Terminal Set Research Articles

Terminal region characterization and stability analysis of discrete time quasi-infinite horizon nonlinear model predictive control

A terminal penalty term and terminal constraints were introduced in the nonlinear MPC (NMPC) formulation for establishing the nominal closed loop stability. A large terminal set gives rise to a large region of attraction for the closed loop system and can also help in reducing the on-line computation cost. In this work, two novel approaches have been developed for characterization of the terminal region for a discrete time quasi-infinite horizon NMPC formulation that employs quadratic stage cost. Similar to the continuous time QIH NMPC formulation by Chen and Allgöwer [1], a stabilizing linear controller developed using linearization at the origin is employed for characterization of the terminal set. The first approach permits use of an arbitrary linear controller while the second approach is based on LQR controller. Using a method of bounding only the higher order nonlinear effects of the system via simulations under linear controller, the proposed approach is further extended to handle terminal region computation for a large dimensional system. Unlike the approaches available in the literature, the proposed approaches provide sufficient degrees of freedom to shape the terminal set. The quadratic control Lyapunov function in the terminal set together with the quadratic stage cost is further used to establish exponential stability of the discrete time QIH NMPC formulation under nominal conditions. Additionally, it is shown that discrete time QIH-NMPC based on the nominal model is input to state stable in the face of bounded disturbances in the state dynamics. Efficacy of the proposed approaches for characterization of the terminal region is demonstrated using a two state example from Chen and Allgöwer [1] and a benchmark CSTR system. Moreover the extension to large dimensional systems is demonstrated using a system consisting of two distillation columns in series. Parametric studies reveal that the choice of sampling interval and the choices of the tuning matrices in both approaches have significant influence on the sizes of terminal sets. Moreover, the simulation results demonstrate that the systems under consideration converge asymptotically to the origin under the nominal conditions and are input to state stable in the face of bounded disturbance.

Shrinking horizon parametrized predictive control with application to energy-efficient train operation

A nonlinear model predictive control approach is studied, for problems where a fixed terminal instant and corresponding terminal set to be reached are imposed. The new technique features a shrinking horizon, rather than the most common receding one, and an input parametrization strategy to reduce computational burden. The property of transferability of the parametrization strategy is introduced. Under this property, theoretical convergence guarantees in nominal conditions are obtained by construction. Two relaxed techniques are then proposed to retain recursive feasibility in presence of bounded additive input disturbance. A bound on the constraint violation achieved by these relaxed techniques as a function of the uncertainty bound is derived, too. The developed strategy is applied to the problem of energy-efficient operation of trains, in either a fully autonomous mode (with continuous input values) or a driver assistance mode (with discrete input values, resulting in a nonlinear integer program if no parametrization is used). Realistic simulation results in this context illustrate the effectiveness of the approach.

Single-phase transformerless power conditioner based on a two-leg of a nine-switch converter

An interesting solution for problems associated with system voltage, such as sags and swells, as well as those associated with current such as low power factor and harmonic distortion is the unified power quality conditioner. However, one of its drawbacks is the high number of semiconductor devices since its conventional topology presents two full-bridge converters in a back-to-back configuration. Although the six-switch two-leg converter has a feature of presenting two sets of single-phase output terminals, the same as two full-bridge converters, but with a reduced number of switches (six, instead of eight), it has never been used in single-phase power conditioning systems. Therefore, the aim of this paper is to propose a single-phase transformerless power conditioner based on the six-switch two-leg converter. In this solution, there are two sets of single-phase outputs, each set behaving as an independent converter. The top unit of the converter is connected in parallel to the load by means of a series LC filter tuned to a specific frequency, working as a hybrid power filter and being responsible for the dc-link voltage regulation and the compensation of current harmonics generated by the non-linear load. The bottom unit works as a dynamic voltage restorer and it is responsible for compensating harmonics, sags or swells in the grid voltage, in such way that the load receives a sinusoidal voltage waveform. The challenges of the single-phase transformerless power conditioner that is proposed in this paper are different of the three-phase systems based on nine-switch converter previously proposed in literature. Dealing with the circulating current makes mathematical model and the modulation strategy completely different and, therefore, all equations have been developed for this specific single-phase power conditioner application. The proposed power conditioner presents four main advantages when compared with other configurations available in literature: (a) it is a transformerless solution; (b) it has a reduced number of switches; (c) it has a reduced dc-link voltage and rated power because of its hybrid power filter characteristics; (d) it does not have to handle with dc-link voltage unbalance. Experimental results demonstrate the validity and the effectiveness of the proposed topology.

