Stabilizability and optimal control of switched differential algebraic equations

In this thesis control of dynamical systems with switches is considered. Examples of such systems are electronic circuits and mechanical systems. The switches are induced by abrupt structural changes due to component failure or physical switches. In the case of constraints on the dynamics, the state of the system can only take certain values and not only differential equations are involved in modeling the system, but also algebraic equations. An important question in control problems is often how well a certain controller performs. Some controllers require little energy, but induce undesired behavior of the system, whereas others perform well in terms of the systems behavior but require a lot of energy. It turns out that in general an optimal controller does not exist. However, necessary and sufficient conditions for the existence of optimal controller given a quadratic cost functional are presented in this thesis. Besides quantitative properties also some qualitative properties are investigated. The systems considered exhibit discontinuous behavior and Dirac impulses, whereas especially Dirac impulses are practically undesirable. Dirac impulses occur in practice in the form of hydraulic shocks in fluid networks or sparks in electronic circuits. The possibility to avoid Dirac impulses is also studied and necessary and sufficient conditions are given

Robust model-based fault estimation and fault-tolerant control : towards an integration

To maintain robustly acceptable system performance, fault estimation (FE) is adopted to reconstruct fault signals and a fault-tolerant control (FTC) controller is employed to compensate for the fault effects. The inevitably existing system and estimation uncertainties result in the so-called bi-directional robustness interactions defined in this work between the FE and FTC functions, which gives rise to an important and challenging yet open integrated FE/FTC design problem concerned in this thesis. An example of fault-tolerant wind turbine pitch control is provided as a practical motivation for integrated FE/FTC design.To achieve the integrated FE/FTC design for linear systems, two strategies are proposed. A H∞ optimization based approach is first proposed for linear systems with differentiable matched faults, using augmented state unknown input observer FE and adaptive sliding mode FTC. The integrated design is converted into an observer-based robust control problem solved via a single-step linear matrix inequality formulation.With the purpose of an integrated design with more freedom and also applicable for a range of general fault scenarios, a decoupling approach is further proposed. This approach can estimate and compensate unmatched non-differentiable faults and perturbations by combined adaptive sliding mode augmented state unknown input observer and backstepping FTC controller. The observer structure renders a recovery of the Separation Principle and allows great freedom for the FE/FTC designs.Integrated FE/FTC design strategies are also developed for Takagi-Sugeno fuzzy modelling nonlinear systems, Lipschitz nonlinear systems, and large-scale interconnected systems, based on extensions of the H∞ optimization approach for linear systems.Tutorial examples are used to illustrate the design strategies for each approach. Physical systems, a 3-DOF (degree-of-freedom) helicopter and a 3-machine power system, are used to provide further evaluation of the proposed integrated FE/FTC strategies. Future research on this subject is also outlined

Correct-By-Construction Fault-Tolerant Control

Correct-by-construction control synthesis methods refer to a collection of model-based techniques to algorithmically generate controllers/strategies that make the systems satisfy some formal specifications. Such techniques attract much attention as they provide formal guarantees on the correctness of cyber-physical systems, where corner cases may arise due to the interaction among different modules. The controllers synthesized through such methods, however, may still malfunction due to faults, such as physical component failures and unexpected operating conditions, which lead to a sudden change of the system model. In these cases, we want to guarantee that the performance of the faulty system degrades gracefully, and hence achieve fault tolerance. This thesis is about 1) incorporating fault detection and detectability analysis algorithms in correct-by-construction control synthesis, 2) formalizing the graceful degradation specification for fault tolerant systems with temporal logic, and 3) developing algorithms to synthesize correct-by-construction controllers that achieve such graceful degradation, with possible delay in the fault detection. In particular, two sets of approaches from the temporal logic planning domain, i.e., abstraction-based synthesis and optimization-based path planning, are considered. First, for abstraction-based approaches, we propose a recursive algorithm to reduce the fault tolerant controller synthesis problem into multiple small synthesis problems with simpler specifications. Such recursive reduction leverages the structure of the fault propagation and hence avoids the high complexity of solving the problem monolithically as one general temporal logic game. Furthermore, by exploring the structural properties in the specifications, we show that, even when the fault is detected with delay, the problem can be solved by a similar recursive algorithm without constructing the belief space. Secondly, optimization-based path planning is considered. The proposed approach leverages the recently developed temporal logic encodings and state-of-art mixed integer programming (MIP) solvers. The novelty of this work is to enhance the open-loop strategy obtained through solving the MIP so that it can react contingently to faults and disturbance. Finally, the control synthesis techniques developed for discrete state systems is shown to be applicable to continuous states systems. This is demonstrated by fuel cell thermal management application. Particularly, to apply the abstraction-based synthesis methods to complex systems such as the fuel cell thermal management system, structural properties (e.g., mixed monotonicity) of the system are explored and leveraged to ease abstraction computation, and techniques are developed to improve the scalability of synthesis process whenever the system has a large number of control actions.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/155031/1/yliren_1.pd