Abstract
In this thesis, we use ideas and results from control theory to study several problems for nonsmooth dynamical systems.
The first problem that we study is the problem of disturbance decoupling for linear multi-modal systems. In such systems, the state space is divided into several regions, each with a corresponding linear subsystem. Depending on where the state is at a certain time, a different subsystem is active. We present necessary conditions and sufficient conditions for disturbance decoupling for such systems and special cases under which these conditions coincide. All presented conditions are geometric in nature and easily verifiable.
The second problem that we address is the fault detection and isolation problem for bimodal piecewise linear systems. Using a geometric approach, we present sufficient conditions for the existence of a fault detector. Next, we study the fault detection and isolation problem for a class of multi-agent systems. These systems are defined on an undirected graph, containing faultable vertices and observer vertices. We present graph-theoretical conditions under which we can see from the outputs of the observer vertices if the faultable vertices are subject to faults, and if so, which vertices are faulty.
The last problem is a consensus problem for multi-agent systems with a directed communication graph that contains a directed spanning tree. On both the vertices and the edges there can be sign-preservering nonlinear discontinuous functions. We present sufficient conditions under which all solutions of these consensus protocols reach consensus.
The first problem that we study is the problem of disturbance decoupling for linear multi-modal systems. In such systems, the state space is divided into several regions, each with a corresponding linear subsystem. Depending on where the state is at a certain time, a different subsystem is active. We present necessary conditions and sufficient conditions for disturbance decoupling for such systems and special cases under which these conditions coincide. All presented conditions are geometric in nature and easily verifiable.
The second problem that we address is the fault detection and isolation problem for bimodal piecewise linear systems. Using a geometric approach, we present sufficient conditions for the existence of a fault detector. Next, we study the fault detection and isolation problem for a class of multi-agent systems. These systems are defined on an undirected graph, containing faultable vertices and observer vertices. We present graph-theoretical conditions under which we can see from the outputs of the observer vertices if the faultable vertices are subject to faults, and if so, which vertices are faulty.
The last problem is a consensus problem for multi-agent systems with a directed communication graph that contains a directed spanning tree. On both the vertices and the edges there can be sign-preservering nonlinear discontinuous functions. We present sufficient conditions under which all solutions of these consensus protocols reach consensus.
| Original language | English |
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| Qualification | Doctor of Philosophy |
| Awarding Institution |
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| Supervisors/Advisors |
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| Award date | 2-Dec-2016 |
| Place of Publication | [Groningen] |
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| Print ISBNs | 978-90-367-9270-7 |
| Electronic ISBNs | 978-90-367-9269-1 |
| Publication status | Published - 2016 |