Ivo Puncochar

Rolling horizon for active fault detection

This paper presents a feasible design of suboptimal active fault detection system in multiple-model framework. The optimal solution for finite horizon is approximated by means of well known rolling horizon scheme which belongs to the class of limited look-ahead policies. The suboptimal input signal which is chosen from given discrete set is obtained by l-step closed loop optimization. It is shown that such input signal can improve fault detection.

Constrained Active Fault Detection and Control

The technical note introduces a constrained optimization approach to active fault detection and control. Detection and control aims can be expressed either as a part of an objective function or as a constraint. Five principal formulations of active fault detection and control problem are proposed and investigated in the technical note. Three formulations are focused on alternative detection and control aims combinations while the other formulations represent marginal cases that outline a relationship to the well know fields of optimal control and active fault detection. The underlying difficulty of the optimal solution is discussed and a suboptimal solution is proposed that makes use of nonlinear programming techniques.

An optimization approach to resolve the competing aims of active fault detection and control

The paper deals with the problem of active fault detection and control for multiple models. It is assumed that a fault detector is given and the goal is to design an input signal generator such that detection and control aims are achieved. Since these two aim are conflicting, it is necessary to express a desired compromise between them. The paper investigates three formulations that allow for respecting both competing aims. In the first formulation both aims are combined into a single criterion. In other two formulations, one aim is reflected in the criterion and the other aim is enforced as a constraint.

On infinite horizon active fault diagnosis for a class of non-linear non-Gaussian systems

Abstract The paper considers the problem of active fault diagnosis for discrete-time stochastic systems over an infinite time horizon. It is assumed that the switching between a fault-free and finitely many faulty conditions can be modelled by a finite-state Markov chain and the continuous dynamics of the observed system can be described for the fault-free and each faulty condition by non-linear non-Gaussian models with a fully observed continuous state. The design of an optimal active fault detector that generates decisions and inputs improving the quality of detection is formulated as a dynamic optimization problem. As the optimal solution obtained by dynamic programming requires solving the Bellman functional equation, approximate techniques are employed to obtain a suboptimal active fault detector.

Infinite time horizon active fault diagnosis based on approximate dynamic programming

The paper deals with designing an approximate active fault detector for stochastic linear Markovian switching systems over an infinite time horizon. The problem is formulated as a functional optimization problem that can be solved using approximate dynamic programming. First, the Generalized Pseudo Bayes (GPB) algorithm is employed to solve the state estimation problem. Then the original formulation is restated by introducing a hyper-state that comprises a finite dimensional statistics obtained from the GPB algorithm. Since the hyper-state is of a higher dimension, a nonparametric local approximation of the Bellman function is used together with the value iteration algorithm to design the approximate active fault detector. The performance of the designed approximate active fault detector is demonstrated through a numerical example.

Approximation methods for optimal active fault detection

In this paper the problem of active fault detection for a non-linear discrete-time stochastic system over an infinite time horizon is considered. The faults in the system are modeled by switching between fault-free and finitely many faulty models. The optimal active fault detector is derived by reformulating the original problem and solving corresponding Bellmans functional equation. A suboptimal solution is based on application of the value iteration or the policy iteration algorithms and a representation of the continuous hyper-state space by a uniform grid. A comparison of both algorithms for solving Bellmans functional equation is illustrated in a numerical example.

Optimal active decision making for control

The paper deals with a general formulation of the optimal active change detection and control problem for stochastic systems, which includes several design problems as special cases. The special case treated in this paper can be characterized as a decision making problem where decisions are transformed into inputs of a system and the aim is to control the system. The utilization of the general formulation naturally leads to an optimal solution that makes use of the closed loop information processing strategy. Since the optimal solution is computationally intractable, the paper also discusses some approximate design techniques available for obtaining a feasible active generator for a given controller. The results are illustrated in a numerical example.

Optimal active fault diagnosis by temporal-difference learning

In this paper, a novel solution to the active fault diagnosis problem for stochastic linear Markovian switching systems on the infinite-time horizon is proposed. The imperfect state information problem of designing an active fault detector that minimizes a general detection cost criterion is reformulated as the perfect state information problem using sufficient statistics. The reformulation decreases theoretical complexity and enables to find a suboptimal solution by dynamic programming. However, classical approaches are computationally complex or fail to identify the most representative states of the system. This paper combines the active fault detection, state estimation, and reinforcement learning. In the proposed algorithm, temporal difference learning is used to train the active fault detector based on input-output data from the system simulation. The designed detector can be then used online. A numerical example is presented to verify the proposed algorithm.

Temporal-difference Q-learning in active fault diagnosis

The paper deals with a novel design of an approximate active fault detector for discrete-time stochastic linear Markovian switching systems on the infinite-time horizon. The problem is formulated as an optimization problem with the aim to minimize a general discounted detection cost criterion. The proposed solution is inspired by approximate dynamic programming and reinforcement learning. The active fault detector is trained by a temporal-difference Q-learning algorithm with a linear parametric Q-function approximation adjusted to fit the true Q-function. The main advantage is that this approach is computationally less expensive than a temporal-difference learning with a value function.

Directional Splitting for Structure Adaptation of Bayesian Filters

The paper deals with state estimation of nonlinear stochastic dynamic systems. The state is estimated within the Bayesian framework using the Gaussian filter and the Gaussian mixture filter. The paper is concerned with the joint Gaussianity assumption of the Gaussian filter and monitoring its validity. For cases, in which the assumption becomes invalid, the paper proposes a structure adaptation of the filter by directional splitting of the Gaussian distribution to a Gaussian mixture distribution. Both the monitoring and the directional splitting are based on a non-Gaussianity measure. The proposed directional splitting is illustrated using a numerical example.