The main principles of the approach to the construction of combined windings with one set of terminations

The principle of the construction of an AC combined winding with one set of terminations with p1 and p2 polarities of the MMF is proposed. Equations of the MMF and the turn phase of the combined winding, which create accordant and counter-rotating harmonics of the MMF polarity p1 and p2, are obtained. The cases of construction of CO with accordant- and counter-rotating harmonics of MMF of different polarity are considered in detail. The main relation for the distribution of conductors in the slots is presented. The spatial pattern of accordant and counter-rotating harmonics of the MMF polarity p1=5 and p2=3 with equal angular frequencies are shown.

A decision-support framework for the stowage of maritime containers in inland shipping

The typical voyage of a barge transporting maritime containers inland, consists of visiting a set of terminals where loading/unloading operations occur. The required stowage plans must meet stability requirements during all transport phases and avoid costly re-handling operations. In this paper, we formalize this problem and consider a typical dry-port transport system. We propose a comprehensive mathematical model that seeks to maximize stowed containers. To solve it, we develop a hybrid metaheuristic approach, based on local search and an industrial solver. Numerical experiments, based on real-world data, provide insights into the performances of the proposed framework and current stowage practices.

Distributed Model Predictive Control for Tracking Consensus of Linear Multiagent Systems With Additive Disturbances and Time-Varying Communication Delays.

In this article, we investigate a robust distributed model predictive control (DMPC) scheme for tracking the consensus of linear multiagent systems (MASs) subject to additive disturbances and time-varying communication delays. A terminal constraint set is constructed by the Lyapunov-Razumikhin functional, and a corresponding local controller is designed for each agent. Furthermore, the sufficient conditions ensure that the terminal constraint set is provided in the form of linear matrix inequalities (LMIs). The recursive feasibility of the proposed algorithm is guaranteed based on the designed terminal constraint set, terminal cost, and local controller. Moreover, the closed-loop system is shown to be input-to-state stable (ISS). An illustrative example is given to verify the effectiveness of the presented approach.

Operational Analyses and Control Scheme of Nine-Arm Modular Multilevel Converter

Nine-arm modular multilevel converter (9A-MMC) can be applied in many medium-/high-voltage applications with two sets of three-phase terminals, such as medium-voltage dual-motor drives and unified power flow controller, to replace two conventional modular multilevel converters for reducing the volume and cost. This article thoroughly investigated the operational principle of 9A-MMC, and proposed a unique operational mode that the number of submodules in each arm can be a variable. The mathematical model of 9A-MMC and steady-state analyses of capacitor voltage fluctuations and circulating current were studied in this article as well. Subsequently, a complete control scheme of 9A-MMC, including capacitor voltage balancing control and circulating current suppression control is systematically presented. Finally, the simulation and experimental results verified the performance of 9A-MMC and the effectiveness of the presented control methods.

Sex-Specific Differences in End-of-Life Burdensome Interventions and Antibiotic Therapy in Nursing Home Residents With Advanced Dementia

Nursing home residents with advanced dementia have limited life expectancies yet are commonly subjected to burdensome interventions at the very end of life. Whether sex-specific differences in the receipt of these interventions exist and what levels of physical restraints and antibiotics are used in this terminal setting are unknown. To evaluate the population-based frequency, factors, and sex differences in burdensome interventions and antibiotic therapy among nursing home residents with advanced dementia. This population-based cohort study from Ontario, Canada, used linked administrative databases held at ICES, including the Continuing Care Resident Reporting System Long-Term Care database, which contains data from the Resident Assessment Instrument Minimum Data Set, version 2.0. Nursing home residents (n = 27 243) with advanced dementia who died between June 1, 2010, and March 31, 2015, at 66 years or older were included in the analysis. Initial statistical analysis was completed in May 2017, and analytical revisions were conducted from November 2018 to January 2019. Sex of the nursing home resident. Burdensome interventions (transitions of care, invasive procedures, and physical restraints) and antibiotic therapy in the last 30 days of life. The final cohort included 27 243 nursing home residents with advanced dementia (19 363 [71.1%] women) who died between June 1, 2010, and March 31, 2015, at the median (interquartile range) age of 88 (83-92) years. In the last 30 days of life, burdensome interventions were common, especially among men: 5940 (21.8%) residents were hospitalized (3661 women [18.9%] vs 2279 men [28.9%]; P < .001), 2433 (8.9%) had an emergency department visit (1579 women [8.2%] vs 854 men [10.8%]; P < .001), and 3701 (13.6%) died in an acute care facility (2276 women [11.8%] vs 1425 men [18.1%]; P < .001). Invasive procedures were also common; 2673 residents (9.8%) were attended for life-threatening critical care (1672 women [8.6%] vs 1001 men [12.7%]; P < .001), and 210 (0.8%) received mechanical ventilation (113 women [0.6%] vs 97 men [1.2%]; P < .001). Among the 9844 residents (36.1%) who had a Resident Assessment Instrument Minimum Data Set, version 2.0, completed in the last 30 days of life, 2842 (28.9%) were physically restrained (2002 women [28.3%] vs 840 men [30.4%]; P = .005). More than one-third (9873 [36.2%]) of all residents received an antibiotic (6599 women [34.1%] vs 3264 men [41.4%]; P < .001). In multivariable models, men were more likely to have a transition of care (adjusted odds ratio, 1.41; 95% CI, 1.33-1.49; P < .001) and receive antibiotics (adjusted odds ratio, 1.33; 95% CI, 1.26-1.41; P < .001). Only 3309 residents (12.1%; 2382 women [12.3%] vs 927 men [11.8%]) saw a palliative care physician in the year before death, but those who did experienced greater than 50% lower odds of an end-of-life transition of care (adjusted odds ratio, 0.48; 95% CI, 0.43-0.54); P < .001) and greater than 25% lower odds of receiving antibiotics (adjusted odds ratio, 0.74; 95% CI, 0.68-0.81; P < .001). In this study, many nursing home residents with advanced dementia, especially men, received burdensome interventions and antibiotics in their final days of life. These findings appear to emphasize the need for sex-specific analysis in dementia research as well as the expansion of palliative care and end-of-life antimicrobial stewardship in nursing homes.

