Jan Lunze

Brief paper: A state-feedback approach to event-based control

This paper proposes a new method for event-based state-feedback control in which a control input generator mimics a continuous feedback between two consecutive event times. The performance of the event-based control system is evaluated by comparing this loop with the continuous state-feedback loop. An upper bound of the difference between both loops is derived, which shows that the approximation of the continuous state-feedback loop by the event-based control loop can be made arbitrarily tight by appropriately choosing the threshold parameter of the event generator.

Qualitative modelling of linear dynamical systems with quantized state measurements

Abstract The paper considers a discrete-time continuous-variable autonomous system for which only a quantized state measurement [ x (k) ] is available. The problem is to set up a qualitative model that for a given quantized initial state [x(0)] describes the sequence of quantized states [ x (k) ]. First it is shown that the relation between [x(0)] and [ x (k) ] is ambiguous. Hence, the qualitative model is nondeterministic. Second, necessary and sufficient conditions are derived under which nondeterministic or stochastic automata represent qualitative models of a linear autonomous system. The results are illustrated by an oscillator.

Synchronization of Heterogeneous Agents

The task of synchronizing autonomous agents is solved by a networked controller that steers the agents towards a common trajectory. This technical note extends existing analysis and design methods towards sets of linear agents with individual dynamics. A necessary and sufficient synchronization condition is proved and it is shown that the agents can be synchronized by an appropriate networked controller if and only if their dynamics intersect.

Control Reconfiguration After Actuator Failures Using Disturbance Decoupling Methods

This paper addresses the control of a system after an actuator has failed: A reconfiguration of the control structure is sought which keeps the system operational. The goal is to find a different set of actuators for controlling the plant and to use them in such a way that the plant output is identical to the output of the nominal closed-loop system. It is further required that the nominal controller remains part of the reconfigured control loop. This paper shows that this reconfiguration problem is equivalent to a disturbance decoupling problem which is solved by means of the geometric approach. The resulting solution is a reconfiguration block, which generates suitable inputs for the faulty plant based on the output of the nominal controller. The feasibility of this approach is demonstrated by a physical experiment with a helicopter model

Deterministic discrete-event representations of linear continuous-variable systems

The paper concerns linear continuous-variable systems whose state can be measured only through a quantiser. As for an observer the system together with the quantiser behaves like a discrete-event system, the problem of representing this system by some deterministic finite state machine is considered. The main difficulty of this representation problem occurs due to the nondeterminism introduced by the state quantisation. It is investigated under what conditions on the linear continuous-variable system and on the state quantisation the discrete-event behaviour is deterministic. The main results are sufficient conditions for this property.

Diagnosis and Fault-tolerant Control, 2nd edition

Fault-tolerant control aims at a gradual shutdown response in automated systems when faults occur. It satisfies the industrial demand for enhanced availability and safety, in contrast to traditional reactions to faults, which bring about sudden shutdowns and loss of availability. The book presents effective model-based analysis and design methods for fault diagnosis and fault-tolerant control. Architectural and structural models are used to analyse the propagation of the fault through the process, to test the fault detectability and to find the redundancies in the process that can be used to ensure fault tolerance. It also introduces design methods suitable for diagnostic systems and fault-tolerant controllers for continuous processes that are described by analytical models of discrete-event systems represented by automata. The book is suitable for engineering students, engineers in industry and researchers who wish to get an overview of the variety of approaches to process diagnosis and fault-tolerant control. The authors have extensive teaching experience with graduate and PhD students, as well as with industrial experts. Parts of this book have been used in courses for this audience. The authors give a comprehensive introduction to the main ideas of diagnosis and fault-tolerant control and present some of their most recent research achievements obtained together with their research groups in a close cooperatio n with European research projects. The third edition resulted from a major re-structuring and re-writing of the former edition, which has been used for a decade by numerous research groups. New material includes distributed diagnosis of continuous and discrete-event systems, methods for reconfigurability analysis, and extensions of the structural methods towards fault-tolerant control. The bibliographical notes at the end of all chapters have been up-dated. The chapters end with exercises to be used in lectures.

Event-based output-feedback control

Event-based control aims at reducing the information exchange over the communication network in control systems. This paper extends an event-based state-feedback approach published recently towards event-based output feedback. The measurable output is affected by measurement noise. The analysis shows that by incorporating a state observer in the event generator, a stable behavior of the event-based control loop can be guaranteed. Moreover, it will be shown that the maximum communication frequency within the control loop is bounded.

Sensor and actuator fault diagnosis of systems with discrete inputs and outputs

The paper describes a method for detecting and identifying faults that occur in the sensors or in the actuators of dynamical systems with discrete-valued inputs and outputs. The model used in the diagnosis is a stochastic automaton. The generalized observer scheme (GOS), which has been proposed for systems with continuous-variable inputs and outputs some years ago, are developed for discrete systems. This scheme solves the diagnostic problem as an observation problem, which is set up here for discrete-event systems. As the system under consideration is described by a stochastic automaton rather than a differential equation, the mathematical background and the diagnostic algorithms obtained are completely different from the well-known observers developed for continuous-variable systems. The GOS is extended here by a fault detection module to cope with plant faults that are different from actuator or sensor faults. The diagnostic algorithm consists of two steps, the first detecting the existence of a fault and the second isolating possible sensor or actuator faults or identifying plant faults. The results are applied to quantized systems whose discrete inputs and outputs result from a quantization of the continuous-variable input and output signals. Experimental results illustrate the proposed diagnostic method.

Reconfigurable control of piecewise affine systems with actuator and sensor faults: Stability and tracking

A reconfigurable control approach for continuous-time piecewise affine (PWA) systems subject to actuator and sensor faults is presented. The approach extends the concept of virtual actuators and virtual sensors from linear to PWA systems on the basis of the fault-hiding principle that provides the underlying conceptual idea: the fault is hidden from the nominal controller and the fault effects are compensated. Sufficient linear matrix inequality (LMI) conditions for the existence of virtual actuators and virtual sensors are given that guarantee the recovery of closed-loop stability and the tracking of constant reference inputs. Since LMIs are efficiently solvable, this solution leads to a tractable computational algorithm that solves the reconfiguration problem. The approach is proven to be robust against model uncertainties and inaccurate fault diagnosis, and is evaluated using an example system of interconnected tanks.

State Observation and Diagnosis of Discrete-Event SystemsDescribed by Stochastic Automata

The problems ofstate observation and diagnosis are solved for discrete–eventsystems, which are described by stochastic automata. As manysystems are not observable in the sense that it is possible toreconstruct the state unambiguously, the observation problemis set up as the problem of determining the smallest possibleset of states that are compatible with the measured input andoutput sequences. The diagnostic problem is shown to be, in principle,an observation problem. Conditions for the observability anddiagnosability of stochastic automata are presented. The resultsare illustrated by examples.