Controlling dynamical systems with bounded probability of failure

A computer-based system comprising:

• a controller for a dynamical system to operate in an uncertain environment within a bounded probability of failure, wherein the dynamical system has a state space and a control space;
• at least one computer-based processor configured to:
• diffuse a risk constraint associated with the dynamical system that corresponds to the bounded probability of failure into a martingale that represents a level of risk tolerance associated with the dynamical system over time;
• augment the state space and the control space of the dynamical system with the martingale to create an augmented model for the dynamical system, wherein the augmented model has an augmented state space and an augmented control space;
• if additional time is available before a control signal needs to be returned to the dynamical system, then iteratively construct one or more Markov Decision Processes (MDPs), wherein each iterative MDP represents an incrementally refined model of the dynamical system, relative to the augmented model and any previously-constructed MDP iteration;
• and
• compute a first solution based on the augmented model or, if additional time was available, based on one of the MDP iterations.

A non-transitory, computer-readable medium that stores instructions executable by at least one computer-based processor to perform the operations comprising:

• diffusing a risk constraint associated with a dynamical system that corresponds to a bounded probability of failure into a martingale that represents a level of risk tolerance associated with the dynamical system over time;
• augmenting a state space and a control space of the dynamical system with the martingale to create an augmented model for the dynamical system, wherein the augmented model has an augmented state space and an augmented control space;
• if additional time is available before a control signal needs to be returned to the dynamical system, then iteratively constructing one or more Markov Decision Processes (MDPs), wherein each iterative MDP represents an incrementally refined model of the dynamical system, relative to the augmented model and any previously-constructed MDP iteration;
• and
• computing a first solution based on the augmented model or, if additional time was available, based on one of the MDP iterations.