Sampling Instants Research Articles

Recurrent Neural Network-Based Joint Chance Constrained Stochastic Model Predictive Control*

A novel recurrent neural network (RNN)-based approach is proposed in this work to handle joint chance-constrained stochastic model predictive control (SMPC) problem. In the proposed approach, the joint chance constraint (JCC) is first reformulated as a quantile-based inequality to reduce the complexity in approximation. Then, the quantile function (QF) in the quantile-based inequality is replaced by the empirical QF using sample average approximation (SAA). Afterwards, the empirical QF is approximated via an RNN-based surrogate model, which is embedded into the SMPC problem formulation to predict quantile values at different sampling instants. By employing the RNN-based approximation, the resulting deterministic optimization problem is finally solved through a nonlinear optimization solver. The proposed approach is applied to a hydrodesulphurisation process to demonstrate its efficiency in handling the SMPC problem.

Polyhedral Regions of Stability for Aperiodic Sampled-Data Linear Control Systems With Saturating Inputs

This work proposes a method to assess the local asymptotic stability and to provide polyhedral estimates of the region of attraction of the origin (RAO) of linear systems under aperiodic sampled-data control and saturating inputs. The approach is based on a discrete-time model that describes the behavior of the system state between consecutive sampling instants. It corresponds to a difference inclusion defined from a partition of the intersampling interval and from the saturated and nonsaturated (SNS) embedding of saturation functions. A method to construct a contractive polyhedral set for this model is proposed. It is shown that this set induces a local Lyapunov function strictly decreasing at the sampling instants and that it is an estimate of the RAO of the continuous-time closed-loop system.

Addressing uncertainty and bias in land use, land use change, and forestry greenhouse gas inventories

National greenhouse gas inventories (NGHGIs) will play an increasingly important role in tracking country progress against United Nations (UN) Paris Agreement commitments. Yet uncertainty in land use, land use change, and forestry (LULUCF) NGHGHI estimates may undermine international confidence in emission reduction claims, particularly for countries that expect forests and agriculture to contribute large near-term GHG reductions. In this paper, we propose an analytical framework for implementing the uncertainty provisions of the UN Paris Agreement Enhanced Transparency Framework, with a view to identifying the largest sources of LULUCF NGHGI uncertainty and prioritizing methodological improvements. Using the USA as a case study, we identify and attribute uncertainty across all US NGHGI LULUCF “uncertainty elements” (inputs, parameters, models, and instances of plot-based sampling) and provide GHG flux estimates for omitted inventory categories. The largest sources of uncertainty are distributed across LULUCF inventory categories, underlining the importance of sector-wide analysis: forestry (tree biomass sampling error; tree volume and specific gravity allometric parameters; soil carbon model), cropland and grassland (DayCent model structure and inputs), and settlement (urban tree gross to net carbon sequestration ratio) elements contribute over 90% of uncertainty. Net emissions of 123 MMT CO2e could be omitted from the US NGHGI, including Alaskan grassland and wetland soil carbon stock change (90.4 MMT CO2), urban mineral soil carbon stock change (34.7 MMT CO2), and federal cropland and grassland N2O (21.8 MMT CO2e). We explain how these findings and other ongoing research can support improved LULUCF monitoring and transparency.

Dynamic self-triggered control for nonlinear systems with delays

Self-triggered control (STC) is a resource efficient approach to determine sampling instants for Networked Control Systems (NCS). Recently, a dynamic STC strategy based on hybrid Lyapunov functions for nonlinear NCS has been proposed in Hertneck and Allgöwer (2021b), however with limitation to NCS without transmission delays. In this paper, we extend this strategy for nonlinear NCS with transmission delays. The capability to handle systems with delays makes it possible to use the resulting dynamic STC mechanism in many practical scenarios where instant transmissions without delays cannot be guaranteed. The proposed dynamic STC mechanism guarantees stability despite bounded transmission delays. The effectiveness of the mechanism is illustrated with a numerical example and compared to state-of-the art literature.

