Average reachability of continuous-time Markov jump linear systems and the linear minimum mean square estimator

. In this paper we study the average reachability gramian for continuous-time linear systems with additive noise and jump parameters driven by a general Markov chain. We define a rather natural reachability concept by requiring that the average reachability gramian be positive definite. Aiming at a testable condition, we introduce a set of reachability matrices for this class of systems and employ invariance properties of the null space of the noise coefficient matrices to show that the system is reachable if and only if these matrices are of full rank. We also show for reachable systems that the state second moment is positive definite. One consequence of this result in the context of linear minimum mean square state estimation for reachable systems is that the expectation of the error covariance matrix is positive definite. Moreover, the average boundedness of the error covariance matrix is invariant to a type of perturbation in the noise model, meaning that the estimates are not overly sensitive, which consists in a property that is desirable in applications and sometimes referred to as stability of the estimator

A Convex Optimization Approach to the Design of Multiobjective Discrete Time Systems

One of the most important contributions of robust control theory has been the devel opment of a new framework for the design and analysis of feedback systems satisfying mixed time-frequency specifications. This framework is given by the Linear Matrix Inequality (LMI) approach where design and analysis problems are posed as convex optimization problems subject to affine matrix constraints. Most of the focus in this area has been on continuous-time systems design with very few results for discretetime systems. One of the main contributions of this work is the development and implementation of a MATLAB toolbox for discrete-time controller design using the LMI approach. Another important contribution is the development of a new linear matrix inequality for peak-to-peak gain minimization that allows the use of projec tion formulas for l1-design. In order to illustrate the advantages and effectiveness of the LMI framework to multiobjective design problems it was applied to design a noise-shaping feedback coder. This nonlinear circuit is an important component of (Sigma) - (Delta) modulators. This work shows that a robust control approach based on LMIs provides a rigorous framework for the systematic analysis and design of these coders in contrast to existing ad hoc methods used traditionally for such designs

A Model-Based Framework for the Smart Manufacturing of Polymers

It is hard to point a daily activity in which polymeric materials or plastics are not involved. The synthesis of polymers occurs by reacting small molecules together to form, under certain conditions, long molecules. In polymer synthesis, it is mandatory to assure uniformity between batches, high-quality of end-products, efficiency, minimum environmental impact, and safety. It remains as a major challenge the establishment of operational conditions capable of achieving all objectives together. In this dissertation, different model-centric strategies are combined, assessed, and tested for two polymerization systems. The first system is the synthesis of polyacrylamide in aqueous solution using potassium persulfate as initiator in a semi-batch reactor. In this system, the proposed framework integrates nonlinear modelling, dynamic optimization, advanced control, and nonlinear state estimation. The objectives include the achievement of desired polymer characteristics through feedback control and a complete motoring during the reaction. The estimated properties are close to experimental values, and there is a visible noise reduction. A 42% improvement of set point accomplishment in average is observed when comparing feedback control combined with a hybrid discrete-time extended Kalman filter (h-DEKF) and feedback control only. The 4-state geometric observer (GO) with passive structure, another state estimation strategy, shows the best performance. Besides achieving smooth signal processing, the observer improves 52% the estimation of the final molecular weight distribution when compared with the h-DEKF. The second system corresponds to the copolymerization of ethylene with 1,9-decadiene using a metallocene catalyst in a semi-batch reactor. The evaluated operating conditions consider different diene concentrations and reaction temperatures. Initially, the nonlinear model is validated followed by a global sensitivity analysis, which permits the selection of the important parameters. Afterwards, the most important kinetic parameters are estimated online using an extended Kalman filter (EKF), a variation of the GO that uses a preconditioner, and a data-driven strategy referred as the retrospective cost model refinement (RCMR) algorithm. The first two strategies improve the measured signal, but fail to predict other properties. The RCMR algorithm demonstrates an adequate estimation of the unknown parameters, and the estimates converge close to theoretical values without requiring prior knowledge

Structural properties and estimation of delay systems.

Thesis. 1975. Ph.D.--Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.Vita.Includes bibliographical references.Ph.D

Fault estimation algorithms: design and verification

The research in this thesis is undertaken by observing that modern systems are becoming more and more complex and safety-critical due to the increasing requirements on system smartness and autonomy, and as a result health monitoring system needs to be developed to meet the requirements on system safety and reliability. The state-of-the-art approaches to monitoring system status are model based Fault Diagnosis (FD) systems, which can fuse the advantages of system physical modelling and sensors' characteristics. A number of model based FD approaches have been proposed. The conventional residual based approaches by monitoring system output estimation errors, however, may have certain limitations such as complex diagnosis logic for fault isolation, less sensitiveness to system faults and high computation load. More importantly, little attention has been paid to the problem of fault diagnosis system verification which answers the question that under what condition (i.e., level of uncertainties) a fault diagnosis system is valid. To this end, this thesis investigates the design and verification of fault diagnosis algorithms. It first highlights the differences between two popular FD approaches (i.e., residual based and fault estimation based) through a case study. On this basis, a set of uncertainty estimation algorithms are proposed to generate fault estimates according to different specifications after interpreting the FD problem as an uncertainty estimation problem. Then FD algorithm verification and threshold selection are investigated considering that there are always some mismatches between the real plant and the mathematical model used for FD observer design. Reachability analysis is drawn to evaluate the effect of uncertainties and faults such that it can be quantitatively verified under what condition a FD algorithm is valid. First the proposed fault estimation algorithms in this thesis, on the one hand, extend the existing approaches by pooling the available prior information such that performance can be enhanced, and on the other hand relax the existence condition and reduce the computation load by exploiting the reduced order observer structure. Second, the proposed framework for fault diagnosis system verification bridges the gap between academia and industry since on the one hand a given FD algorithm can be verified under what condition it is effective, and on the other hand different FD algorithms can be compared and selected for different application scenarios. It should be highlighted that although the algorithm design and verification are for fault diagnosis systems, they can also be applied for other systems such as disturbance rejection control system among many others

