Stochastic Parameter Uncertainties Research Articles

Designing Decentralized Multi-Variable Robust Controllers: A Multi-Objective Approach Considering Nearly Optimal Solutions

This article presents a new methodology for designing a robust, decentralized control structure that considers stochastic parametric uncertainty and uses a multi-objective approach. This design tunes the loop pairing and controller to be implemented. The proposed approach obtains the optimal and nearly optimal controllers relevant to the nominal scenario. Once obtained, the robustness of these solutions is analyzed. This methodology is compared with a traditional approach for selecting the most robust control pairings. The traditional approach obtains lightly robust controllers, i.e., the most robust controllers with an acceptable performance for the nominal scenario, and it obtains trade-offs between robustness and nominal performance. However, the traditional approach has a high computational cost because it is necessary to consider uncertainty in the optimization stage. The proposed approach mathematically guarantees the acquisition of at least one neighbor controller for each existing lightly robust controller. Therefore, this approach obtains solutions similar to lightly robust solutions with a significantly lower computational cost. Furthermore, the proposed approach provides the designer with more diversity and interesting solutions that are not lightly robust. The different approaches are compared using an example of a multi-variable process with two alternative control structures. The results show the usefulness of the proposed methodology.

Advantages of using relevant nearly optimal solutions in multi-objective tuning of robust controllers

This paper presents a new approach for the multiobjective optimal design of robust controllers in systems with stochastic parametric uncertainty. Traditionally, uncertainty is incorporated into the optimization process. However, this can generate two problems: (1) low performance in the nominal scenario; and (2) high computational cost. For the first point, it is possible to ensure that the controllers produce an acceptable performance for the nominal scenario in exchange for being lightly robust. For the second point, the methodology proposed in this work reduces the computational cost significantly. This approach addresses uncertainty by analyzing the robustness of optimal and nearly optimal controllers in the nominal scenario. The methodology guarantees obtaining controllers that are similar/neighboring to lightly robust controllers. Two examples of controller design are shown: one for a linear model and another for a nonlinear model. Both examples demonstrate the usefulness of the proposed new approach.

Integration of design and control for renewable energy systems with an application to anaerobic digestion: A deep deterministic policy gradient framework

In recent years, the urgent need to develop sustainable processes to curb the effects of climate change has gained global attention and led to the transition into green technologies, such as Anaerobic Digestion Systems (AD). As these technologies present a complex dynamic behavior, there is a motivation to seek for new ways to optimize these systems. This study presents a Deep Deterministic Policy Gradient (DDPG) strategy for integration of process design and control. DDPG is a state-of-the-art reinforcement learning algorithm used to search for optimal solutions. The proposed approach considers stochastic disturbances and parametric uncertainty. Also, a penalty function included in the reward function is considered to account for process constraints. The proposed approach was tested in AD systems involving Tequila vinasses. Two reactor AD configurations were explored under multiple scenarios using the proposed DDPG strategy. While the two-stage AD system required a larger capital investment in exchange of higher amounts of biogas being produced, the single-stage AD system required less investment in capital costs in exchange of producing less biogas and therefore lower revenues than the two-stage system. The results showed that DDPG was able to identify optimal design and control profiles thus making it an attractive method for optimal process design and operations management of renewable systems.

Robust Data-Driven Iterative Learning Control for Linear-Time-Invariant and Hammerstein-Wiener Systems.

Iterative learning control (ILC) relies on a finite-time interval output predictor to determine the output trajectory in each trial. Robust ILCs intend to model the uncertainties in the predictor and to guarantee the convergence of the learning process subject to such model errors. Despite the vast literature in ILCs, parameterizing the uncertainties with the stochastic errors in the predictor parameters identified from system I/O data and thus robustifying the ILC have not yet been targeted. This work is devoted to solving such problems in a data-driven fashion. The main contributions are two-fold. First, a data-driven ILC method is developed for LTI systems. The relationship is established between the errors in the predictor matrix and the stochastic disturbances to the system. Its robust monotonic convergence (RMC) is then linked with the closed-loop learning gain matrix that contains the predictor uncertainties and is analyzed based on a closed-form expectation of this gain matrix multiplied with its own transpose, that is, in a mean-square sense (MS-RMC). Second, the data-driven ILC and MS-RMC analysis are extended to nonlinear Hammerstein-Wiener (H-W) systems. The advantages of the proposed methods are finally verified via extensive simulations in terms of their convergence and uncorrelated tracking performance with the stochastic parametric uncertainties.