Non-Causal State Estimation for Improved State Tracking in Iterative Learning Control

State-tracking Iterative Learning Control (ILC) yields perfect state-tracking performance at each n sample instances for systems that perform repetitive tasks, where n stands for the order of the system. By achieving perfect state-tracking, oscillatory intersample behavior often encountered in output-tracking ILC has been mitigated. However, state-tracking ILC only assures the estimated state error to converge to a significantly small value, meaning the accuracy of the state estimation takes a critical role. State estimation using a causal state observer has had an inevitable trade-off between the estimation delay and the noise sensitivity. By utilizing the non-causal operation of ILC, a non-causal state estimation can be designed. This non-causal state estimation performs beyond the trade-off of causal estimation, improving the estimation delay without compromising the noise sensitivity. The aim of this paper is to implement the non-causal state observer to state-tracking ILC, and present the improved state tracking by applying it to a second order system.

Distributed multi-rate sampled-data [formula omitted] consensus filtering for cyber-physical systems under denial-of-service attacks

This paper addresses the problem of designing the distributed sampled-data H∞ consensus filters for cyber-physical systems when the sampling rate of the sensors is different from that of the filters, and the measurement channels from the sensors to the filters and the communication links between the filters are subject to the denial-of-service attacks. First, a new sequence is defined to unify the sampling instants of the sensors and filters. Based on this new sequence and the detectability decomposition, distributed multi-rate sampled-data H∞ consensus filters are designed, and the resilience of the proposed filters to the denial-of-service attacks is analyzed. It is shown that the attacks on the measurement channels will degrade the performance of the state estimations of both detectable part and undetectable part of the system state, while the attacks on the communication links only affect the performance of the state estimations of the undetectable part of the system state. At last, an example is provided to demonstrate the effectiveness of the proposed method.

Severity-insensitive fault diagnosis method for heat pump systems based on improved benchmark model and data scaling strategy

The fault diagnosis of heat pump systems is of great significance to reduce system energy consumption and ensure stable operation. Intelligent algorithms based on deep learning have a good diagnostic effect on complex thermal systems such as heat pump systems, but they also face the application problem of poor model generalization, which makes them unable to adapt to complex and actual dynamic scenarios. This paper focuses on the specific problems of the heat pump system's varying severity of fault conditions that cause the actual diagnosis accuracy of the model to decrease. Then, a new self-adaptive diagnosis method was proposed based on a residual data training framework combined with data scaling strategy, which adapts varying severity diagnosis under the condition that the training data derives from a single severity level. This paper analyzes the thermodynamic validity of the residual data training framework and, correspondingly, proposes a benchmark model based on the attention mechanism to greatly improve the quality of the residual data. Analyzing the thermodynamic laws of different fault severity and proposing a local scaling strategy for residual data allows for the residual sample instance of a single severity to be transferred to the residual sample space of multiple severity. Finally, verification of the ASHRAE RP-1043 data set revealed that the fault diagnosis method based on residual data can significantly improve the diagnosis accuracy and generalization. Furthermore, the higher accuracy of the benchmark model results in more obvious performance improvement. At the same time, the local data scaling strategy can significantly improve the upward and downward compatibility of the diagnostic model. It proves that the method proposed in this paper can effectively reduce the sensitivity of the diagnosis model to the severity of the fault, and it must be known that this self-adaptive method can also solve the problems of other actual diagnosis scenarios, such as different systems, varying environments, and varying loads.

Sampled-data distributed protocol for coordinated aggregation of multi-agent systems subject to communication delays

This paper studies the coordinated aggregation problem of a multi-agent system. Particularly, all the agents reach a consensus within a pre-specified target region. However, only a subset of agents have access to this target region, and each agent merely interacts with its neighbors by communication. Moreover, there exist unknown heterogeneous delays in communication channels. The underlying communication topology is characterized by a digraph. To accommodate the practical digital disposal, a sampled-data distributed protocol is proposed, where the sampling is asynchronous in the sense that the sampling periods of distinct agents are heterogeneous. The resulting closed-loop system from the proposed sampled-data distributed protocol is in a hybrid fashion that the continuous system is fed-back by using discrete states at sampling instants. The convergence performance of this hybrid closed-loop system is analyzed based on the contraction theory. More specifically, it is first shown that all the states are coordinated to aggregate within the target region, i.e., coordinated aggregation. With this result, it is next shown that all the states are coordinated towards a consensus, i.e., state agreement. These together guarantee the fulfillment of the concerned coordinated aggregation objective. Finally, a simulation example is given to validate the theoretical results.

