Property:Abstract
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A
We introduce an algorithm for the optimal con- trol of stochastic nonlinear systems subject to temporal logic constraints on their behavior. We directly compute on the state space of the system, avoiding the expensive pre-computation of a discrete abstraction. An automaton that corresponds to the temporal logic specification guides the computation of a control policy that maximizes the probability that the system satisfies the specification. This reduces controller synthesis to solving a sequence of stochastic constrained reachability problems. The solution to each reachability problem corresponds to the solution to a corresponding Hamilton-Jacobi-Bellman (HJB) partial differential equation. To increase the efficiency of our approach, we exploit a class of systems where the HJB equation is linear due to structural assumptions on the noise. The linearity of the PDE allows us to pre-compute control policy primitives and then compose them, at essentially zero cost, to satisfy a complex temporal logic specification. +
We introduce an algorithm for the optimal control of stochastic nonlinear systems subject to temporal logic constraints on their behavior. We compute directly on the state space of the system, avoiding the expensive pre-computation of a discrete abstraction. An automaton that corresponds to the temporal logic specification guides the computation of a control policy that maximizes the probability that the system satisfies the specification. This reduces controller synthesis to solving a sequence of stochastic constrained reachability problems. Each individual reachability problem is solved via the Hamilton-Jacobi-Bellman (HJB) partial differential equation of stochastic optimal control theory. To increase the efficiency of our approach, we exploit a class of systems where the HJB equation is linear due to structural assumptions on the noise. The linearity of the partial differential equation allows us to pre-compute control policy primitives and then compose them, at essentially zero cost, to conservatively satisfy a complex temporal logic specification. +
D
We investigate nonlinear dynamical models for self- sustained
oscillations in the flow past a rectangular cavity. The models are
based on the method of Proper Orthogonal Decomposition (POD) and
Galerkin projection, and we introduce an inner product and formulation
of the equations of motion which enables one to use vector-valued POD
modes for compressible flows. We obtain models between 3 and 20
states, which accurately describe both the short-time and long-time
dynamics. This is a substantial improvement over previous models
based on scalar-valued POD modes,which capture the dynamics for short
time, but deviate for long time. +
M
We present a Python-based software package to automatically obtain phenomenological models of input-controlled synthetic biological circuits that guide the design using chemical reaction-level descriptive models. From the parts and mechanism description of a synthetic biological circuit, it is easy to obtain a chemical reaction model of the circuit under the assumptions of mass-action kinetics using various existing tools. However, using these models to guide design decisions during an experiment is difficult due to a large number of reaction rate parameters and species in the model. Hence, phenomenological models are often developed that describe the effective relationships among the circuit inputs, outputs, and only the key states and parameters. In this paper, we present an algorithm to obtain these phenomenological models in an automated manner using a Python package for circuits with inputs that control the desired outputs. This model reduction approach combines the common assumptions of time-scale separation, conservation laws, and species’ abundance to obtain the reduced models that can be used for design of synthetic biological circuits. We consider an example of a simple gene expression circuit and another example of a layered genetic feedback control circuit to demonstrate the use of the model reduction procedure. +
R
We present a counterexample-guided inductive synthesis approach to controller synthesis for cyber-physical systems subject to signal temporal logic (STL) specifications, operating in potentially adversarial nondeterministic environments. We encode STL specifications as mixed integer-linear constraints on the variables of a discrete-time model of the system and environment dynamics, and solve a series of optimization problems to yield a satisfying control sequence. We demonstrate how the scheme can be used in a receding horizon fashion to fulfill properties over unbounded horizons, and present experimental results for reactive controller synthesis for case studies in building climate control and autonomous driving. +
B
We present a detailed dynamical model of the behavior of
transcription-translation circuits in vitro that makes explicit the roles
played by essential molecular resources. A set of simple two-gene test
circuits operating in a cell-free biochemical âbreadboardâ validate this
model and highlight the consequences of limited resource availability. In
particular, we are able to confirm the existence of biomolecular âcrosstalkâ
and isolate its individual sources. The implications of crosstalk for
biomolecular circuit design and function are discussed. +
M
We present a framework for applying the method of Proper Orthogonal Decomposition
(POD) and Galerkin projection to compressible fluids. For incompressible flows,
only the kinematic variables are important, and the techniques are well known. In
a compressible flow, both the kinematic and thermodynamic variables are dynamically
important, and must be included in the configuration space. We introduce
an energy-based inner product which may be used to obtain POD modes for this
configuration space. We then obtain an approximate version of the Navier-Stokes
equations, valid for cold flows at moderate Mach number, and project these equations
onto a POD basis. The resulting equations of motion are quadratic, and are
much simpler than projections of the full compressible Navier-Stokes equations. +
T