Recursive Feasibility and Stability for Stochastic MPC based on Polynomial Chaos

This paper deals with stochastic model predictive control (SMPC) based on polynomial chaos expansion (PCE) for linear systems with time-invariant stochastic parametric uncertainties and time-varying stochastic additive disturbances subject to chance constraints on states and inputs. Exploiting terminal ingredients in the SMPC problem and a hybrid update strategy, a recursively feasible optimization problem is formulated. Moreover, stability of the system of PCE coefficients can be shown. Furthermore, in the paper the performance and computational complexity of SMPC based on PCEs is compared to tube-based SMPC and robust model predictive control (RMPC) is analyzed and benefits are demonstrated in simulation.

Distributed Fusion Estimation for Stochastic Uncertain Systems With Network-Induced Complexity and Multiple Noise.

This article investigates an issue of distributed fusion estimation under network-induced complexity and stochastic parameter uncertainties. First, a novel signal selection method based on event trigger is developed to handle network-induced packet dropouts, as well as packet disorders resulting from random transmission delays, where the H2/H∞ performance of the system is analyzed in different noise environments. In addition, a linear delay compensation strategy is further employed for solving the complex network-induced problem, which may deteriorate system performance. Moreover, a weighted fusion scheme is used to integrate multiple resources through an error cross-covariance matrix. Several case studies validate the proposed algorithm and demonstrate satisfactory system performance in target tracking.

Comparison of Alternative Methods to Assess the Cost-Effectiveness of Tumor-Agnostic Therapies: A Triangulation Approach Using Larotrectinib as a Case Study

ObjectivesThe study objective was to investigate the economic value of tumor-agnostic therapies when only single-arm effectiveness data are available at launch by applying multiple methodologies to establish comparative effectiveness. MethodsIn the absence of direct comparative data, 3 methods were used to estimate the counterfactual: (1) a historical control based on a systematic literature review for each tumor site from the larotrectinib trials, (2) an intracohort comparison using the previous line of therapy time to progression from larotrectinib trials, and (3) a nonresponder control that applied outcomes for larotrectinib nonresponders. Cost-effectiveness was modeled using the partitioned survival approach. Stochastic parameter uncertainty was assessed in a probabilistic sensitivity analysis (PSA). A triangulated estimate of the mean cost-effectiveness result was generated combining all 3 counterfactual estimates. ResultsIncremental cost-effectiveness ratios were similar across the 3 methodologies in the deterministic analysis ranging from £83 868 (95% uncertainty interval [UI] £65 698-£107 668) to £104 922 per quality-adjusted life-year (95% UI £80 132-£139 658). PSA results for each method substantially overlapped when plotted on the cost-effectiveness plane. Weighting PSA results for each method equally in the triangulation method produced an incremental cost-effectiveness ratios of £95 587 per quality-adjusted life-year gained (95% UI £70 449-£137 431). ConclusionsIn the absence of direct comparative data, different methods of estimating a counterfactual are possible, each with strengths and limitations. Triangulating results across the methods provides a composite view of the total uncertainty and a more consistent estimation of the cost-effectiveness of the tumor-agnostic intervention compared with choosing a single method.

Resilient Asynchronous State Estimation for Markovian Jump Neural Networks Subject to Stochastic Nonlinearities and Sensor Saturations.

This article studies the problem of dissipativity-based asynchronous state estimation for a class of discrete-time Markov jump neural networks subject to randomly occurring nonlinearities, sensor saturations, and stochastic parameter uncertainties. First, two stochastic nonlinearities occurring in the system are described by statistical means and obey two Bernoulli processes independently. Then, the hidden Markov model is used to characterize the real communication environment closely between the designed estimator and the system model due to the networked-induced phenomenons that also lead to randomly occurring parametric uncertainties of the estimator considered modeled by two Bernoulli processes. A new criterion is established to guarantee that the resulting error system is stochastically stable with predefined dissipativity performance. Finally, we provide a simulation example to validate the theoretical analysis.

Integration of Scheduling and Control Under Stochastic Parametric Uncertainty with Varying Unit Operation Times for Chemical Batch Plants: A Back-Off Approach

Abstract A new back-off methodology is presented in this work as an approach for solving MIDO formulations arising for the optimal scheduling and control of flow-shop batch plants under stochastic parametric uncertainty. The proposed algorithm decomposes the MIDO problem into a scheduling problem, a dynamic optimization problem and a unit time operation minimization problem. These problems are solved iteratively using back-off terms. Parametric uncertainty is modeled using statistical distribution functions and are embedded in the algorithm to ensure dynamic feasibility of the optimal control actions under stochastic realizations in those parameters. The proposed algorithm identifies scheduling and control decisions offline. To exemplify this methodology, the integration of scheduling and control of a flow-shop batch plant is considered. The results show that unit operation times chosen from optimization are better suited to accommodate stochastic parametric uncertainty while the control actions enforce process operational and product quality constraints at reasonable costs.

