A semidefinite relaxation procedure for fault-tolerant observer design

A fault-tolerant observer design methodology is proposed. The aim is to guarantee a minimum level of closed-loop performance under all possible sensor fault combinations while optimizing performance under the nominal, fault-free condition. A novel approach is proposed to tackle the combinatorial nature of the problem, which is computationally intractable even for a moderate number of sensors, by recasting the problem as a robust performance problem, where the uncertainty set is composed of all combinations of a set of binary variables. A procedure based on an elimination lemma and an extension of a semidefinite relaxation procedure for binary variables is then used to derive sufficient conditions (necessary and sufficient in the case of one binary variable) for the solution of the problem which significantly reduces the number of matrix inequalities needed to solve the problem. The procedure is illustrated by considering a fault-tolerant observer switching scheme in which the observer outputs track the actual sensor fault condition. A numerical example from an electric power application is presented to illustrate the effectiveness of the design

Fault-tolerant observer design with a tolerance measure for systems with sensor failure

A fault-tolerant switching observer design methodology is proposed. The aim is to maintain a desired level of closed-loop performance under a range of sensor fault scenarios while the fault-free nominal performance is optimized. The range of considered fault scenarios is determined by a minimum number p of assumed working sensors. Thus the smaller p is, the more fault tolerant is the observer. This is then used to define a fault tolerance measure for observer design. Due to the combinatorial nature of the problem, a semidefinite relaxation procedure is proposed to deal with the large number of fault scenarios for systems that have many vulnerable sensors. The procedure results in a significant reduction in the number of constraints needed to solve the problem. Two numerical examples are presented to illustrate the effectiveness of the fault-tolerant observer design

Fault-tolerant wide-area control of power systems

In this thesis, the stability and performance of closed-loop systems following the loss of sensors or feedback signals (sensor faults) are studied. The objective is to guarantee stability in the face of sensor faults while optimising performance under nominal (no sensor fault) condition. One of the main contributions of this work is to deal effectively with the combinatorial binary nature of the problem when the number of sensors is large. Several fault-tolerant controller and observer architectures that are suitable for different applications are proposed and their effectiveness demonstrated. The problems are formulated in terms of the existence of feasible solutions to linear matrix inequalities. The formulations presented in this work are described in a general form and can be applied to a large class of systems. In particular, the use of fault-tolerant architectures for damping inter-area oscillations in power systems using wide-area signals has been demonstrated. As an extension of the proposed formulations, regional pole placement to enhance the damping of inter-area modes has been incorporated. The objective is to achieve specified damping ratios for the inter-area modes and maximise the closed-loop performance under nominal condition while guaranteeing stability for all possible combinations of sensors faults. The performances of the proposed fault-tolerant architectures are validated through extensive nonlinear simulations using a simplified equivalent model of the Nordic power system.Open Acces

Quantum machine learning: a classical perspective

Recently, increased computational power and data availability, as well as algorithmic advances, have led machine learning techniques to impressive results in regression, classification, data-generation and reinforcement learning tasks. Despite these successes, the proximity to the physical limits of chip fabrication alongside the increasing size of datasets are motivating a growing number of researchers to explore the possibility of harnessing the power of quantum computation to speed-up classical machine learning algorithms. Here we review the literature in quantum machine learning and discuss perspectives for a mixed readership of classical machine learning and quantum computation experts. Particular emphasis will be placed on clarifying the limitations of quantum algorithms, how they compare with their best classical counterparts and why quantum resources are expected to provide advantages for learning problems. Learning in the presence of noise and certain computationally hard problems in machine learning are identified as promising directions for the field. Practical questions, like how to upload classical data into quantum form, will also be addressed.Comment: v3 33 pages; typos corrected and references adde

A probabilistic interpretation of set-membership filtering: application to polynomial systems through polytopic bounding

Set-membership estimation is usually formulated in the context of set-valued calculus and no probabilistic calculations are necessary. In this paper, we show that set-membership estimation can be equivalently formulated in the probabilistic setting by employing sets of probability measures. Inference in set-membership estimation is thus carried out by computing expectations with respect to the updated set of probability measures P as in the probabilistic case. In particular, it is shown that inference can be performed by solving a particular semi-infinite linear programming problem, which is a special case of the truncated moment problem in which only the zero-th order moment is known (i.e., the support). By writing the dual of the above semi-infinite linear programming problem, it is shown that, if the nonlinearities in the measurement and process equations are polynomial and if the bounding sets for initial state, process and measurement noises are described by polynomial inequalities, then an approximation of this semi-infinite linear programming problem can efficiently be obtained by using the theory of sum-of-squares polynomial optimization. We then derive a smart greedy procedure to compute a polytopic outer-approximation of the true membership-set, by computing the minimum-volume polytope that outer-bounds the set that includes all the means computed with respect to P

Regelungstheorie

The workshop “Regelungstheorie” (control theory) covered a broad variety of topics that were either concerned with fundamental mathematical aspects of control or with its strong impact in various fields of engineering

A Study on Fault Tolerant Wide-Area Controller Design to Damp Inter-Area Oscillations in Power Systems

Due to increased power supply demand, power system oscillations has become a major concern to have stable and secure system operation. One of the major concern in a power system is to damp inter-area oscillations. Lack of proper damping of oscillations may limit power transfer capability and blackouts. Power system stabilizer is used to damp local oscillations but not efficient to damp inter-area oscillations due to less observability of wide-area signals. Wide-Area Measurement Systems is used to overcome this issue and damp inter-area modes to an adequate level. In order to select feedback signals and controller location, wide-area loop selection method using geometrical measure approach is performed. However, while obtaining local and remote signals, a time-delay is introduced that may degrade the performance of system or may lead to instability. Two configurations are defined depending on feedback i.e. synchronous and non-synchronous feedback and modeled with 2nd order Pade approximation. The controller is synthesized based on H8 mixed sensitivity method with regional pole placement for a 4 machine 11 bus power system. It can be found that WDC damps out oscillations quickly and improves performance. Next problem considered is to design a controller when there is a sudden loss of remote signal. A conventional control (CC) method is used to design controller considering a local signal always available and a comparison is made in plants performance for normal and faulty conditions. It is found that conventional control method degrades performance in faulty situation and may lead to instability. To address this problem, a passive fault tolerant control (FTC) method is used where an iterative procedure is used and found that the system maintains adequate stability even in faulty conditions. For FTC method, the control effort required was more compared to CC method but FTC provides acceptable performance than CC controller

Stabilization of Continuous-Time Random Switching Systems via a Fault-Tolerant Controller

This paper focuses on the stabilization problem of continuous-time random switching systems via exploiting a fault-tolerant controller, where the dwell time of each subsystem consists of a fixed part and random part. It is known from the traditional design methods that the computational complexity of LMIs related to the quantity of fault combination is very large; particularly system dimension or amount of subsystems is large. In order to reduce the number of the used fault combinations, new sufficient LMI conditions for designing such a controller are established by a robust approach, which are fault-free and could be solved directly. Moreover, the fault-tolerant stabilization realized by a mode-independent controller is considered and suitably applied to a practical case without mode information. Finally, a numerical example is used to demonstrate the effectiveness and superiority of the proposed methods