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• Aspects of Geometric Mechanics and Control of Mechanical Systems  + (any interesting control systems are mechan … any interesting control systems are mechanical control systems. In spite of</br>this, there has not been much effort to develop methods which use the special</br>structure of mechanical systems to obtain analysis tools which are</br>suitable for these systems. In this dissertation we take the first steps</br>towards a methodical treatment of mechanical control systems.</br><p></br>First we develop a framework for analysis of certain classes of</br>mechanical control systems. In the Lagrangian formulation we study ``simple</br>mechanical control systems'' whose Lagrangian is ``kinetic energy minus</br>potential energy.'' We propose a new and useful definition of</br>controllability for these systems and obtain a computable set of conditions</br>for this new version of controllability. We also obtain decompositions of</br>simple mechanical systems in the case when they are not controllable. In the</br>Hamiltonian formulation we study systems whose control vector fields are</br>Hamiltonian. We obtain decompositions which describe the controllable and</br>uncontrollable dynamics. In each case, the dynamics are shown to be</br>Hamiltonian in a suitably general sense.</br><p></br>Next we develop intrinsic descriptions of Lagrangian and Hamiltonian</br>mechanics in the presence of external inputs. This development is a first</br>step towards a control theory for general Lagrangian and Hamiltonian</br>control systems. Systems with constraints are also studied. We first give a</br>thorough overview of variational methods including a comparison of the</br>``nonholonomic'' and ``vakonomic'' methods. We also give a generalised</br>definition for a constraint and, with this more general definition, we are</br>able to give some preliminary controllability results for constrained systems.inary controllability results for constrained systems.)
• Specification and Synthesis of Reactive Protocols for Aircraft Electric Power Distribution  + (he increasing complexity of electric power … he increasing complexity of electric power systems leads to challenges in integration and verification. We consider the problem of designing a control protocol for an aircraft electric power system that meets a set of requirements describing the correct behaviors of the system and reacts dynamically to changes in internal system states. We formalize the requirements by translating them into a temporal logic specification language and apply game-based, temporal logic formal methods to automatically synthesize a controller protocol that satisfies these overall properties and requirements. Through a case study, we perform a design exploration to show the benefits and tradeoffs between centralized and distributed control architectures.zed and distributed control architectures.)

• Efficient control synthesis for augmented finite transition systems with an application to switching protocols  + (ugmented finite transition systems general … ugmented finite transition systems generalize nondeterministic transition systems with additional liveness conditions. We propose efficient algorithms for synthesizing control protocols for augmented finite transition systems to satisfy high-level specifications expressed in a fragment of linear temporal logic (LTL). We then use these algorithms within a framework for switching protocol synthesis for discrete-time dynamical systems, where augmented finite transition systems are used for abstracting the underlying dynamics. We introduce a notion of minimality for abstractions of certain fidelity and show that such minimal abstractions can be exactly computed for switched affine systems. Additionally, based on this framework, we present a procedure for computing digitally implementable switching protocols for continuous-time systems. The effectiveness of the proposed framework is illustrated through two examples of temperature control for buildings.ples of temperature control for buildings.)
• Designing Robustness to Temperature in a Feedforward Loop Circuit  + (âIncoherent feedforward loopsâ represent i … âIncoherent feedforward loopsâ represent important biomolecular circuit elements capable of a rich set of dynamic behavior including adaptation and pulsed responses. Temperature can modulate some of these properties through its effect on the underlying reaction rate parameters. It is generally unclear how to design a circuit where these properties are robust to variations in temperature. Here, we address this issue using a combination of tools from control and dynamical systems theory as well as preliminary experimental measurements towards such a design. Using a structured uncertainty representation, we analyze a standard incoherent feedforward loop circuit, noting mechanisms that intrinsically confer temperature robustness to some of its properties. Further, we study design variants that can enhance this robustness to temperature, including different negative feedback configurations as well as conditions for perfect temperature compensation. Finally, we find that the response of an incoherent feedforward loop circuit in cells can change with temperature. These results present groundwork for the design of a temperature-robust incoherent feedforward loop circuit.obust incoherent feedforward loop circuit.)