Domitilla Del Vecchio

Heejin Ahn, Andrea Rizzi, Alessandro Colombo et al.

We present the design and validation of a centralized controller, called a supervisor, for collision avoidance of multiple human-driven vehicles at a road intersection, considering measurement errors, unmodeled dynamics, and uncontrolled vehicles. We design the supervisor to be least restrictive, that is, to minimize its interferences with human drivers. This performance metric is given a precise mathematical form by splitting the design process into two subproblems: verification problem and supervisor-design problem. The verification problem determines whether an input signal exists that makes controlled vehicles avoid collisions at all future times. The supervisor is designed such that if the verification problem returns yes, it allows the drivers' desired inputs; otherwise, it overrides controlled vehicles to prevent collisions. As a result, we propose exact and efficient supervisors. The exact supervisor solves the verification problem exactly but with combinatorial complexity. In contrast, the efficient supervisor solves the verification problem within a quantified approximation bound in polynomially bounded time with the number of controlled vehicles. We validate the performances of both supervisors through simulation and experimental testing.

Jichi Wang, Eduardo D. Sontag, Domitilla Del Vecchio

In several applications, including in synthetic biology, one often has input/output data on a system composed of many modules, and although the modules' input/output functions and signals may be unknown, knowledge of the composition architecture can significantly reduce the amount of training data required to learn the system's input/output mapping. Learning the modules' input/output functions is also necessary for designing new systems from different composition architectures. Here, we propose a modular learning framework, which incorporates prior knowledge of the system's compositional structure to (a) identify the composing modules' input/output functions from the system's input/output data and (b) achieve this by using a reduced amount of data compared to what would be required without knowledge of the compositional structure. To achieve this, we introduce the notion of modular identifiability, which allows recovery of modules' input/output functions from a subset of the system's input/output data, and provide theoretical guarantees on a class of systems motivated by genetic circuits. We demonstrate the theory on computational studies showing that a neural network (NNET) that accounts for the compositional structure can learn the composing modules' input/output functions and predict the system's output on inputs outside of the training set distribution. By contrast, a neural network that is agnostic of the structure is unable to predict on inputs that fall outside of the training set distribution. By reducing the need for experimental data and allowing module identification, this framework offers the potential to ease the design of synthetic biological circuits and of multi-module systems more generally.

Mohammad Naghnaeian, Domitilla Del Vecchio

The Chemical Master Equation (CME) is used to stochastically model biochemical reaction networks, under the Markovian assumption. The low-order statistical moments induced by the CME are often the key quantities that one is interested in. However, in most cases, the moments equation is not closed; in the sense that the first $n$ moments depend on the higher order moments, for any positive integer $n$. In this paper, we develop a moment closure technique in which the higher order moments are approximated by an affine function of the lower order moments. We refer to such functions as the affine Moment Closure Functions (MCF) and prove that they are optimal in the worst-case context, in which no a priori information on the probability distribution is available. Furthermore, we cast the problem of finding the optimal affine MCF as a linear program, which is tractable. We utilize the affine MCFs to derive a finite dimensional linear system that approximates the low-order moments. We quantify the approximation error in terms of the $% l_{\infty }$ induced norm of some linear system. Our results can be effectively used to approximate the low-order moments and characterize the noise properties of the biochemical network under study.

Heejin Ahn, Domitilla Del Vecchio

This paper presents the design of a supervisory algorithm that monitors safety at road intersections and overrides drivers with a safe input when necessary. The design of the supervisor consists of two parts: safety verification and control design. Safety verification is the problem to determine if vehicles will be able to cross the intersection without colliding with current drivers' inputs. We translate this safety verification problem into a jobshop scheduling problem, which minimizes the maximum lateness and evaluates if the optimal cost is zero. The zero optimal cost corresponds to the case in which all vehicles can cross each conflict area without collisions. Computing the optimal cost requires solving a Mixed Integer Nonlinear Programming (MINLP) problem due to the nonlinear second-order dynamics of the vehicles. We therefore estimate this optimal cost by formulating two related Mixed Integer Linear Programming (MILP) problems that assume simpler vehicle dynamics. We prove that these two MILP problems yield lower and upper bounds of the optimal cost. We also quantify the worst case approximation errors of these MILP problems. We design the supervisor to override the vehicles with a safe control input if the MILP problem that computes the upper bound yields a positive optimal cost. We theoretically demonstrate that the supervisor keeps the intersection safe and is non-blocking. Computer simulations further validate that the algorithms can run in real time for problems of realistic size.

Heejin Ahn, Domitilla Del Vecchio

In this paper, we design a supervisor to prevent vehicle collisions at intersections. An intersection is modeled as an area containing multiple conflict points where vehicle paths cross in the future. At every time step, the supervisor determines whether there will be more than one vehicle in the vicinity of a conflict point at the same time. If there is, then an impending collision is detected, and the supervisor overrides the drivers to avoid collision. A major challenge in the design of a supervisor as opposed to an autonomous vehicle controller is to verify whether future collisions will occur based on the current drivers choices. This verification problem is particularly hard due to the large number of vehicles often involved in intersection collision, to the multitude of conflict points, and to the vehicles dynamics. In order to solve the verification problem, we translate the problem to a job-shop scheduling problem that yields equivalent answers. The job-shop scheduling problem can, in turn, be transformed into a mixed-integer linear program when the vehicle dynamics are first-order dynamics, and can thus be solved by using a commercial solver.