A Survey on Continuous Time Computations

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature

On the Method of Interconnection and Damping Assignment Passivity-Based Control for the Stabilization of Mechanical Systems

Interconnection and damping assignment passivity-based control (IDA-PBC) is an excellent method to stabilize mechanical systems in the Hamiltonian formalism. In this paper, several improvements are made on the IDA-PBC method. The skew-symmetric interconnection submatrix in the conventional form of IDA-PBC is shown to have some redundancy for systems with the number of degrees of freedom greater than two, containing unnecessary components that do not contribute to the dynamics. To completely remove this redundancy, the use of quadratic gyroscopic forces is proposed in place of the skew-symmetric interconnection submatrix. Reduction of the number of matching partial differential equations in IDA-PBC and simplification of the structure of the matching partial differential equations are achieved by eliminating the gyroscopic force from the matching partial differential equations. In addition, easily verifiable criteria are provided for Lyapunov/exponential stabilizability by IDA-PBC for all linear controlled Hamiltonian systems with arbitrary degrees of underactuation and for all nonlinear controlled Hamiltonian systems with one degree of underactuation. A general design procedure for IDA-PBC is given and illustrated with examples. The duality of the new IDA-PBC method to the method of controlled Lagrangians is discussed. This paper renders the IDA-PBC method as powerful as the controlled Lagrangian method

Orbit control of asteroids in libration point orbits for resource exploitation

The fascinating idea of shepherding asteroids for science and resource utilisation is being considered as a very credible concept in a not too distant future. Past studies have identified asteroids which could be injected into manifolds which wind onto periodic orbits around collinear Lagrangian points of the Sun-Earth system, by means of a low-cost manoeuvre. However, the periodic orbits as well as the manifolds are highly unstable, and small errors in the capture manoeuvre would bring to complete mission failure, with potential danger of collision with the Earth itself. The main source of injection error in position and velocity is the epistemic uncertainty of the asteroid mass, which cannot be measured directly. For this reason, asteroid orbit control will be a strict requirement for such mission. This paper investigates the controllability of some asteroids during the transfer and along the period orbits, assuming the use of a solar-electric low-thrust engine. The control scheme is based on a linear quadratic regulator. A stochastic simulation with a Monte Carlo approach is used to simulate a range of different perturbed initial conditions. Results show that only a small subset of the considered combinations of trajectories/asteroids are reliably controllable, and therefore controllability must be taken into account in the selection of potential targets