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Register a new userRethinking the Mathematical Framework and Optimality of Set-Membership Filtering
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Set-Membership Filter (SMF) has been extensively studied for state estimation in the presence of bounded noises with unknown statistics. Since it was first introduced in the 1960s, the studies on SMF have used the set-based description as its mathematical framework. One important issue that has been overlooked is the optimality of SMF. In this work, we put forward a new mathematical framework for SMF using concepts of uncertain variables. We first establish two basic properties of uncertain variables, namely, the law of total range (a non-stochastic version of the law of total probability) and the equivalent Bayes rule. This enables us to put forward a general SMFing framework with established optimality. Furthermore, we obtain the optimal SMF under a non-stochastic Markov condition, which is shown to be fundamentally equivalent to the Bayes filter. Note that the classical SMF in the literature is only equivalent to the optimal SMF we obtained under the non-stochastic Markov condition. When this condition is violated, we show that the classical SMF is not optimal and it only gives an outer bound on the optimal estimation.
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This paper studies a dynamic real-time optimization in the context of model-based time-optimal operation of batch processes under parametric model mismatch. In order to tackle the model-mismatch issue, a receding-horizon policy is usually followed with frequent re-optimization. The main problem addressed in this study is the high computational burden that is usually required by such schemes. We propose an approach that uses parameterized conditions of optimality in the adaptive predictive-control fashion. The uncertainty in the model predictions is treated explicitly using reachable sets that are projected into the optimality conditions. Adaptation of model parameters is performed online using set-membership estimation. A class of batch membrane separation processes is in the scope of the presented applications, where the benefits of the presented approach are outlined.
This paper deals with the design of discrete-time algorithms for the robust filtering differentiator. Two discrete-time realizations of the filtering differentiator are introduced. The first one, which is based on an exact discretization of the continuous differentiator, is an explicit one, while the second one is an implicit algorithm which enables to remove the numerical chattering phenomenon and to preserve the estimation accuracy properties. Some numerical comparisons between the proposed scheme and an existing discrete-time algorithm show the interest of the proposed implicit discrete-time realization of the filtering differentiator, especially when large sampling periods are considered.
Power electronic converters for integrating renewable energy resources into power systems can be divided into grid-forming and grid-following inverters. They possess certain similarities, but several important differences, which means that the relationship between them is quite subtle and sometimes obscure. In this article, a new perspective based on duality is proposed to create new insights. It successfully unifies the grid interfacing and synchronization characteristics of the two inverter types in a symmetric, elegant, and technology-neutral form. Analysis shows that the grid-forming and grid-following inverters are duals of each other in several ways including a) synchronization controllers: frequency droop control and phase-locked loop (PLL); b) grid-interfacing characteristics: current-following voltage-forming and voltage-following current-forming; c) swing characteristics: current-angle swing and voltage-angle swing; d) inner-loop controllers: output impedance shaping and output admittance shaping; and e) grid strength compatibility: strong-grid instability and weak-grid instability. The swing equations are also derived in dual form for two inverter types, which reveal the dynamic interaction between the grid strength, the synchronization controllers, and the inner-loop controllers. Insights are generated into cases of poor stability. The theoretical analysis and time-domain simulation results are used to illustrate cases of instability for simple single-inverter-infinite-bus systems and a multi-inverter power network.
This paper presents methods for using zonotopes and constrained zonotopes to improve the practicality of a wide variety of set-based operations commonly used in control theory. The proposed methods extend the use of constrained zonotopes to represent sets resulting from operations including halfspace intersections, convex hulls, robust positively invariant sets, and Pontryagin differences. Order reduction techniques are also presented that provide lower-complexity inner-approximations of zonotopes and constrained zonotopes. Numerical examples are used to demonstrate the efficacy and computational advantages of using zonotope-based set representations for dynamic system analysis and control.
Location of non-stationary forced oscillation (FO) sources can be a challenging task, especially in cases under resonance condition with natural system modes, where the magnitudes of the oscillations could be greater in places far from the source. Therefore, it is of interest to construct a global time-frequency (TF) representation (TFR) of the system, which can capture the oscillatory components present in the system. In this paper we develop a systematic methodology for frequency identification and component filtering of non-stationary power system forced oscillations (FO) based on multi-channel TFR. The frequencies of the oscillatory components are identified on the TF plane by applying a modified ridge estimation algorithm. Then, filtering of the components is carried out on the TF plane applying the anti-transform functions over the individual TFRs around the identified ridges. This step constitutes an initial stage for the application of the Dissipating Energy Flow (DEF) method used to locate FO sources. Besides, we compare three TF approaches: short-time Fourier transform (STFT), STFT-based synchrosqueezing transform (FSST) and second order FSST (FSST2). Simulated signals and signals from real operation are used to show that the proposed method provides a systematic framework for identification and filtering of power systems non-stationary forced oscillations.
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