The demand for automated decision making, learning and inference in uncertain, risk sensitive and dynamically changing situations presents a challenge: to design computational approaches that promise to be widely deployable and flexible to adapt on the one hand, while offering reliable guarantees on safety on the other. The tension between these desiderata has created a gap that, in spite of intensive research and contributions made from a wide range of communities, remains to be filled. This represents an intriguing challenge that provided motivation for much of the work presented in this thesis. With these desiderata in mind, this thesis makes a number of contributions towards the development of algorithms for automated decision-making and inference under uncertainty. To facilitate inference over unobserved effects of actions, we develop machine learning approaches that are suitable for the construction of models over dynamical laws that provide uncertainty bounds around their predictions. As an example application for conservative decision-making, we apply our learning and inference methods to control in uncertain dynamical systems. Owing to the uncertainty bounds, we can derive performance guarantees of the resulting learning-based controllers. Furthermore, our simulations demonstrate that the resulting decision-making algorithms are effective in learning and controlling under uncertain dynamics and can outperform alternative methods. Another set of contributions is made in multi-agent decision-making which we cast in the general framework of optimisation with interaction constraints. The constraints necessitate coordination, for which we develop several methods. As a particularly challenging application domain, our exposition focusses on collision avoidance. Here we consider coordination both in discrete-time and continuous-time dynamical systems. In the continuous-time case, inference is required to ensure that decisions are made that avoid collisions with adjustably high certainty even when computation is inevitably finite. In both discrete-time and finite-time settings, we introduce conservative decision-making. That is, even with finite computation, a coordination outcome is guaranteed to satisfy collision-avoidance constraints with adjustably high confidence relative to the current uncertain model. Our methods are illustrated in simulations in the context of collision avoidance in graphs, multi-commodity flow problems, distributed stochastic model-predictive control, as well as in collision-prediction and avoidance in stochastic differential systems. Finally, we provide an example of how to combine some of our different methods into a multi-agent predictive controller that coordinates learning agents with uncertain beliefs over their dynamics. Utilising the guarantees established for our learning algorithms, the resulting mechanism can provide collision avoidance guarantees relative to the a posteriori epistemic beliefs over the agents' dynamics.

Autonomous aerial vehicles like missiles and unmanned aerial vehicles (UAVs) have attracted various military and civilian applications. The primary guidance objective of any autonomous vehicle is to reach the desired destination point (target or waypoint). However, many practical engagements impose additional constraints like minimum control effort, a desired final velocity direction or a predefined engagement time. This thesis addresses engagement time constrained guidance problems pertaining to missiles and UAVs. The first part of the thesis discusses a nonlinear guidance law for impact time control of missiles against stationary target. The guidance law is designed with a particular choice of missile heading error variation as a function of ran to-target. The proposed heading error variation leads to an exact closed-form expression for the impact time. controlling the impact time, a closed-form relation is derived relating the control parameter to the desired impact time. A new Lyapunov based guidance law with a monotonically decreasing lateral acceleration is proposed in the next part of the thesis. An exact expression for impact time with minimum and maximum achievable impact times is derived. A control parameter is proposed with a closed-form relationship to the desired impact time. Using the concept of predicted interception point, the two guidance laws are extended for impact time control against non-maneuvering and moving targets. The proposed guidance models are extended to three-dimensional engagements by deducing yaw and pitch lateral accelerations satisfying the desired heading error profile. Extensive simulation studies are carried out for single missile and salvo attack scenarios. The last part of the thesis presents a guidance methodology governing the arrival time of a UAV at a waypoint. A specific arrival angle is considered as an additional constraint. The arrival constraints are satisfied by varying the navigation gain of the proportional navigation guidance law. The methodology is applied for simultaneous and sequential arrival of UAVs at a waypoint.