Event-triggered fuzzy adaptive control of nonlinear switched systems with predefined accuracy and mismatched switching

A fuzzy adaptive switching event-triggered control strategy is obtained for a class of uncertain nonlinear switched systems with predefined accuracy. Since the switching may occur between two adjacent sampling instants and may lead to trigger a new event, it raises the mismatched switching and brings severe challenges to avoid the Zeno behavior of the subsystem controllers. The formidable problems are successfully addressed by a new switching event-triggering mechanism without restrictive assumptions. With the proposed fuzzy adaptive switching control approach, the adverse effects of mismatched switching between the subsystem and the controller are addressed, and no subsystem controllers exhibit the Zeno behavior. Furthermore, by using a projection operator-based adaptation strategy and constructing a class of continuous functions, the convergence accuracy of the switched system appears explicitly in design parameters. It allows designers to make decisions in advance based on the requirement of convergence accuracy. Finally, theoretical results are verified by two illustrative examples.

Stability analysis for interconnected system with quantized sampled-data control

In this paper, we investigate the stability analysis for interconnected system, which is composed of multiple subsystems with sampled-data control and state quantization. The controlled interconnected system is modeled as a time-delay system with time-varying delays. By employing the information of sampling instants, a discontinuous Lyapunov functional is constructed. Using this functional, we derive tractable sufficient conditions to ensure the well-posedness and asymptotic stability of the considered system by taking the interconnected structure into consideration. These conditions depend only on the sampling interval, quantizer parameters and matrices parameters of individual subsystem, making them attractive in computation verification for large scale interconnected system. Furthermore, a grid search based optimization algorithm is proposed to reduce the total number of sampled data for the whole system. The effectiveness and applicability of the main results are shown by two examples.

Distributed Bandit Online Convex Optimization With Time-Varying Coupled Inequality Constraints

Distributed bandit online convex optimization with time-varying coupled inequality constraints is considered, motivated by a repeated game between a group of learners and an adversary. The learners attempt to minimize a sequence of global loss functions and at the same time satisfy a sequence of coupled constraint functions, where the constraints are coupled across the distributed learners at each round. The global loss and the coupled constraint functions are the sum of local convex loss and constraint functions, respectively, which are adaptively generated by the adversary. The local loss and constraint functions are revealed in a bandit manner, i.e., only the values of loss and constraint functions are revealed to the learners at the sampling instance, and the revealed function values are held privately by each learner. Both one- and two-point bandit feedback are studied with the two corresponding distributed bandit online algorithms used by the learners. We show that sublinear expected regret and constraint violation are achieved by these two algorithms, if the accumulated variation of the comparator sequence also grows sublinearly. In particular, we show that <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(T^{\theta })$</tex-math></inline-formula> expected static regret and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(T^{7/4-\theta })$</tex-math></inline-formula> constraint violation are achieved in the one-point bandit feedback setting, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(T^{\max \lbrace \kappa,1-\kappa \rbrace })$</tex-math></inline-formula> expected static regret and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(T^{1-\kappa /2})$</tex-math></inline-formula> constraint violation in the two-point bandit feedback setting, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\theta \in (3/4,5/6]$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\kappa \in (0,1)$</tex-math></inline-formula> are user-defined tradeoff parameters. Finally, the tightness of the theoretical results is illustrated by numerical simulations of a simple power grid example, which also compares the proposed algorithms to algorithms existing in the literature.

Resilient stabilization of discrete-time Takagi-Sugeno fuzzy systems: Dynamic trade-off between conservatism and complexity

This paper is concerned with the problem of developing more efficient stabilization conditions for discrete-time Takagi-Sugeno fuzzy systems, i.e., not only reducing the conservatism but also (at the same time) alleviating the complexity of fuzzy control synthesis. Firstly, under the framework of traditional fuzzy stabilization, the recent multiple-sums-based method reported in the literature is improved by removing all the redundant variables, and thus the same feasible stabilization range can be obtained at the cost of more economical computational burden. Secondly, in order to further enhance the control efficiency, a dynamic trade-off between conservatism and complexity is established by proposing a new online evaluator of the updated system variation information across two adjacent sampling instants, and thus the so-called resilient stabilization is developed for reducing the conservatism without increasing or even alleviating the complexity. Moreover, all the determined matrices at the farthest sampling instant can be entirely removed without introducing any conservatism due to the proposed substitution technique. Finally, the superiority and effectiveness of our proposed methods are illustrated by a set of simulation comparisons with relevant research results reported in recent literature.

