the system state belongs to the terminal set. We prove that the strategy guarantees the algorithm feasibility and the closed-loop stability if the controller parameters satisfy the proposed conditions. Simulation and comparison studies verify effectiveness and advantages over the existing results.

Imbalance compensation of active magnetic bearing systems using model predictive control based on linear parameter-varying models

Active magnetic bearing (AMB) is a suspension system to levitate a rotating shaft freely without any physical contact which allows extremely fast rotation speeds. One big control challenge of the AMB systems, which appears during high rotation speeds, is the non-uniform distribution of the rotor weight about its rotating axis. This is usually referred to as the rotor imbalance problem which produces sinusoidal disturbance forces. These disturbances lead to undesirable vibrations and large deviations of the rotor shaft from its desired trajectories. We adopt in this work model predictive control (MPC) to reduce the effect of these sinusoidal disturbances and to achieve a stable levitation of the rotor shaft while tracking a reference trajectory. Owing to the MPC capability of handling constraints in an optimal manner, physical input constraints can be committed. Moreover, state constraints can be imposed to ensure safety of operation. For tractable implementation, we embed the nonlinear dynamics of the system in a linear parameter-varying (LPV) representation. To guarantee stability of the closed-loop system, a terminal cost and a terminal constraint set are included in the MPC optimization problem. For tractable computations of these terminal ingredients, a reduced LPV model is considered. The performance of the proposed LPV-MPC scheme is validated via simulation on the nonlinear model of an experimental setup of an AMB system and it is compared with two other classical controllers commonly used for these AMB systems in practice.

AUTOMATION OF THE OF SYMBOLS CORRECTNESS ANALYSIS IN SCIENTIFIC WORKS

In paper we propose the system of automated formation of the list of symbols in scientific works as kind of hybrid language texts, which are presented in the format of Tex. We describe the main system components. To analyze the text, it is suggested to use LL1 grammar. For grammar, terminal and nonterminal sets and a set of rules are defined. The rules for recognizing variables are described. The usage of LL1 grammar allows expanding the system for new characters of mathematical packages and combining the stages of parsing the text and forming a list. The system can be useful for improving the quality of presentation of texts in hybrid languages.

Sum-of-Norms Periodic Model Predictive Control for Space Rendezvous

Model predictive control (MPC) is receiving increasing attention in space applications, as a key technology for enhancing autonomy of the flight control system. Sum-of-norms formulations are specifically suited to this context, because they allow to optimize meaningful performance figures and to promote control sparsity. This brief presents a sum-of-norms MPC scheme for linear periodically time-varying systems. Closed-loop stability is proven by suitably defining periodic sequences of terminal weights and terminal sets. The proposed solution is applied to a rendezvous case study involving periodic dynamics due to geopotential effects and solar eclipses.

Practical implementable controller design with guaranteed asymptotic stability for nonlinear systems

Establishing the stability of model predictive control formulation is challenging. Using a combination of the terminal cost term and the terminal inequality constraint i.e. terminal set results in nominal asymptotic stability. Larger terminal set results in shorter minimum prediction horizon length required for feasibility from identical initial condition. Current work presents novel linear quadratic Gaussian regulator based approach for the terminal set characterization for the discrete time model predictive control scheme. Proposed approach provides large degrees of freedom in the form of additive matrices as tuning parameters for enlarging the terminal sets as against a single scalar for the literature approaches. Efficacy of the novel approach is demonstrated using a benchmark four tank system. It was observed that the average computation time reduces to significantly when compared to the approaches from the literature for identical initial conditions. This makes the controller design suitable for practical implementation.

Real-time tunable approximated explicit MPC

Tunability is a major obstacle in the creation and subsequent application of the explicit model predictive control (MPC). The main bottleneck lies in the need to reconstruct the parametric solution each time weighting factors changes. Such an operation makes the implementation of the explicit MPC impractical. This manuscript addresses the problem of producing a suboptimal parametric solution to the optimal control problem, where the change of the weighting factor does not warrant the reconstruction of the explicit MPC. The solution is achieved by interpolating between two boundary explicit solutions for a range of values in weighing factors. Furthermore, we show that the suboptimal solution enforces the closed-loop stability and recursive feasibility. The stability and recursive feasibility are maintained by carefully choosing the terminal penalty and terminal set in those boundary explicit solutions.

Interspecific morphological variation in Juglandoideae resting bud organization: a winter's tale?

