The theatre programme : a public discourse at a staging of Maxwell Anderson's "Anne of the Thousand Days"

The term ’public discourses’ describes a range of texts or signifiers that inform the conditions of audience reception. Public discourses include myriad written, visual, spatial, auditory and sensory texts experienced by an audience at a particular theatrical event. Ric Knowles first introduced this term in his recent work Reading the Material Theatre. Whereas Knowles was interested in how public discourses modified the conditions of reception, my broader research is to explore how these public discourses become texts in themselves. This paper will discuss one public discourse, the theatre programme, as it related to a staging of Maxwell Anderson’s Anne of the Thousand Days at the Brisbane Powerhouse in June 2006. The significance of the programme was explored at symposiums held after the performances. Audiences generally view programmes before a performance and after a performance and its significance as a written text changes. The program became a sign vehicle that worked to expound and explicate the meaning of the play for the audience. This public discourse became a significant written text contributing to the textual whole of the theatrical event.

Low rank Runge-Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise

In this paper we extend the ideas of Brugnano, Iavernaro and Trigiante in their development of HBVM($s,r$) methods to construct symplectic Runge-Kutta methods for all values of $s$ and $r$ with $s\geq r$. However, these methods do not see the dramatic performance improvement that HBVMs can attain. Nevertheless, in the case of additive stochastic Hamiltonian problems an extension of these ideas, which requires the simulation of an independent Wiener process at each stage of a Runge-Kutta method, leads to methods that have very favourable properties. These ideas are illustrated by some simple numerical tests for the modified midpoint rule.

Structure-preserving Runge-Kutta methods for stochastic Hamiltonian equations with additive noise

There has been considerable recent work on the development of energy conserving one-step methods that are not symplectic. Here we extend these ideas to stochastic Hamiltonian problems with additive noise and show that there are classes of Runge-Kutta methods that are very effective in preserving the expectation of the Hamiltonian, but care has to be taken in how the Wiener increments are sampled at each timestep. Some numerical simulations illustrate the performance of these methods.

Port-Hamiltonian control of fully actuated underwater vehicles

This chapter presents a novel control strategy for trajectory tracking of underwater marine vehicles that are designed using port-Hamiltonian theory. A model for neutrally buoyant underwater vehicles is formulated as a PHS, and then the tracking controller is designed for the horizontal plane-surge, sway and yaw. The control design is done by formulating the error dynamics as a set-point regulation port-Hamiltonian control problem. The control design is formulated in two steps. In the first step, a static-feedback tracking controller is designed, and the second step integral action is added. The global asymptotic stability of the closed loop system is proved and the performance of the controller is illustrated using a model of an open-frame offshore underwater vehicle.

Dynamic positioning of marine craft using a port-Hamiltonian framework

Dynamic positioning of marine craft refers to the use of the propulsion system to regulate the vessel position and heading. This type of motion control is commonly used in the offshore industry for surface vessels, and it is also used for some underwater vehicles. In this paper, we use a port-Hamiltonian framework to design a novel nonlinear set-point-regulation controller with integral action. The controller handles input saturation and guarantees internal stability, rejection of unknown constant disturbances, and (integral-)input-to-state stability.

Control of an underactuated-slender-hull unmanned underwater vehicle using Port-Hamiltonian theory

This paper presents a control design for tracking of attitude and speed of an underactuated slender-hull unmanned underwater vehicle (UUV). The control design is based on Port-Hamiltonian theory. The target dynamics (desired dynamic response) is shaped with particular attention to the target mass matrix so that the influence of the unactuated dynamics on the controlled system is suppressed. This results in achievable dynamics independent of uncontrolled states. Throughout the design, insight of the physical phenomena involved is used to propose the desired target dynamics. The performance of the design is demonstrated through simulation with a high-fidelity model.

Total energy shaping of a class of underactuated Port-Hamiltonian Systems using a new set of closed-loop potential shape variables

This paper proposes a method for designing set-point regulation controllers for a class of underactuated mechanical systems in Port-Hamiltonian System (PHS) form. A new set of potential shape variables in closed loop is proposed, which can replace the set of open loop shape variables-the configuration variables that appear in the kinetic energy. With this choice, the closed-loop potential energy contains free functions of the new variables. By expressing the regulation objective in terms of these new potential shape variables, the desired equilibrium can be assigned and there is freedom to reshape the potential energy to achieve performance whilst maintaining the PHS form in closed loop. This complements contemporary results in the literature, which preserve the open-loop shape variables. As a case study, we consider a robotic manipulator mounted on a flexible base and compensate for the motion of the base while positioning the end effector with respect to the ground reference. We compare the proposed control strategy with special cases that correspond to other energy shaping strategies previously proposed in the literature.

Manoeuvring control of underactuated surface vessels using manifold regulation for Port-Hamiltonian systems

This paper considers the manoeuvring of underactuated surface vessels. The control objective is to steer the vessel to reach a manifold which encloses a waypoint. A transformation of configuration variables and a potential field are used in a Port-Hamiltonian framework to design an energy-based controller. With the proposed controller, the geometric task associated with the manoeuvring problem depends on the desired potential energy (closed-loop) and the dynamic task depends on the total energy and damping. Therefore, guidance and motion control are addressed jointly, leading to model-energy-based trajectory generation.

Manoeuvring control of fully-actuated marine vehicles : a Port-Hamiltonian system approach to tracking

This paper presents a novel control strategy for trajectory tracking of marine vehicles manoeuvring at low speed. The model of the marine vehicle is formulated as a Port-Hamiltonian system, and the tracking controller is designed using energy shaping and damping assignment. The controller guarantees global asymptotic stability and includes integral action for output variables with relative degree greater than one.

Port-Hamiltonian theory of motion control for marine craft

Port-Hamiltonian Systems (PHS) have a particular form that incorporates explicitly a function of the total energy in the system (energy function) and also other functions that describe structure of the system in terms of energy distribution. For PHS, the product of the input and output variables gives the rate of energy change. This type of systems have the property that under certain conditions on the energy function, the system is passive; and thus, stable. Therefore, if one can design a controller such that the closed-loop system retains - or takes - a PHS form, such closed-loop system will inherit the properties of passivity and stability. In this paper, the classical model of marine craft is put into a PHS form. It is shown that models used for positioning control do not have a PHS form due to a kinematic transformation, but a control design can be done such that the closed-loop system takes a PHS form. It is further shown how integral action can be added and how the PHS-form can be exploited to provide a procedure for control design that ensures passivity and thus stability.

Tracking control of a class of Hamiltonian mechanical systems with disturbances

This paper presents a trajectory-tracking control strategy for a class of mechanical systems in Hamiltonian form. The class is characterised by a simplectic interconnection arising from the use of generalised coordinates and full actuation. The tracking error dynamic is modelled as a port-Hamiltonian Systems (PHS). The control action is designed to take the error dynamics into a desired closed-loop PHS characterised by a constant mass matrix and a potential energy with a minimum at the origin. A transformation of the momentum and a feedback control is exploited to obtain a constant generalised mass matrix in closed loop. The stability of the close-loop system is shown using the close-loop Hamiltonian as a Lyapunov function. The paper also considers the addition of integral action to design a robust controller that ensures tracking in spite of disturbances. As a case study, the proposed control design methodology is applied to a fully actuated robotic manipulator.