Necmiye Ozay

TuLiP: a software toolbox for receding horizon temporal logic planning

This paper describes TuLiP, a Python-based software toolbox for the synthesis of embedded control software that is provably correct with respect to an expressive subset of linear temporal logic (LTL) specifications. TuLiP combines routines for (1) finite state abstraction of control systems, (2) digital design synthesis from LTL specifications, and (3) receding horizon planning. The underlying digital design synthesis routine treats the environment as adversary; hence, the resulting controller is guaranteed to be correct for any admissible environment profile. TuLiP applies the receding horizon framework, allowing the synthesis problem to be broken into a set of smaller problems, and consequently alleviating the computational complexity of the synthesis procedure, while preserving the correctness guarantee.

A Contract-Based Methodology for Aircraft Electric Power System Design

In an aircraft electric power system, one or more supervisory control units actuate a set of electromechanical switches to dynamically distribute power from generators to loads, while satisfying safety, reliability, and real-time performance requirements. To reduce expensive redesign steps, this control problem is generally addressed by minor incremental changes on top of consolidated solutions. A more systematic approach is hindered by a lack of rigorous design methodologies that allow estimating the impact of earlier design decisions on the final implementation. To achieve an optimal implementation that satisfies a set of requirements, we propose a platform-based methodology for electric power system design, which enables independent implementation of system topology (i.e., interconnection among elements) and control protocol by using a compositional approach. In our flow, design space exploration is carried out as a sequence of refinement steps from the initial specification toward a final implementation by mapping higher level behavioral and performance models into a set of either existing or virtual library components at the lower level of abstraction. Specifications are first expressed using the formalisms of linear temporal logic, signal temporal logic, and arithmetic constraints on Boolean variables. To reason about different requirements, we use specialized analysis and synthesis frameworks and formulate assume guarantee contracts at the articulation points in the design flow. We show the effectiveness of our approach on a proof-of-concept electric power system design.

Synthesis of Reactive 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 (LTL). The synthesized protocols are robust against exogenous disturbances on the continuous dynamics and can react to possibly adversarial events (both external and internal). Finite-state approximations that abstract the behavior of the underlying continuous dynamics are defined using finite transition systems. Such approximations allow us to transform the continuous switching synthesis problem into a discrete synthesis problem in the form of a two-player game between the system and the environment, where the winning conditions represent the high-level temporal logic specifications. Restricting to an expressive subclass of LTL formulas, these temporal logic games are amenable to solutions with polynomial-time complexity. By construction, existence of a discrete switching strategy for the discrete synthesis problem guarantees the existence of a switching protocol that can be implemented at the continuous level to ensure the correctness of the nonlinear switched system and to react to the environment at run time.

A Sparsification Approach to Set Membership Identification of Switched Affine Systems

This paper addresses the problem of robust identification of a class of discrete-time affine hybrid systems, switched affine models, in a set membership framework. Given a finite collection of noisy input/output data and some minimal a priori information about the set of admissible plants, the objective is to identify a suitable set of affine models along with a switching sequence that can explain the available experimental information, while minimizing either the number of switches or subsystems. For the case where it is desired to minimize the number of switches, the key idea of the paper is to reduce this problem to a sparsification form, where the goal is to maximize sparsity of a suitably constructed vector sequence. Our main result shows that in the case of ℓ∞ bounded noise, this sparsification problem can be exactly solved via convex optimization. In the general case where the noise is only known to belong to a convex set N, the problem is generically NP-hard. However, as we show in the paper, efficient convex relaxations can be obtained by exploiting recent results on sparse signal recovery. Similarly, we present both a sparsification formulation and a convex relaxation for the (known to be NP hard) case where it is desired to minimize the number of subsystems. These results are illustrated using two non-trivial problems arising in computer vision applications: video-shot and dynamic texture segmentation.

A sparsification approach to set membership identification of a class of affine hybrid systems

This paper addresses the problem of robust identification of a class of discrete-time affine hybrid systems, switched affine models, in a set membership framework. Given a finite collection of noisy input/output data and some minimal a priori information about the set of admissible plants, the objective is to identify a suitable set of affine models along with a switching sequence that can explain the available experimental information, while optimizing a performance criteria (either minimum number of switches or minimum number of plants). Our main result shows that this problem can be reduced to a sparsification form, where the goal is to maximize sparsity of a given vector sequence. Although in principle this leads to an NP-hard problem, as we show in the paper, efficient convex relaxations can be obtained by exploiting recent results on sparse signal recovery. These results are illustrated using two non-trivial problems arising in computer vision applications: video-shot and dynamic texture segmentation.