Dormant resting buds are frequently regarded as static units, with protective cataphylls on the outside and embryonic foliage leaves on the inside. How the presence of cataphylls influences the dynamic, cyclical, annually repeating sequence of leaf forms that a resting bud gives rise to has rarely been interrogated. To examine the connection between dormant structure and growing-season development, we compare the complete seasonal heteroblastic sequence of leaf forms of six species of temperate Juglandaceae with distinctly different vegetative resting bud structures. These include buds with cataphylls; buds without cataphylls; and buds with caducous cataphylls that are lost before the onset of winter. In a common garden setting over a 7-month growing season, the dimensions of 2249 individual vegetative metamers were tracked from first exposure to abscission along the shoots of saplings and mature trees. The timing of metamer initiation within terminal buds was investigated using micro-CT scanning. Character state transitions of resting bud types were estimated using a phylogenetic tree of Juglandaceae. The presence of cataphylls within a heteroblastic sequence is associated with a single cohort of foliage leaves that flush and abscise synchronously. This growing pattern is highly determinate, with next year's terminal-bud cataphylls already initiated before spring leaf out. In contrast, in sequences without cataphylls, shorter-lived foliage leaves appear and abscise in a staggered fashion. Despite these differences in leaf demography, all examined heteroblastic sequences produce a series of small, caducous leaf forms that precede terminal bud set. The ubiquity of caducous leaf forms in Juglandoideae may point to the importance of shoot tip protection far beyond the dormant season. In addition, the presence or absence of cataphylls in resting buds is indicative of distinct shoot ontogenetic patterns, and functional strategies, in summer.

The vehicle allocation problem: Alternative formulation and branch-and-price method

The Vehicle Allocation Problem (VAP) consists of repositioning empty vehicles across a set of terminals over a given planning horizon so as to maximize the profits generated from serving demand for transportation of goods between pair of terminals. This problem has been classically modeled using an extended space–time network which captures the staging of the decision-making process. The present paper proposes a new integer linear programming (ILP) model based on the idea of representing the demands to be met as nodes on a graph. We also derive a Dantzig–Wolfe reformulation which is solved with a branch-and-price (BP) method. The proposed BP uses a stabilized interior-point column generation approach and a branching procedure that imposes constraints in the master problem, thus not damaging the structure of the subproblems. Additionally, we show that these subproblems can be solved efficiently using a shortest path algorithm on directed acyclic graphs (DAG). Computational experiments are carried out on realistic-sized benchmark instances commonly used in the literature. The results show the efficacy of the proposed strategies. In particular, the BP method solved the whole set of instances to proven optimality for the first time and in faster competitive times.

A novel feature selection for evolving compact dispatching rules using genetic programming for dynamic job shop scheduling

Because of advances in computational power and machine learning algorithms, the automated design of scheduling rules using Genetic Programming (GP) is successfully applied to solve dynamic job shop scheduling problems. Although GP-evolved rules usually outperform dispatching rules reported in the literature, intensive computational costs and rule interpretability persist as important limitations. Furthermore, the importance of features in the terminal set varies greatly among scenarios. The inclusion of irrelevant features broadens the search space. Therefore, proper selection of features is necessary to increase the convergence speed and to improve rule understandability using fewer features. In this paper, we propose a new representation of the GP rules that abstracts the importance of each terminal. Moreover, an adaptive feature selection mechanism is developed to estimate terminals’ weights from earlier generations in restricting the search space of the current generation. The proposed approach is compared with three GP algorithms from the literature and 30 human-made rules from the literature under different job shop configurations and scheduling objectives, including total weighted tardiness, mean tardiness, and mean flow time. Experimentally obtained results demonstrate that the proposed approach outperforms methods from the literature in generating more interpretable rules in a shorter computational time without sacrificing solution quality.

Quasipolynomial Multicut-mimicking Networks and Kernels for Multiway Cut Problems

We show the existence of an exact mimicking network of k O ( log k ) edges for minimum multicuts over a set of terminals in an undirected graph, where k is the total capacity of the terminals, i.e., the sum of the degrees of the terminal vertices. Furthermore, using the best available approximation algorithm for Small Set Expansion , we show that a mimicking network of k O ( log3 k ) edges can be computed in randomized polynomial time. As a consequence, we show quasipolynomial kernels for several problems, including Edge Multiway Cut , Group Feedback Edge Set for an arbitrary group, and Edge Multicut parameterized by the solution size and the number of cut requests. The result combines the matroid-based irrelevant edge approach used in the kernel for s -Multiway Cut with a recursive decomposition and sparsification of the graph along sparse cuts. This is the first progress on the kernelization of Multiway Cut problems since the kernel for s -Multiway Cut for constant value of s (Kratsch and Wahlström, FOCS 2012).