Property:Abstract
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S
Modern aircraft increasing rely on electric power, resulting in high safety-criticality and complexity in their electric power generation and distribution systems. Moti- vated by the resulting rapid increase in the costs and duration of the design cycles for such systems, we investigate the use of formal specification and automated, correct-by-construction control protocols synthesis for primary distribution in vehicular electric power networks. We discuss a design workflow that aims to transition from the traditional âdesign+verifyâ approach to a âspecify+synthesizeâ approach. We give an overview of a subset of the recent advances in the synthesis of reactive control proto- cols. We apply these techniques in the context of reconfiguration of the networks in reaction to the changes in their operating environment. We also validate these automatically synthesized control protocols on high-fidelity simulation models and on an academic-scale hardware testbed. +
A
An Aircraft Electric Power Testbed for Validating Automatically Synthesized Reactive Control Protocols +
Modern aircraft increasingly rely on electric power for sub- systems that have traditionally run on mechanical power. The complexity and safety-criticality of aircraft electric power systems have therefore increased, rendering the design of these systems more challenging. This work is mot vated by the potential that correct-by-construction reactive controller synthesis tools may have in increasing the effectiveness of the electric power system design cycle. In particular, we have built an experimental hardware platform that captures some key elements of aircraft electric power systems within a simplified setting. We intend to use this plat- form for validating the applicability of theoretical advances in correct-by-construction control synthesis and for study- ing implementation-related challenges. We demonstrate a simple design workflow from formal specifications to auto- generated code that can run on software models and be used in hardware implementation. We show some preliminary results with different control architectures on the developed hardware testbed. +
F
Modern safety-critical systems are difficult to formally verify, largely due to their large scale. In particular, the widespread use of lookup tables in embedded systems across diverse industries, such as aeronautics and automotive systems, create a critical obstacle to the scala- bility of formal verification. This paper presents a novel approach for the formal verification of large-scale systems with lookup tables. We use a learning-based technique to automatically learn abstractions of the lookup tables and use the abstractions to then prove the desired property. If the verification fails, we propose a falsification heuristic to search for a violation of the specification. In contrast with previous work on lookup table verification, our technique is completely automatic, making it ideal for deployment in a production environment. To our knowledge, our approach is the only technique that can automatically verify large-scale systems lookup with tables.
We illustrate the effectiveness of our technique on a benchmark which cannot be handled by the commer- cial tool SLDV, and we demonstrate the performance improvement provided by our technique. +
B
Bistable State Switch Enables Ultrasensitive Feedback Control in Heterogeneous Microbial Populations +
Molecular feedback control circuits can improve robustness of gene expression at the single cell-level. This achievement can be offset by requirements of rapid protein expression, that may induce cellular stress, known as burden, that reduces colony growth. To begin to address this challenge we take inspiration by ‘division-of-labor’ in heterogeneous cell populations: we propose to combine bistable switches and quorum sensing systems to coordinate gene expression at the population-level. We show that bistable switches in individual cells operating in parallel yield an ultrasensitive response, while cells maintain heterogeneous levels of gene expression to avoid burden across all cells. Within a feedback loop, these switches can achieve robust reference tracking and adaptation to disturbances at the population-level. We also demonstrate that molecular sequestration enables tunable hysteresis in individual switches, making it possible to obtain a wide range of stable population-level expressions. +
R
Most automated systems operate in uncertain or adversarial conditions, and have to be capable of reliably reacting to changes in the environment. The focus of this paper is on automatically synthesizing reactive controllers for cyber-physical systems subject to signal temporal logic (STL) specifications. We build on recent work that encodes STL specifications as mixed integer linear constraints on the variables of a discrete-time model of the system and environment dynamics. To obtain a reactive controller, we present solutions to the worst-case model predictive control (MPC) problem using a suite of mixed integer linear programming techniques. We demonstrate the comparative effectiveness of several existing worst-case MPC techniques, when applied to the problem of control subject to temporal logic specifications; our empirical results emphasize the need to develop specialized solutions for this domain. +
Motion planning in environments with multiple agents is critical to many important autonomous applications such as autonomous vehicles and assistive robots. This paper considers the problem of motion planning, where the controlled agent shares the environment with multiple uncontrolled agents. First, a predictive model of the uncontrolled agents is trained to predict all possible trajectories within a short horizon based on the scenario. The prediction is then fed to a motion planning module based on model predictive control. We proved generalization bound for the predictive model using three different methods, post-bloating, support vector machine (SVM), and conformal analysis, all capable of generating stochastic guarantees of the correctness of the predictor. The proposed approach is demonstrated in simulation in a scenario emulating autonomous highway driving. +