Prior informed regularization of recursively updated latent-variables-based models with missing observations

Many data-driven modeling techniques identify locally valid, linear representations of time-varying or nonlinear systems, and thus the model parameters must be adaptively updated as the operating conditions of the system vary, though the model identification typically does not consider prior knowledge. In this work, we propose a new regularized partial least squares (rPLS) algorithm that incorporates prior knowledge in the model identification and can handle missing data in the independent covariates. This latent variable (LV) based modeling technique consists of three steps. First, a LV-based model is developed on the historical time series data. In the second step, the missing observations in the new incomplete data sample are estimated. Finally, the future values of the outputs are predicted as a linear combination of estimated scores and loadings. The model is recursively updated as new data are obtained from the system. The performance of the proposed rPLS and rPLS with exogenous inputs (rPLSX) algorithms are evaluated by modeling variations in glucose concentration (GC) of people with Type 1 diabetes (T1D) in response to meals and physical activities for prediction windows up to one hour, or 12 sampling instances, into the future. The proposed rPLS family of GC prediction models are evaluated with both in-silico and clinical experiment data and compared with the performance of recursive time series and kernel-based models. The root mean squared error (RMSE) with simulated subjects in the multivariable T1D simulator where physical activity effects are incorporated in GC variations are 2.52 and 5.81 mg/dL for 30 and 60 mins ahead predictions (respectively) when information for all meals and physical activities are used, increasing to 2.70 and 6.54 mg/dL (respectively) when meals and activities occurred, but the information is withheld from the modeling algorithms. The RMSE is 10.45 and 14.48 mg/dL for clinical study with prediction horizons of 30 and 60 mins, respectively. The low RMSE values demonstrate the effectiveness of the proposed rPLS approach compared to the conventional recursive modeling algorithms.

Neural Network-Based Sampled-Data Control for Switched Uncertain Nonlinear Systems

This article investigates the sampled-data stabilization problem of a class of switched nonlinear systems. All subsystems of the considered system are allowed to be unstabilizable. To relax the restrictions on unknown nonlinear functions in some existing results, we use the nonlinear approximation ability of radial basis function neural networks. Novel mode-dependent adaptive laws and sampled-data control laws are constructed by only using the system states' information at sampling instants. A novel sampled-data switching condition is derived, which can avoid Zeno behavior effectively. To guarantee that all states of the closed-loop system (CLS) are bounded, a new allowable sampling period is deduced. Finally, we demonstrate the proposed method's effectiveness through two examples.

Aperiodic sampled-data control for local stabilization of memristive neural networks subject to actuator saturation: Discrete-time Lyapunov approach

In this paper, the local stabilization of memristive neural networks (MNNs) with actuator saturation is investigated via aperiodic sampled-data control. Inspired by the characteristic of the control scheme, a novel sampling-interval-dependent Lyapunov functional (SIDLF) is constructed. The main contribution of the developed Lyapunov functional lies in that the requirement on its positive definiteness is replaced by a looped condition. Then, using some inequality techniques and the discrete-time Lyapunov approach, two sufficient criteria are derived to ensure the locally asymptotical stability of the trivial solutions of closed-loop systems. A unified work is developed that can deal with the presence of the saturation nonlinearity effects, aperiodic sampled-data control, as well as SIDLF. Additionally, two convex optimization schemes, aiming at enlarging the admissible initial region (AIR) and maximizing the upper bound of sampling interval, are respectively presented for designing the desired saturated sampled-data controller gains. A quantitative relationship between the maximum sampling interval and AIR is revealed. Finally, two numerical examples are given to illustrate the advantages and effectiveness of the derived theoretical conclusions.

Periodic event‐triggered bipartite consensus for multi‐agent systems with partial information transmission

AbstractThis paper investigates the periodic event‐triggered bipartite consensus for the single integral multi‐agent systems. A fully distributed periodic event‐triggered protocol is designed for a general case that only partial information can be transmitted among agents. Then, we construct a state‐dependent and time‐dependent event detector to determine whether the sampled data should be sent out at sampling instants. Under structurally balanced signed digraphs, it is proved that all agents achieve consensus with the same magnitude but opposite sign. Notably, compared with the existing event‐triggered strategies, the limitation on sampling period can be removed and the Zeno behavior is automatically excluded. Finally, the simulation results illustrate the validity of the provided protocol.