Abstraction, discretization, and robustness in temporal logic control of dynamical systems

Abstraction-based, hierarchical approaches to control synthesis from temporal logic specifications for dynamical systems have gained increased popularity over the last decade. Yet various issues commonly encountered and extensively dealt with in control systems have not been adequately discussed in the context of temporal logic control of dynamical systems, such as inter-sample behaviors of a sampled-data system, effects of imperfect state measurements and un-modeled dynamics, and the use of time-discretized models to design controllers for continuous-time dynamical systems. We discuss these issues in this paper. The main motivation is to demonstrate the possibility of accounting for the mismatches between a continuous-time control system and its various types of abstract models used for control synthesis. We do this by incorporating additional robustness measures in the abstract models. Such robustness measures are gained at the price of either increased non-determinism in the abstracted models or relaxed versions of the specification being realized. Under a unified notion of abstraction, we provide concrete means of incorporating these robustness measures and establish results that demonstrate their effectiveness in dealing with the above mentioned issues.

Robust identification of switched affine systems via moments-based convex optimization

This paper addresses the problem of robust identification of a class of discrete-time affine hybrid systems, switched affine models, in a set membership framework. Given a finite collection of noisy input/output data and a bound on the number of subsystems, the objective is to identify a suitable set of affine models along with a switching sequence that can explain the available experimental information. Our method builds upon an algebraic procedure proposed by Vidal et al. for noise free measurements. In the presence of norm bounded noise, this algebraic procedure leads to a very challenging nonconvex polynomial optimization problem. Our main result shows that this problem can be reduced to minimizing the rank of a matrix whose entries are affine in the optimization variables, subject to a convex constraint imposing that these variables are the moments of an (unknown) probability distribution function with finite support. Appealing to well known convex relaxations of rank leads to an overall semi-definite optimization problem that can be efficiently solved. These results are illustrated with two examples showing substantially improved identification performance in the presence of noise.

Set membership identification of switched linear systems with known number of subsystems

This paper addresses the problem of robust identification of a class of discrete-time linear hybrid systems, switched linear models, in a set membership framework. Given a finite collection of input/output data from a noisy process the objective is twofold: (i) establish whether this data was generated by a system that switches amongst an a priori known number of subsystems, and (ii) in that case identify a suitable set of linear models along with a switching sequence that can explain the available experimental information. Our main result shows that these problems are equivalent to minimizing the rank of a matrix whose entries are affine in the optimization variables, subject to a convex constraint imposing that these variables are the moments of an (unknown) Borel measure with finite support. The use of well known (tight) convex relaxations of rank allows for further reducing the problem to a semidefinite optimization that can be efficiently solved. In the second part of the paper we extend these results to handle sensor failures that result in corrupted input/output measurements. Assuming that these failures are infrequent, we show that the problem can be recast into an optimization form where the objective is to simultaneously minimize the rank of a matrix and the number of nonzero rows of a second one. In both cases, appealing to well known convex relaxations of rank and sparsity leads to overall semidefinite optimization problems that can be efficiently solved. These results are illustrated with multiple examples showing substantially improved identification performance in the presence of noise and sensor faults.

Incremental synthesis of switching protocols via abstraction refinement

We consider the problem of synthesizing switching protocols that regulate the modes of a switched system in order to guarantee that the trajectories of the system satisfy certain high-level specifications. In particular, we develop a computational framework for incremental synthesis of switching protocols. Augmented finite transition systems are used as abstract representations of continuous dynamics. Inspired by counter-example guided abstraction refinement procedures for hybrid system verification, we start with a coarse abstraction and gradually refine it according to preorder relations on augmented finite transition systems. At each iteration, the proposed procedure can produce either a switching protocol that ensures the satisfaction of the specification, a certificate for nonexistence of such a protocol, or a refinement suggestion together with a partial solution to be used in the next iteration. Although the procedure is not guaranteed to terminate in general, we illustrate its practical applicability with two simple examples.

Computing augmented finite transition systems to synthesize switching protocols for polynomial switched systems

This work is motivated by the problem of synthesizing mode sequences for continuous-time polynomial switched systems in order to guarantee that the trajectories of the system satisfy certain high-level specifications expressed in linear temporal logic. We use augmented finite transition systems as abstract models of continuous switched systems. Augmented finite transition systems are equipped with liveness properties that can be used to enforce progress in accordance with the underlying dynamics. We then introduce abstraction and refinement relations that induce a preorder on this class of finite transition systems. By construction, the resulting preorder respects the feasibility (i.e., realizability) of the synthesis problem. Hence, existence of a discrete switching strategy for one of these abstract finite transition systems guarantees the existence of a mode sequence for the continuous system such that all of its trajectories satisfy the specification. We also present an algorithm, which can be implemented using sum-of-squares based relaxations, to compute such high fidelity abstract models in a computationally tractable way. Finally, these ideas are illustrated on an example.