S
Motivated by current technological advances in the design of real-time embedded systems, this work deals with the digital control of a continuous-time linear time-invariant (LTI) system whose output can be sampled at a high frequency. Since a typical sampled-data controller operating at a high sampling frequency needs heavy (high-precision) computation to alleviate its sensitivity to measurement and computational errors, the objective is to design a robust hybrid controller for high- frequency applications with limited computational power. To this end, we exploit our recent results on delay-based controller design and propose a digital-control scheme that can implement every continuous-time stabilizing (LTI) controller. This robust hybrid controller, which consists of an ideal sampler, a digital controller, a number of modified second-order holds and possibly a unity feedback, can operate at arbitrarily high sampling frequencies without requiring expensive, high-precision computation. Later on, it is discussed how to find a continuous-time LTI controller satisfying prescribed design specifications so that its correspond- ing digital controller requires the least processing time. +
I
Motivated by exploration of communication- constrained underground environments using robot teams, we study the problem of planning for intermittent connectivity in multi-agent systems. We propose a novel concept of information-consistency to handle situations where the plan is not initially known by all agents, and suggest an integer linear program for synthesizing information-consistent plans that also achieve auxiliary goals. Furthermore, inspired by network flow problems we propose a novel way to pose connectivity constraints that scales much better than previous methods. In the second part of the paper we apply these results in an exploration setting, and propose a clustering method that separates a large exploration problem into smaller problems that can be solved independently. We demonstrate how the resulting exploration algorithm is able to coordinate a team of ten agents to explore a large environment. +
S
Motivated by problems in flight control, we present a technique for
stabilizing a chain
of integrators in the presence of rate limitations on the input. Our
technique improves on several existing techniques in the literature
and has a number of interesting features. The controller is
evaluated experimentally on a pitch axis flight control experiment at
Caltech. The experimental results show that even in the presence of
rate limits that cause a linear controller to go unstable, the
time-varying controller stabilizes the system with minimal loss in performance. +
E
Motivated by problems such as active control of rotating stall in compression systems,
an analysis of the effects of controller magnitude saturation in feedback stabilization of
steady-state bifurcations is performed. In particular the region of attraction to the
stabilized bifurcated equilibria is solved for feedback controllers with magnitude
saturation limits using the technique of center manifold reduction and bifurcation
analysis. It has been shown that the stability boundary is the saturation envelope formed
by the unstable (or stable) equilibria for the closed loop system when the controllers
saturate. The framework allows the design of feedback control laws to achieve desirable
size of region of attraction when the noise is modeled as a closed set of initial
conditions in the phase space. It is also possible to extend the techniques and results to
Hopf bifurcations. +
Motivated by robotic motion planning, we develop a framework for control policy synthesis for both non-deterministic transition systems and Markov decision processes that are subject to temporal logic task specifications. We introduce a fragment of linear temporal logic that can be used to specify common motion planning tasks such as safe navigation, response to the environment, surveillance, and persistent coverage. This fragment is computationally efficient; the complexity of control policy synthesis is a doubly-exponential improvement over standard linear temporal logic for both non-deterministic transition systems and Markov decision processes. This improvement is possible since we compute directly on the original system, as opposed to the automata-based approach commonly used for linear temporal logic. We give simulation results for representative motion planning tasks and compare to generalized reactivity(1). +
D
Motivated by the availability of different types of delays in embedded systems and biological circuits, the objective of this work is to study the benefits that delay can provide in simplifying the implementation of controllers for continuous-time systems. Given a continuous-time linear time-invariant (LTI) controller, we propose three methods to approximate this controller arbitrarily precisely by a simple controller composed of delay blocks, a few integrators and possibly a unity feedback. Different problems associated with the approximation procedures, such as finding the optimal number of delay blocks or studying the robustness of the designed controller with respect to delay values, are then investigated. We also study the design of an LTI continuous-time controller satisfying given control objectives whose delay-based implementation needs the least number of delay blocks. A direct application of this work is in the sampled-data control of a real-time embedded system, where the sampling frequency is relatively high and/or the output of the system is sampled irregularly. Based on our results on delay-based controller design, we propose a digital-control scheme that can implement every continuous-time stabilizing (LTI) controller. Unlike a typical sampled-data controller, the hybrid controller introduced here---consisting of an ideal sampler, a digital controller, a number of modified second-order holds and possibly a unity feedback---is robust to sampling jitter and can operate at arbitrarily high sampling frequencies without requiring expensive, high-precision computation. +