Improved prediction of solubility of gases in polymers using an innovative non-equilibrium lattice fluid/Flory-Huggins model

A combination of Flory-Huggins and non-equilibrium lattice fluid models are utilized for predicting the solubility coefficients of CO2, CH4, N2, n-C4H10 and i-C4H10 in low and high-density polyethylene, polysulfone and polycarbonate. The genetic programming has been used to acquire the appropriate function for this model. The solubility coefficients at infinite dilution are calculated based on non-equilibrium lattice fluid theory and the gas-polymer interaction is expressed by the Flory-Huggins interaction parameter. The solubility coefficients at infinite dilution, Flory-Huggins interaction parameter and pressure were selected as terminal sets and some simple mathematical functions and operators such as multiplication, division, summation, power and absolute value were regarded as mathematical function sets. The adjustable parameters of the proposed function were determined for each gas-polymer system based on nonlinear data fitting. The first adjustable model parameter was in the form of constant power and the second was obtained as a variable coefficient in the form of quadratics function of temperature. The results of the presented model demonstrate improved ability to predict the solubility of investigated gases in the considered polymers at high pressures in comparison to non-equilibrium lattice fluid and Sanchez-Lacombe equation of state models. In some cases, the absolute errors between experimental and predicted values of solubility coefficients were below 1% at the considered conditions.

Upper Bounds via Lamination on the Constrained Secrecy Capacity of Hypergraphical Sources

Hypergraphical sources are a natural class of sources for secret key generation, within which different subsets of terminals sharing secrets are allowed to discuss publicly in order to agree upon a global secret key. While their secrecy capacity, i.e., the maximum rate of a secret key that can be agreed upon by the entire set of terminals, is well-understood, what remains open is the maximum rate of a secret key that can be generated when there is a restriction on the overall rate of public discussion allowed. In this paper, we obtain a family of explicitly computable upper bounds on the number of bits of secret key that can be generated per bit of public discussion. These upper bounds are derived using a lamination technique based on the submodularity of the entropy function. In particular, a specific instance of these upper bounds, called the edge-partition bound, is shown to be tight for the pairwise independent network model, a special case of the hypergraphical source when the hypergraph is a graph. The secret key generation scheme achieving this upper bound is the tree-packing protocol of Nitinawarat et al. , thereby resolving in the affirmative the discussion rate optimality of the tree-packing protocol.

Distributed Model Predictive Control for Linear Systems With Adaptive Terminal Sets

We propose a distributed model predictive control scheme for linear time-invariant constrained systems that admit a separable structure. To exploit the merits of distributed computation algorithms, the terminal cost and invariant terminal set of the optimal control problem need to respect the coupling structure of the system. Existing methods to address this issue typically separate the synthesis of terminal controllers and costs from the one of terminal sets, and do not explicitly consider the effect of the current and predicted system states on this synthesis process. These limitations can adversely affect performance due to small or even empty terminal sets. Here, we present a unified framework to encapsulate the synthesis of both the stabilizing terminal controller and invariant terminal set into the same optimization problem. Conditions for Lyapunov stability and invariance are imposed in the synthesis problem in a way that allows the terminal cost and invariant terminal set to admit the desired distributed structure. We illustrate the effectiveness of the proposed method on several numerical examples.