We present a framework for merging unit tests for autonomous systems. Typically, it is intractable to test an autonomous system for every scenario in its operating environment. The question of whether it is possible to design a single test for multiple requirements of the system motivates this work. First, we formally define three attributes of a test: a test specification that characterizes behaviors observed in a test execution, a test environment, and a test policy. Using the merge operator from contract-based design theory, we provide a formalism to construct a merged test specification from two unit test specifications. Temporal constraints on the merged test specification guarantee that non-trivial satisfaction of both unit test specifications is necessary for a successful merged test execution. We assume that the test environment remains the same across the unit tests and the merged test. Given a test specification and a test environment, we synthesize a test policy filter using a receding horizon approach, and use the test policy filter to guide a search procedure (e.g. Monte-Carlo Tree Search) to find a test policy that is guaranteed to satisfy the test specification. This search procedure finds a test policy that maximizes a pre-defined robustness metric for the test while the filter guarantees a test policy for satisfying the test specification. We prove that our algorithm is sound. Furthermore, the receding horizon approach to synthesizing the filter ensures that our algorithm is scalable. Finally, we show that merging unit tests is impactful for designing efficient test campaigns to achieve similar levels of coverage in fewer test executions. We illustrate our framework on two self-driving examples in a discrete-state setting. +
C
Characterization of Integrase and Excisionase Activity in Cell-free Protein Expression System Using a Modeling and Analysis Pipeline +
We present a full-stack modeling, analysis, and parameter identification pipeline to guide the modeling and design of biological systems starting from specifications to circuit implementations and parameterizations. We demonstrate this pipeline by characterizing the integrase and excisionase activity in cell-free protein expression system. We build on existing Python tools — BioCRNpyler, AutoReduce, and Bioscrape — to create this pipeline. For enzyme-mediated DNA recombination in cell-free system, we create detailed chemical reaction network models from simple high-level descriptions of the biological circuits and their context using BioCRNpyler. We use Bioscrape to show that the output of the detailed model is sensitive to many parameters. However, parameter identification is infeasible for this high-dimensional model, hence, we use AutoReduce to automatically obtain reduced models that have fewer parameters. This results in a hierarchy of reduced models under different assumptions to finally arrive at a minimal ODE model for each circuit. Then, we run sensitivity analysis-guided Bayesian inference using Bioscrape for each circuit to identify the model parameters. This process allows us to quantify integrase and excisionase activity in cell extracts enabling complex-circuit designs that depend on accurate control over protein expression levels through DNA recombination. The automated pipeline presented in this paper opens up a new approach to complex circuit design, modeling, reduction, and parameterization. +
T
We present a general framework for the control of Lagrangian systems with as many
inputs as degrees of freedom. Relying on the geometry of mechanical systems on manifolds,
we propose a design algorithm for the tracking problem. The notion of error function and
transport map lead to a proper definition of configuration and velocity error. These are
the crucial ingredients in designing a proportional derivative feedback and feedforward
controller. The proposed approach includes as special cases a variety of results on
control of manipulators, pointing devices and autonomous vehicles. Our design provides
particular insight into both aerospace and underwater applications where the configuration
manifold is a Lie group. +
O
We present a mathematical programming-based method for optimal con- trol of nonlinear systems subject to temporal logic task specifications. We specify tasks using a fragment of linear temporal logic (LTL) that allows both finite- and infinite-horizon properties to be specified, including tasks such as surveillance, periodic motion, repeated assembly, and environmental monitoring. Our method di- rectly encodes an LTL formula as mixed-integer linear constraints on the system variables, avoiding the computationally expensive process of creating a finite ab- straction. Our approach is efficient; for common tasks our formulation uses significantly fewer binary variables than related approaches and gives the tightest possible convex relaxation. We apply our method on piecewise affine systems and certain classes of differentially flat systems. In numerical experiments, we solve temporal logic motion planning tasks for high-dimensional (10+) continuous systems. +
M
We present a mathematical programming-based method for model predictive control of cyber-physical systems subject to signal temporal logic (STL) specifications. We describe the use of STL to specify a wide range of properties of these systems, including safety, response and bounded liveness. For synthesis, we encode STL specifications as mixed integer-linear constraints on the system variables in the optimization problem at each step of a receding horizon control framework. We prove correctness of our algorithms, and present experimental results for controller synthesis for building energy and climate control. +
We present a mathematical programming-based method for model predictive control of discrete-time cyber- physical systems subject to signal temporal logic (STL) speci- fications. We describe the use of STL to specify a wide range of properties of these systems, including safety, response and bounded liveness. For synthesis, we encode STL specifications as mixed integer-linear constraints on the system variables in the optimization problem at each step of model predictive control. We present experimental results for controller synthesis on simplified models of a smart micro-grid and HVAC system. +
O
