Robust Control of Uncertain Markov Decision Processes with Temporal Logic Specifications

We present a method for designing robust controllers 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 $\epsilon$-suboptimal robust control policy with time complexity $O(\log 1/\epsilon)$ times that for the non-robust case. We then implement this control policy on the original dynamical system

Synthesis of Switching Protocols from Temporal Logic Specifications

We propose formal means for synthesizing switching protocols that determine the sequence in which the modes of a switched system are activated to satisfy certain high-level specifications in linear temporal logic. The synthesized protocols are robust against exogenous disturbances on the continuous dynamics. Two types of finite transition systems, namely under- and over-approximations, that abstract the behavior of the underlying continuous dynamics are defined. In particular, we show that the discrete synthesis problem for an under-approximation can be formulated as a model checking problem, whereas that for an over-approximation can be transformed into a two-player game. Both of these formulations are amenable to efficient, off-the-shelf software tools. By construction, existence of a discrete switching strategy for the discrete synthesis problem guarantees the existence of a continuous switching protocol for the continuous synthesis problem, which can be implemented at the continuous level to ensure the correctness of the nonlinear switched system. Moreover, the proposed framework can be straightforwardly extended to accommodate specifications that require reacting to possibly adversarial external events. Finally, these results are illustrated using three examples from different application domains

Convex Optimal Uncertainty Quantification

Optimal uncertainty quantification (OUQ) is a framework for numerical extreme-case analysis of stochastic systems with imperfect knowledge of the underlying probability distribution. This paper presents sufficient conditions under which an OUQ problem can be reformulated as a finite-dimensional convex optimization problem, for which efficient numerical solutions can be obtained. The sufficient conditions include that the objective function is piecewise concave and the constraints are piecewise convex. In particular, we show that piecewise concave objective functions may appear in applications where the objective is defined by the optimal value of a parameterized linear program.Comment: Accepted for publication in SIAM Journal on Optimizatio

Quantum network of neutral atom clocks

We propose a protocol for creating a fully entangled GHZ-type state of neutral atoms in spatially separated optical atomic clocks. In our scheme, local operations make use of the strong dipole-dipole interaction between Rydberg excitations, which give rise to fast and reliable quantum operations involving all atoms in the ensemble. The necessary entanglement between distant ensembles is mediated by single-photon quantum channels and collectively enhanced light-matter couplings. These techniques can be used to create the recently proposed quantum clock network based on neutral atom optical clocks. We specifically analyze a possible realization of this scheme using neutral Yb ensembles.Comment: 13 pages, 11 figure

Synthesis of Reactive Protocols for Vehicle-to-Vehicle Communication

We present a synthesis method for communication protocols for active safety applications that satisfy certain formal specifications on quality of service requirements. The protocols are developed to provide reliable communication services for automobile active safety applications. The synthesis method transforms a specification into a distributed implementation of senders and receivers that together satisfy the quality of service requirements by transmitting messages over an unreliable medium. We develop a specification language and an execution model for the implementations, and demonstrate the viability of our method by developing a protocol for a traffic scenario in which a car runs a red light at a busy intersection

Application of asymptotic waveform evaluation for time domain analysis of nonlinear circuits

Cataloged from PDF version of article.A method is described to exploit asymptotic waveform evaluation (ATNE) in the time-domain analysis of nonlinear circuits by using SPICE models for nonlinear devices such as diodes, transistors, etc. Although AWE has been used for linearized circuits only, the aim is to enhance the accuracy of the simulation while preserving the computational efficiency obtained with AWE and to eliminate the piecewise-linear modelling problem. Practical examples are given to illustrate significant improvements in accuracy. For circuits containing weakly nonlinear devices, it is demonstrated that this method is typically at least one order of magnitude faster than SPICE

Specification and Synthesis of Reactive Protocols for Aircraft Electric Power Distribution

The increasing complexity of electric power systems leads to challenges in integration and verification. We consider the problem of designing a control protocol for an aircraft electric power system that meets a set of requirements describing the correct behaviors of the system and reacts dynamically to changes in internal system states. We formalize the requirements by translating them into a temporal logic specification language and apply game-based, temporal logic formal methods to automatically synthesize a controller protocol that satisfies these overall properties and requirements. Through a case study, we perform a design exploration to show the benefits and tradeoffs between centralized and distributed control architectures

A novel algorithm for DC analysis of piecewise-linear circuits: popcorn

Cataloged from PDF version of article.A fast and convergent iteration method for piecewise-linear analysis of nonlinear resistive circuits is presented. Most of the existing algorithms are applicable only to a limited class of circuits. In general, they are either not convergent or too slow for large circuits. The new algorithm presented in the paper is much more efficient than the existing ones and can be applied to any piecewise-linear circuit. It is based on the piecewise-linear version of the Newton-Raphson algorithm. As opposed to the Newton-Raphson method, the new algorithm is globally convergent from an arbitrary starting point. It is simple to understand and it can be easily programmed. Some numerical examples are given in order to demonstrate the effectiveness of the proposed algorithm in terms of the amount of computation