C
Motivated by the desire to analyze high dimen- sional control systems without explicitly forming computation- ally expensive linear matrix inequality (LMI) constraints, we seek to exploit special structure in the dynamics matrix. By using Jordan algebraic techniques we show how to analyze continuous time linear dynamical systems whose dynamics are exponentially invariant with respect to a symmetric cone. This allows us to characterize the families of Lyapunov functions that suffice to verify the stability of such systems. We highlight, from a computational viewpoint, a class of systems for which stability verification can be cast as a second order cone program (SOCP), and show how the same framework reduces to linear programming (LP) when the system is internally positive, and to semidefinite programming (SDP) when the system has no special structure. +
A
A geometric and structural approach to the analysis and design of biological circuit dynamics: a theory tailored for synthetic biology +
Much of the progress in developing our ability to successfully design genetic circuits with predictable dynamics has followed the strategy of molding biological systems to fit into conceptual frameworks used in other disciplines, most notably the engineering sciences. Because biological systems have fundamental differences from systems in these other disciplines, this approach is challenging and the insights obtained from such analyses are often not framed in a biologically-intuitive way. Here, we present a new theoretical framework for analyzing the dynamics of genetic circuits that is tailored towards the unique properties associated with biological systems and experiments. Our framework approximates a complex circuit as a set of simpler circuits, which the system can transition between by saturating its various internal components. These approximations are connected to the intrinsic structure of the system, so this representation allows the analysis of dynamics which emerge solely from the system’s structure. Using our framework, we analyze the presence of structural bistability in a leaky autoactivation motif and the presence of structural oscillations in the Repressilator. +
I
Neural networks in real-world applications have to satisfy critical properties such as safety and reliability. The analysis of such properties typically involves extracting informa- tion through computing pre-images of neural networks, but it is well-known that explicit computation of pre-images is intractable. We introduce new methods for computing compact symbolic abstractions of pre-images. Our approach relies on computing approximations that provably overapproximate and underapproximate the pre-images at all layers. The abstraction of pre-images enables formal analysis and knowl- edge extraction without modifying standard learning algo- rithms. We show how to use inverse abstractions to automatically extract simple control laws and compact representations for pre-images corresponding to unsafe outputs. We illustrate that the extracted abstractions are often interpretable and can be used for analyzing complex properties. +
R
New control paradigms are needed for large networks of wireless sensors and actuators in order to efficiently utilise system resources. In this study, the authors consider the problem of discrete-tie state estimation over a wireless sensor network. Given a tree that represents the sensor communications with the fusion centre, the authors derive the optimal estimation algorithm at the fusion centre, and provide a closed-form expression for the steady-state error covariance matrix. They then present a tree reconfiguration algorithm that produces a sensor tree that has low overall energy consumption and guarantees a desired level of estimation quality at the fusion centre. The authors further propose a sensor tree construction and scheduling algorithm that leads to a longer network lifetime than the tree reconfiguration algorithm. Examples are provided throughout the paper to demonstrate the algorithms and theory developed. +
F
Finding stationary solutions to the chemical master equation by gluing state spaces at one or two states recursively +
Noise is indispensible to key cellular activities, including gene expression coordination and probabilistic differentiation. Stochastic models, such as the chemical master equation (CME), are essential to model noise in the levels of cellular components. In the CME framework, each state is associated with the molecular counts of all component species, and specifies the probability for the system to have that set of molecular counts. Analytic solutions to the CME are rarely known but can bring exciting benefits. For instance, simulations of biochemical reaction networks that are multiscale in time can be sped up tremendously by incorporating analytic solutions of the slow time-scale dynamics. Ana- lytic solutions also enable the design of stationary distributions with properties such as the modality of the distribution, the mean expression level, and the level of noise. One way to derive the analytic steady state response of a biochemical reaction network was re- cently proposed by (Mélykúti et al. 2014). The paper recursively glues simple state spaces together, for which we have analytic solutions, at one or two states.
