Ram Padmanabhan

Ratnangshu Das, Ram Padmanabhan, Melkior Ornik et al.

In environments with uncertainties or undesirable influences, control systems can require additional energy to achieve their task while remaining resilient to these influences. In this paper, we present an energetic resilience metric that quantifies the maximal additional energy used by a system under undesired effects, while satisfying complex specifications encoded through temporal logic. We prove that this metric satisfies properties that enable its computation even for compositions of these specifications, thus allowing considerations of sequential reachability and safety tasks. For specifications related to finite-horizon reachability and safety, we describe how synthesizing a control input and computing this metric reduces to solving efficient quadratic programs. Two case studies on a fighter-jet model and a planar mobile robot illustrate how the synthesized control inputs satisfy given specifications despite undesired and potentially adversarial effects. Further, we demonstrate how the energetic resilience metric varies with the initial state as well as the magnitude of undesired effects.

Ram Padmanabhan, Melkior Ornik

This paper presents a technique to drive the state of a constrained nonlinear system to a specified target state in finite time, when the system suffers a partial loss in control authority. Our technique builds on a recent method to control constrained nonlinear systems by building a simple, linear driftless approximation at the initial state. We construct a partition of the finite time horizon into successively smaller intervals, and design controlled inputs based on the approximate dynamics in each partition. Under conditions that bound the length of the time horizon, we prove that these inputs result in bounded error from the target state in the original nonlinear system. As successive partitions of the time horizon become shorter, the error reduces to zero despite the effect of uncontrolled inputs. A simulation example on the model of a fighter jet demonstrates that the designed sequence of controlled inputs achieves the target state despite the system suffering a loss of control authority over one of its inputs.