This study addresses orbit design and optimisation for the situation of satellite interception in which the target spacecraft is capable of manoeuvring using continuous magnitude restricted thrust. For the purpose of designing a long-range continuous thrust interception orbit, the orbit motion equations of two satellites with J2 perturbation are constructed. This problem is assumed to be a typical pursuit-evasion problem in differential game theory; using boundary constraint conditions and a performance index function that includes time and fuel consumption, the saddle point solution corresponding to the bilateral optimal is derived, and then this pursuit-evasion problem is transformed into a two-point boundary value problem. A hybrid optimisation method using a genetic algorithm (GA) and sequential quadratic programming (SQP) is derived to obtain the optimal control strategy. The proposed model and algorithm are proved to be feasible for the given simulation cases.

This paper investigates the benefits of international cooperation under uncertainty about global warming through a stochastic dynamic game. We analyze the benefits of cooperation both for the case of symmetric and asymmetric players. It is shown that the players’ combined expected payoffs decrease as climate uncertainty becomes larger, whether or not they cooperate. However, the benefits from cooperation increase with climate uncertainty. In other words, it is more important to cooperate when facing higher uncertainty. At the same time, more transfers will be needed to ensure stable cooperation among asymmetric players.

We compare a general controlled diffusion process with a deterministic systemwhere a second controller drives the disturbance against the firstcontroller. We show that the two models are equivalent withrespect to two properties: the viability (or controlledinvariance, or weak invariance) of closed smooth sets, and theexistence of a smooth control Lyapunov function ensuring thestabilizability of the system at an equilibrium.


We consider the differential game associated with robust control of asystem in a compact state domain, using Skorokhod dynamics on theboundary. A specific class of problems motivated by queueing network controlis considered. A constructive approach to the Hamilton-Jacobi-Isaacsequation is developed which is based on an appropriate family ofextremals, including boundary extremals for which the Skorokhoddynamics are active. A number of technical lemmas and a structuredverification theorem are formulated to support the use of thistechnique in simple examples. Two examples are considered whichillustrate the application of the results. This extends previous workby Ball, Day and others on such problems, but with a new emphasis onproblems for which the Skorokhod dynamics play a critical role. Connections with the viscosity-sense oblique derivative conditions ofLions and others are noted.