Optimal linear recursive estimators for stochastic uncertain systems with time-correlated additive noises and packet dropout compensations

This paper is concerned with the state estimation problem over a packet-dropping network for stochastic uncertain systems with time-correlated additive noises. Additive process and measurement noises are both depicted by first-order Gauss-Markov processes. Stochastic parameter uncertainties are described by correlated white multiplicative noises. When a sensor measurement transmitted over networks is lost, its predictor is used for compensation. The optimal linear recursive full-order state filter, predictor and smoother are proposed under the linear minimum variance (LMV) criterion by an innovation analysis approach. They are calculated in terms of the filter of the product of the multiplicative noise and state, estimators of the process and measurement noises, and cross-covariance matrices for the state and/or noises. The steady-state estimators are also studied. A sufficient condition for convergence of optimal linear estimators is given. The simulation results verify the effectiveness of the proposed algorithms.

A Novel Back-off Algorithm for Integration of Scheduling and Control of Batch Processes under Uncertainty

A novel decomposition algorithm for the integration of scheduling and control of multiproduct, multiunit batch processes under stochastic parameter uncertainty is presented. This iterative algorithm solves a scheduling and dynamic optimization problem around a nominal point while approximating uncertainty through back-off terms, embedded in the operational process constraints. Monte Carlo simulations are performed to propagate uncertainty and to evaluate dynamic feasibility; statistical information is drawn from these simulations to update the back-off terms. Convergence of the algorithm results in a set of scheduling and control decisions that aim to keep the plant dynamically feasible under the effect of uncertainty up to a user-defined tolerance criterion. The proposed algorithm is shown to be successfully applied to a multiproduct, multiunit batch plant under the effects of different probability density functions in the uncertain parameters. The algorithm’s performance is gauged against a fully integr...

State Estimation of Slow-Rate Integrated Measurement Systems in the Presence of Parametric Uncertainties

In this paper, state estimation of integrated measurement systems in the presence of stochastic parametric uncertainties has been studied in the framework of the optimal filtering technique. Integrated measurement is common in chemical processes in which a small amount of material are gradually collected for a period of time from a few minutes to some hours. This material is transported to the laboratories for analysis and measurement. The goal is to estimate slow-rate and fast-rate instantaneous states out of this integrated measurement by using the Kalman filter while parametric uncertainties have been considered in the noise parameters. Also, convergence analysis of this filter has been studied. The effectiveness of this method has been evaluated through simulation on a distillation column model and implementation on a laboratory-scale pH neutralization pilot plant.

Uncertainty quantification of model predictive control for nonlinear systems with parametric uncertainty using hybrid pseudo-spectral method

AbstractIn this paper, a hybrid pseudo-spectral (hPS) method is utilized to analyze the uncertainty of the model predictive control (MPC) for nonlinear systems with stochastic parameter uncertainty...

Optimization Approaches for Durable Reinforced Concrete Structures considering Interval and Stochastic Parameter Uncertainty

AbstractThe durability of reinforced concrete structures is dominated by steel reinforcement corrosion and uncertain service loads, which have to be considered in the lifetime oriented structural design. The transport of corrosive substances into the structure is considerably influenced by load induced cracking. The crack width therefore is a major controlling factor for the lifetime of reinforced concrete structures. To improve the design for durability, finite element models in combination with optimization approaches for polymorphic uncertain data are presented. Here, the crack width at the reinforcement layer is used as the optimization objective to be minimized. The structural reliability is treated as a constraint of the optimization task in terms of the accepted failure probability. The concrete covers of the reinforcement layers are chosen as interval design parameters, with midpoints to be optimized and a given radius to take construction imprecision into account. The structural loading, the Young's modulus of concrete and the corresponding tensile strength are considered as stochastic a priori parameters within the optimization, which is solved by a particle swarm optimization approach in combination with an artificial neural network surrogate model. The polymorphic uncertain structural response is computed by a combination of Monte Carlo simulations and optimization‐based interval analysis to consider the stochastic and interval parameters within the optimization task, respectively. An application example demonstrates the performance of the proposed approach.