<p>
In this work, we explore the benefits and limitations of the gluing technique proposed by Mélykúti et al., and introduce recursive algorithms that use the technique to solve for the analytic steady state response of stochastic biochemical reaction networks. We give formal characterizations of the set of reaction networks whose state spaces can be obtained by carrying out single-point gluing of paths, cycles or both sequentially. We find that the dimension of the state space of a reaction network equals the maximum number of linearly independent reactions in the system. We then characterize the complete set of stochastic biochemical reaction networks that have elementary reactions and two-dimensional state spaces. As an example, we propose a recursive algorithm that uses the gluing technique to solve for the steady state response of a mass-conserving system with two connected monomolecular reversible reactions. Even though the gluing technique can only construct finite state spaces, we find that, by taking the size of a finite state space to infinity, the steady state response can converge to the analytic solution on the resulting infinite state space. Finally, we illustrate the aforementioned ideas with the example of two interconnected transcriptional components, which was first studied by (Ghaemi and Del Vecchio 2012).
R
Recursively constructing analytic expressions for equilibrium distributions of stochastic biochemical reaction networks +
Noise is often indispensable to key cellular activities, such as gene expression, necessitating the use of stochastic models to capture its dynamics. The chemical master equation (CME) is a commonly used stochastic model of Kolmogorov forward equations that describe how the probability distribution of a chemically reacting system varies with time. Finding analytic solutions to the CME can have benefits, such as expediting simulations of multiscale biochemical reaction networks and aiding the design of distributional responses. However, analytic solutions are rarely known. A recent method of computing analytic stationary solutions relies on gluing simple state spaces together recursively at one or two states. We explore the capabilities of this method and introduce algorithms to derive analytic stationary solutions to the CME. We first formally characterize state spaces that can be constructed by performing single-state gluing of paths, cycles or both sequentially. We then study stochastic biochemical reaction networks that consist of reversible, elementary reactions with two-dimensional state spaces. We also discuss extending the method to infinite state spaces and designing the stationary behaviour of stochastic biochemical reaction networks. Finally, we illustrate the aforementioned ideas using examples that include two interconnected transcriptional components and biochemical reactions with two-dimensional state spaces. +
N
Nonlinear control of mechanical systems is a challenging discipline that lies at the
intersection between control theory and geometric mechanics. This thesis sheds new light
on this interplay while investigating motion control problems for Lagrangian systems. Both
stability and motion planning aspects are treated within a unified framework that accounts
for a large class of devices such as robotic manipulators, autonomous vehicles and
locomotion systems.</p>
<p>One distinguishing feature of mechanical systems is the number of control forces. For
systems with as many input forces as degrees of freedom, many control problems are
tractable. One contribution of this thesis is a set of trajectory tracking controllers
designed via the notions of configuration and velocity error. The proposed approach
includes as special cases a variety of results on joint and workspace control of
manipulators as well as on attitude and position control of vehicles.</p>
<p>Whenever fewer input forces are available than degrees of freedom, various control
questions arise. The main contribution of this thesis is the design of motion algorithms
for vehicles, i.e., rigid bodies moving in Euclidean space. First, an algebraic
controllability analysis characterizes the set of reachable configurations and velocities
for a system starting at rest. Then, provided a certain controllability condition is
satisfied, various motion algorithms are proposed to perform tasks such as short range
reconfiguration and hovering. </p>
<p>Finally, stabilization techniques for underactuated systems are investigated. The
emphasis is on relative equilibria, i.e., steady motions for systems that have a conserved
momentum. Local exponential stabilization is achieved via an appropriate splitting of the
control authority. +
B
Nonlinear qualitative analysis is performed on the Moore-Greitzer
model to evaluate the tradeoff of fluid noise, actuator magnitude saturation,
bandwidth, rate limits, and the shape of compressor characteristics in active
control of rotating stall in axial compressors with bleed valve actuators. Model
order reduction is achieved by approximating the dynamics on the invariant manifold
that captures the bifurcations and instabilities. Bifurcations and qualitative
dynamics are obtained by analyzing the reduced system. The operability enhancement
is defined as the extension of operating range for which fully developed rotating
stall is avoided. Analytic formulas are derived for the operability enhancement
as a function of noise level, actuator saturation limits, and the shape of the
compressor characteristic, which is the major nonlinearity in the model. The
shape of the compressor characteristic, especially the unstable part, is critical
to the rate required for robust operability near the peak for the closed loop
system. Experiments are carried out on a single-stage low-speed axial compressor
using different level of steady air injections to generate different compressor
characteristics. The theoretical formulas give good qualitative estimates to
experimental data and simulations using a high fidelity model (37 states). +