A general dissipativity constraint for feedback system design, with emphasis on MPC

SummaryA “general dissipativity constraint” (GDC) is introduced to facilitate the design of stable feedback systems. A primary application is to MPC controllers when it is preferred to avoid the use of “stabilising ingredients” such as terminal constraint sets or long prediction horizons. Some very general convergence results are proved under mild conditions. The use of quadratic functions, replacing GDC by “quadratic dissipativity constraint” (QDC), is introduced to allow implementation using linear matrix inequalities. The use of QDC is illustrated for several scenarios: state feedback for a linear time‐invariant system, MPC of a linear system, MPC of an input‐affine system, and MPC with persistent disturbances. The stability that is guaranteed by GDC is weaker than Lyapunov stability, being “Lagrange stability plus convergence.” Input‐to‐state stability is obtained if the control law is continuous in the state. An example involving an open‐loop unstable helicopter illustrates the efficacy of the approach in practice.

On the Coincidence of the Minimax Solution and the Value Function in a Time-Optimal Game with a Lifeline

We consider time-optimal differential games with a lifeline. In such games, as usual, there is a terminal set to which the first player tries to guide the system as fast as possible, and there is also a set, called a lifeline, such that the second player wins when the system attains this set. The payoff is the result of applying Kruzhkov’s variable change to the time when the system reaches the terminal set. We also consider Hamilton-Jacobi equations corresponding to such games. The existence of a minimax solution of a boundary value problem for a Hamilton-Jacobi type equation is proved. For this, we introduce certain strong assumptions on the dynamics of the game near the boundary of the game domain. More exactly, the first and second players can direct the motion of the system to the terminal set and the lifeline, respectively, if the system is near the corresponding set. Under these assumptions, the value function is continuous in the game domain. The coincidence of the value function and the minimax solution of the boundary value problem is proved under the same assumptions.

Multiple Capture in a Group Pursuit Problem with Fractional Derivatives

In a finite-dimensional Euclidean space, we consider a problem of pursuing one evader by a group of pursuers with equal capabilities of all participants. The dynamics of the problem is described by the system $$D^{(\alpha)}z_i=az_i+u_i-v,\;\;\;u_i,v\in{V},$$ where D(α)f is the Caputo derivative of order α ∈ (1, 2) of a function f. The set of admissible controls V is compact and strictly convex, and a is a real number. The aim of the group of pursuers is to catch the evader by at least m different pursuers, possibly at different times. The terminal sets are the origin. The pursuers use quasi-strategies. We obtain sufficient conditions for the solvability of the pursuit problem in terms of the initial positions. The investigation is based on the method of resolving functions, which allows us to obtain sufficient conditions for the termination of the approach problem in some guaranteed time.

A Method for Reducing the Complexity of Model Predictive Control in Robotics Applications

This letter describes an approach for parametrizing input and state trajectories in model predictive control. The parametrization is designed to be invariant to time shifts, which enables warm-starting the successive optimization problems and reduces the computational complexity of the online optimization. It is shown that in certain cases (e.g., for linear time-invariant dynamics with input and state constraints) the parametrization leads to inherent stability and the recursive feasibility guarantees without additional terminal set constraints. Due to the fact that the number of decision variables are greatly reduced through the parametrization, the warm-starting capabilities are preserved, and the approach is suitable for applications where the available computational resources (memory and CPU-power) are limited.

Enhancing dynamic operation optimization feasibility for constrained model predictive control systems

AbstractThis paper addresses a novel model predictive control algorithm for tracking to achieve an optimal operation for discrete‐time linear systems. The soft constraints characterizing the desired system performance are adjusted to solve the infeasibility problems caused by the original constraints. In this method, based on the principle of steady‐state error and constraints violation minimization, we firstly optimize the transition steady‐state with refined terminal invariant set, and slack variables as well as consider the dynamic constraints of the state constraints. Two types of soft constraints and slack variables are introduced to adjust state constraints online so that the MPC is feasible. Then, a dynamic optimization problem is solved which employs the constraints with minimum slack variables and takes the resulted steady‐state as the temporary target in current control period. The proposed method is able to minimize the violation of constraints and provides more potential to improve the control performance. Besides, the recursive feasibility and closed‐loop stability can be guaranteed by the combination of the new soft constraints adjustment method and tracking scheme. Finally, simulations at different circumstances prove the efficiency of the proposed method.