Symplectic discrete-time energy-based control for nonlinear mechanical systems

We present a novel approach for discrete-time state feedback control implementation which reduces the deteriorating effects of sampling on stability and performance in digitally controlled nonlinear mechanical systems. We translate the argument of energy shaping to discrete time by using the symplectic implicit midpoint rule. The method is motivated by recent results for linear systems, where feedback imposes closed-loop behavior that exactly represents the symplectic discretization of a desired target system. For the nonlinear case, the sampled system and the target dynamics are approximated with second order accuracy using the implicit midpoint rule. The implicit nature of the resulting state feedback requires the numerical solution of an in general nonlinear system of algebraic equations in every sampling interval. For an implementation with pure position feedback, the velocities/momenta have to be approximated in the sampling instants, which gives a clear interpretation of our approach in terms of the Störmer–Verlet integration scheme on a staggered grid. Both the Hamiltonian and the Lagrangian perspective are adopted. We present discrete-time versions of impedance or energy shaping plus damping injection control as well as computed torque tracking control in the simulation examples to illustrate the performance and stability gain compared to the quasi-continuous implementation. We discuss computational aspects and show the structural advantages of the implicit midpoint rule compared to other integration schemes in the appendix.

Completely fair energy scheduling mechanism in a smart distributed multi-microgrid system

In this paper, we have proposed a completely fair energy scheduling mechanism for a smart distributed multi-microgrid system which guarantees that the energy is scheduled fairly among all the buyer microgrids (MGs). It is a non-priority based starvation free mechanism as all the buyers are treated equal and every buyer MG gets at least some portion of its energy requirement fulfilled through the internal trading. The energy scheduling is done in two phases: during phase I, energy is equally distributed among all the buyer MGs. Because of this equal distribution of energy, the buyer MGs are benefited as they are not required to purchase their entire energy requirement from utility grid at higher price. During phase II, Vickrey auction scheme is used to schedule the remaining energy amongst the buyer MGs whose energy requirements were not fulfilled during the first phase. We have evaluated the proposed mechanism for a sample instance of microgrid network by simulating the environment. The simulation demonstrates that using the proposed mechanism the total energy buying cost for all buyer MGs is reduced greatly compared with the schemes where only auctioning is used for internal trading.

Improved nonlinear MPC for aircraft gas turbine engine based on semi-alternative optimization strategy

The development of advanced control systems is motivated to achieve the complicated aircraft engine control, so a novel semi-alternative optimization strategy based model predictive control is proposed. In this proposed controller, a nonlinear state-space model is generated as the predictive model on the basis of a baseline engine model that estimates the current operating state of engine with an extended Kalman filter every sampling instant, and a quadratic constrained problem rather than a higher order nonlinear problem is constructed based on this model. Moreover, a novel control sequence to be optimized based on semi-alternative optimization strategy is proposed, which includes two parts. The first part represents that all the control variables of the engine are optimized for the current sampling instant while the second part represents that different control variables are optimized alternatively for different future sampling instants over the control horizon. The proposed model predictive control method is implemented to a twin-spool turbofan engine. Simulation results demonstrate not only that the proposed method can achieve a smaller control error than the standard model predictive control algorithm does, but also that the proposed controller is more time-saving than the standard model predictive control, which can save up to about 61% optimization time when control horizon increases to nine.

Uniform probabilistic generation of relation instances satisfying a functional dependency

Software engineering includes the runtime evaluation of a prototype by experiments with carefully selected sample inputs. For the development of software intended to operate on relation instances for a given relational schema with a single functional dependency, we are then challenged to generate appropriate sample instances of increasing size. Moreover, studying the impact of varying the sizes of the attribute domains might be important. We focus on seeing uniformly distributed collections of sample instances to be appropriate. If the schema is normalized (in Boyce–Codd normal form with the left-hand side of the functional dependency forming a unique key), then a straightforward heuristic insertion procedure complies with our requirements. However, for a non-normalized schema (the left-hand side not forming a key), based on a complex combinatorial analysis and exploiting an algorithm for restricted integer partitions, we develop a sophisticated probabilistic procedure of high computational complexity for generating any element of such a collection with equal probability. Moreover, we demonstrate that simpler approaches based on uniform local selections, including the heuristic insertion procedure, fail to achieve global uniformity. The conceptual design and analysis are complemented by an experimental evaluation of a prototype implementation.