We present a mathematical programming-based method for optimal control of discrete-time nonlinear systems subject to temporal logic task specifications. We use linear temporal logic (LTL) to specify a wide range of properties and tasks, such as safety, progress, response, surveillance, repeated assembly, and environmental monitoring. Our method directly encodes an LTL formula as mixed-integer linear constraints on the continuous system variables, avoiding the computationally expensive processes of creating a finite abstraction of the system and a Bu Ìchi automaton for the specification. In numerical experiments, we solve temporal logic motion planning tasks for high-dimensional (more than 10 continuous states) dynamical systems. +
A
We present a mathematical reconstruction
of the kinematics and dynamics of flight initiation as observed in high-speed video recordings of the insect Drosophila melanogaster. The behavioral dichotomy observed in the fruit flies' flight initiation sequences, as a response to different stimuli, was reflected in two contrasting sets of dynamics once the flies had become airborne. By reconstructing the dynamics of unconstrained motion during flight initiations, we assess the fly's responses (generation of forces and moments) amidst these two dynamic patterns. Moreover, we introduce a 3D visual tracking algorithm as a tool to analyze the wing kinematics applied by the insect, and investigate their relation(s) to the production of these aerodynamic forces. Using this framework we formulate different hypotheses about the modulation of flight forces and moments during flight initiation as a way torefining our understanding of insect flight control., +
R
We present a method for designing robust con- trollers for dynamical systems with linear temporal logic specifications. We abstract the original system by a finite Markov Decision Process (MDP) that has transition probabilities in a specified uncertainty set. A robust control policy for the MDP is generated that maximizes the worst-case probability of satisfying the specification over all transition probabilities in the uncertainty set. To do this, we use a procedure from probabilistic model checking to combine the system model with an automaton representing the specification. This new MDP is then transformed into an equivalent form that satisfies assumptions for stochastic shortest path dynamic programming. A robust version of dynamic programming allows us to solve for a eps-suboptimal robust control policy with time complexity O(log1/eps) times that for the non-robust case. We then implement this control policy on the original dynamical system. +
P
We present a method for mending strategies for GR(1) specifications. Given the addition or removal of edges from the game graph describing a problem (essentially transition rules in a GR(1) specification), we apply a μ-calculus formula to a neighborhood of states to obtain a âlocal strategyâ that navigates around the invalidated parts of an original synthesized strategy. Our method may thus avoid global resynthesis while recovering correctness with respect to the new specification. We illustrate the results both in simulation and on physical hardware for a planar robot surveillance task. +
R
We present a methodology for automatic synthesis of embedded control software that incorporates a class of linear temporal logic (LTL) specifications sufficient to describe a wide range of properties including safety, stability, progress, obligation, response and guarantee. To alleviate the associated computational complexity of LTL synthesis, we propose a receding horizon framework that effectively reduces the synthesis problem into a set of smaller problems. The proposed control architecture consists of a goal generator, a trajectory planner, and a continuous controller. The goal generator reduces the trajectory generation problem into a sequence of smaller problems of short horizon while preserving the desired system-level temporal properties. Subsequently, in each iteration, the trajectory planner solves the corresponding short-horizon problem with the currently observed state as the initial state and generates a feasible trajectory to be implemented by the continuous controller. Based on the simulation property, we show that the composition of the goal generator, trajectory planner and continuous controller and the corresponding receding horizon framework guarantee the correctness of the system with respect to its specification regardless of the environment in which the system operates. In addition, we present a response mechanism to handle failures that may occur due to a mismatch between the actual system and its model. The effectiveness of the proposed technique is demonstrated through an example of an autonomous vehicle navigating an urban environment. This example also illustrates that the system is not only robust with respect to exogenous disturbances but is also capable of properly handling violation of the environment assumption that is explicitly stated as part of the system specification . +
C
We present a set of primitive operations which forms the core of a robot system
description and control language. The actions of the individual primitives are derived
from the mathematical structure of the equations of motion for constrained mechanical
systems. The recursive nature of the primitives allows composite robots to be constructed
from more elementary daughter robots. We review a few pertinent results of classical
mechanics, describe the functionality of our primitive operations, and present several
different hierarchical strategies for the description and control of a two-fingered hand
holding a box. +
R
We present a simple geometric analysis of wireless
connectivity in vehicle networks. We introduce a localized
notion of connectedness, and construct a function that measures
the robustness of this local connectedness to variations
in position. Under a mild feasibility hypothesis, this function
provides a sufficient condition for global connectedness of
the network. Further, it is distributed, in the sense that
both the function and its gradients can be calculated using
only neighbor-to-neighbor communications. It can thus form
the basis for distributed motion-control algorithms which
respect connectivity constraints. We conclude with two simple
examples of target applications. +