Evolving Predictions for Executive Pay Features in Board Networks

Numerous recent studies in finance literature have shown that board networks are an important inter-corporate setting, influencing corporate decisions made by the board of directors, for example the determination of executive pay features. In this paper, we evolve predictors for the existence and adoption of several important pay features among S&amp;P1500 companies, over the period 2006--2012. We use data from five well-known financial databases, including hundreds of variables containing both director-level and firm-level data. We present two approaches for predicting executive pay features. The first approach is based on a Genetic Algorithm (GA) used to evolve predictors based on weighted vectors of the predicting variables, providing relatively easy to understand prediction rules. The second approach employs Genetic Programming (GP) with sets of functions and terminals we devised specifically for this domain, based on contemporary research in finance. Thus, the GP approach explores a wider problem space and allows for more complex feature combinations. Experiments using both methods attain high quality prediction results, when compared to previous results in finance research. Additionally, our model is capable of successfully predicting combinations of pay features, compared to standard empirical models in finance, under various experimental conditions.

Robust Model Predictive Control of Linear Systems With Predictable Disturbance With Application to Multiobjective Adaptive Cruise Control

This paper presents a novel robust model predictive control (RMPC) concept for linear time-invariant systems with a predictable additive disturbance and linear constraints on the state and the input. Major properties of the approach are that: 1) available knowledge of the disturbance is considered in the optimization and 2) the robustness and the performance are addressed separately. As a result, the control performance is optimized while a less conservative condition on constraint satisfaction and recursive feasibility compared to the existing RMPC schemes is obtained. Traditionally, the Lyapunov function is chosen as the optimum of the objective function which must usually be quadratic in terms of the state and the input and contain a terminal cost term. These standard assumptions for the stability may restrict the flexibility of the optimization problem formulation and, thus, limit the applicability of the related RMPC strategies. To overcome this limitation, this paper proposes an explicit Lyapunov function and ensures the input-to-state stability (ISS) with a quadratic constraint, allowing to use any arbitrary convex objective function. To evaluate the novel RMPC concept, a multiobjective adaptive cruise control (ACC) is proposed and a simulation study using measured velocity profiles for the leading vehicle on a highway is presented. In the evaluation, a less restrictive constraint tightening and a larger terminal constraint set compared to the classical RMPC policies could be found and multiple objectives including driving comfort, energy efficiency, stability, and robust recursive fulfillment of safety, velocity, and further physical constraints could be achieved with the novel RMPC concept.

Characterizing standard genetic parts and establishing common principles for engineering legume and cereal roots.

SummaryPlant synthetic biology and cereal engineering depend on the controlled expression of transgenes of interest. Most engineering in plant species to date has relied heavily on the use of a few, well‐established constitutive promoters to achieve high levels of expression; however, the levels of transgene expression can also be influenced by the use of codon optimization, intron‐mediated enhancement and varying terminator sequences. Most of these alternative approaches for regulating transgene expression have only been tested in small‐scale experiments, typically testing a single gene of interest. It is therefore difficult to interpret the relative importance of these approaches and to design engineering strategies that are likely to succeed in different plant species, particularly if engineering multigenic traits where the expression of each transgene needs to be precisely regulated. Here, we present data on the characterization of 46 promoters and 10 terminators in Medicago truncatula, Lotus japonicus, Nicotiana benthamiana and Hordeum vulgare, as well as the effects of codon optimization and intron‐mediated enhancement on the expression of two transgenes in H. vulgare. We have identified a core set of promoters and terminators of relevance to researchers engineering novel traits in plant roots. In addition, we have shown that combining codon optimization and intron‐mediated enhancement increases transgene expression and protein levels in barley. Based on our study, we recommend a core set of promoters and terminators for broad use and also propose a general set of principles and guidelines for those engineering cereal species.

Design and Evaluation of Synthetic Terminators for Regulating Mammalian Cell Transgene Expression.

Tuning heterologous gene expression in mammalian production hosts has predominantly relied upon engineering the promoter elements driving the transcription of the transgene. Moreover, most regulatory elements have borrowed genetic sequences from viral elements. Here, we generate a set of 10 rational and 30 synthetic terminators derived from nonviral elements and evaluate them in the HT1080 and HEK293 cell lines to demonstrate that they are comparable in terms of tuning gene expression/protein output to the viral SV40 element and often require less sequence footprint. The mode of action of these terminators is determined to be an increase in mRNA half-life. Furthermore, we demonstrate that constructs comprising completely nonviral regulatory elements ( i.e., promoters and terminators) can outperform commonly used, strong viral based elements by nearly 2-fold. Ultimately, this novel set of terminators expanded our genetic toolkit for engineering mammalian host cells.