Adaptive Tracking Control for Mobile Manipulators with Stochastic Disturbances

This paper investigates adaptive tracking control for mobile manipulators with stochastic disturbances and parametric uncertainties. Based on an appropriate reduced dynamic model and an adaptive law, a controller, which is provided by incorporating stochastic control theory with related adaptive technique, overcomes the problem of over-parametrization. It is shown that the designed state-feedback controllers can guarantee that the mean square of the tracking errors can be made arbitrarily small by choosing suitable design parameters. Simulation studies on the control of 2-DOF mobile manipulator shows the effectiveness of the proposed scheme.

Finite-time synchronization control for semi-Markov jump neural networks with mode-dependent stochastic parametric uncertainties

This paper addresses the problem of synchronization control for semi-Markov jump neural networks with mode-dependent stochastic parametric uncertainties covering a finite-time period. A more general semi-Markov jump neural network is developed by the mode-dependent stochastic parametric uncertainties technique, where both upper and lower bounds of parametric uncertainties are taken into consideration in determining the imprecise measurements. The time-varying semi-Markov chain information subject to uncertainty is established, and sufficient conditions are achieved combine with some integral method. Finally, two numerical examples are exhibited to verify the effectiveness of the produced scheme.

Event‐triggered filtering and intermittent fault detection for time‐varying systems with stochastic parameter uncertainty and sensor saturation

SummaryIn this paper, the event‐triggered filtering and intermittent fault detection problems are investigated for a class of time‐varying systems with stochastic parameter uncertainty and sensor saturation. Due to the existence of event‐triggered mechanism, the measured signal could be transmitted only when it satisfies the triggering condition. An event‐triggered filter is developed, which takes the event‐triggered mechanism, parameter uncertainty, and sensor saturation into full consideration but does not depend on any specific uncertainty structure. By utilizing the inductive and stochastic analysis technique, the filter gain is designed to ensure that the upper bound of the estimation error covariance is minimized at each time step. Based on the proposed filter, a residual is generated and the corresponding evaluation function and detection threshold are given to achieve fault detection. At last, two simulation studies are carried out to demonstrate the effectiveness and applicability of the proposed method.

Distributed filtering over wireless sensor networks with parameter and topology uncertainties

ABSTRACT In this paper, the robust distributed filtering problem is investigated for a class of wireless sensor networks with stochastic parameter and topology uncertainties. The local filters collect information not only from itself but also from its neighbouring sensor nodes according to the network topology. A novel robust distributed filter is proposed which takes stochastic parameter and topology uncertainties into full consideration but does not depend on any specific structure of uncertainties. By proper designing of the filter gain, the trace of estimation error covariance is minimised at each time step, where the new stochastic analysis and augmentation transformation techniques are developed to handle the challenges resulting from multiplicative stochastic uncertainties and sparse topology. The corresponding recursive robust distributed filtering algorithm is also presented for real-time online applications. Finally, a simulation study is carried out to illustrate the effectiveness and applicability of our proposed method.

Robust Filtering and Intermittent Fault Detection for Time-varying Systems with Stochastic Parameter Uncertainty and Sensor Saturation

This work is concerned with the filtering and intermittent fault detection problems for a class of time-varying systems with stochastic parameter uncertainty and sensor saturation. A robust filter is proposed which fully considers both stochastic parameter uncertainty and sensor saturation, but does not depend on any specific uncertainty structure. A special effort is made to obtain the upper bound of the estimation error covariance and the filter gain is designed to minimize it at each time step. Based on the proposed filter, a residual is generated and the corresponding fault detection strategy is given. Finally, a simulation study is carried out to illustrate the validity of the proposed methods.

Distributed Robust Fusion Estimation With Application to State Monitoring Systems

This paper studies the distributed robust fusion estimation problem with stochastic and deterministic parameter uncertainties, where the covariance of the Gaussian white noise is unknown, and the covariances of the random variables in the stochastic uncertainties are in a bounded set. By using the discrete-time stochastic bounded real lemma and the matrix analysis approach, each local robust estimator is derived to guarantee an optimal estimation performance for admissible uncertainties, and then necessary and sufficient condition for the distributed robust fusion estimator is presented to obtain an optimal weighting fusion criterion. Note that the local robust estimation problem and the distributed robust fusion estimation problem are both converted into convex optimization problems, which can be easily solved by standard software packages. The advantage and effectiveness of the proposed methods are demonstrated through state monitoring for target tracking system and stirred rank reactor system.