An Integrated Approach to Performance Monitoring and Fault Diagnosis of Nuclear Power Systems

In this dissertation an integrated framework of process performance monitoring and fault diagnosis was developed for nuclear power systems using robust data driven model based methods, which comprises thermal hydraulic simulation, data driven modeling, identification of model uncertainty, and robust residual generator design for fault detection and isolation. In the applications to nuclear power systems, on the one hand, historical data are often not able to characterize the relationships among process variables because operating setpoints may change and thermal fluid components such as steam generators and heat exchangers may experience degradation. On the other hand, first-principle models always have uncertainty and are often too complicated in terms of model structure to design residual generators for fault diagnosis. Therefore, a realistic fault diagnosis method needs to combine the strength of first principle models in modeling a wide range of anticipated operation conditions and the strength of data driven modeling in feature extraction. In the developed robust data driven model-based approach, the changes in operation conditions are simulated using the first principle models and the model uncertainty is extracted from plant operation data such that the fault effects on process variables can be decoupled from model uncertainty and normal operation changes. It was found that the developed robust fault diagnosis method was able to eliminate false alarms due to model uncertainty and deal with changes in operating conditions throughout the lifetime of nuclear power systems. Multiple methods of robust data driven model based fault diagnosis were developed in this dissertation. A complete procedure based on causal graph theory and data reconciliation method was developed to investigate the causal relationships and the quantitative sensitivities among variables so that sensor placement could be optimized for fault diagnosis in the design phase. Reconstruction based Principal Component Analysis (PCA) approach was applied to deal with both simple faults and complex faults for steady state diagnosis in the context of operation scheduling and maintenance management. A robust PCA model-based method was developed to distinguish the differences between fault effects and model uncertainties. In order to improve the sensitivity of fault detection, a hybrid PCA model based approach was developed to incorporate system knowledge into data driven modeling. Subspace identification was proposed to extract state space models from thermal hydraulic simulations and a robust dynamic residual generator design algorithm was developed for fault diagnosis for the purpose of fault tolerant control and extension to reactor startup and load following operation conditions. The developed robust dynamic residual generator design algorithm is unique in that explicit identification of model uncertainty is not necessary. Finally, it was demonstrated that the developed new methods for the IRIS Helical Coil Steam Generator (HCSG) system. A simulation model was first developed for this system. It was revealed through steady state simulation that the primary coolant temperature profile could be used to indicate the water inventory inside the HCSG tubes. The performance monitoring and fault diagnosis module was then developed to monitor sensor faults, flow distribution abnormality, and heat performance degradation for both steady state and dynamic operation conditions. This dissertation bridges the gap between the theoretical research on computational intelligence and the engineering design in performance monitoring and fault diagnosis for nuclear power systems. The new algorithms have the potential of being integrated into the Generation III and Generation IV nuclear reactor I&C design after they are tested on current nuclear power plants or Generation IV prototype reactors

Cooperative optimal preview tracking for linear descriptor multi-agent systems

© 2018 The Franklin Institute. In this paper, a cooperative optimal preview tracking problem is considered for continuous-time descriptor multi-agent systems with a directed topology containing a spanning tree. By the acyclic assumption and state augmentation technique, it is shown that the cooperative tracking problem is equivalent to local optimal regulation problems of a set of low-dimensional descriptor augmented subsystems. To design distributed optimal preview controllers, restricted system equivalent (r.s.e.) and preview control theory are first exploited to obtain optimal preview controllers for reduced-order normal subsystems. Then, by using the invertibility of restricted equivalent relations, a constructive method for designing distributed controller is presented which also yields an explicit admissible solution for the generalized algebraic Riccati equation. Sufficient conditions for achieving global cooperative preview tracking are proposed proving that the distributed controllers are able to stabilize the descriptor augmented subsystems asymptotically. Finally, the validity of the theoretical results is illustrated via numerical simulation

The Kalman filter on time scales

In this work, we study concepts in optimal control for dynamic equations on time scales, which unfies the discrete and continuous cases. After a brief introduction of dynamic equations on time scales, we will examine controllability and observability for linear systems. Then we construct and solve the linear quadratic regulator for arbitrary time scales. Here, we seek to find an optimal control that minimizes a given cost function associated with a linear system. We will find such an input under two different settings; when the final state is fixed and when it is free. Later, we extend these results to deal with linear quadratic tracking on time scales. The main contribution of this dissertation is the construction of the Kalman filter on time scales. In this setting, we seek to find an optimal estimate of a linear stochastic system whose state is corrupted by noisy measurements. Finally, we will make an argument that the linear quadratic regulator and the Kalman filter are mathematically dual to each other --Abstract, page iv