arXiv subjects

Necmiye Ozay

Publications and source records attributed to Necmiye Ozay.

72 records · Page 4Linked to original sources

arXiv2019

Passivity-Based Analysis of Sampled and Quantized Control Implementations

This paper studies the performance of a continuous controller when implemented on digital devices via sampling and quantization, by leveraging passivity analysis. Degradation of passivity indices from a continuous-time control system to its sampled, input and output quantized model is studied using a notion of quasi-passivity. Based on that, the passivity property of a feedback-connected system where the continuous controller is replaced by its sampled and quantized model is studied, and conditions that ensure the state boundedness of the interconnected system are provided. Additionally, the approximate bisimulation-based control implementation where the controller is replaced by its approximate bisimilar symbolic model whose states are also quantized is analyzed. Several examples are provided to illustrate the theoretical results.

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arXiv2019

Correct-by-construction control synthesis for buck converters with event-triggered state measurement

In this paper, we illustrate a new correct-by-construction switching controller for a power converter with event-triggered measurements. The event-triggered measurement scheme is beneficial for high frequency power converters because it requires relatively low-speed sampling hardware and is immune to unmodeled switching transients. While providing guarantees on the closed-loop system behavior is crucial in this application, off-the-shelf abstraction-based techniques cannot be directly employed to synthesize a controller in this setting because controller cannot always get instantaneous access to the current state. As a result, the switching action has to be based on slightly out-of-date measurements. To tackle this challenge, we introduce the out-of-date measurement as an extra state variable and project out the inaccessible real state to construct a belief space abstraction. The properties preserved by this belief space abstraction are analyzed. Finally, an abstraction-based synthesis method is applied to this abstraction. We demonstrate the controller on a constant on-time buck voltage regulator plant with an event-triggered sampler. The simulation verifies the effectiveness of our controller.

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arXiv2019

Learning Constraints from Demonstrations

We extend the learning from demonstration paradigm by providing a method for learning unknown constraints shared across tasks, using demonstrations of the tasks, their cost functions, and knowledge of the system dynamics and control constraints. Given safe demonstrations, our method uses hit-and-run sampling to obtain lower cost, and thus unsafe, trajectories. Both safe and unsafe trajectories are used to obtain a consistent representation of the unsafe set via solving an integer program. Our method generalizes across system dynamics and learns a guaranteed subset of the constraint. We also provide theoretical analysis on what subset of the constraint can be learnable from safe demonstrations. We demonstrate our method on linear and nonlinear system dynamics, show that it can be modified to work with suboptimal demonstrations, and that it can also be used to learn constraints in a feature space.

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arXiv2019

Non-asymptotic Identification of LTI Systems from a Single Trajectory

We consider the problem of learning a realization for a linear time-invariant (LTI) dynamical system from input/output data. Given a single input/output trajectory, we provide finite time analysis for learning the system's Markov parameters, from which a balanced realization is obtained using the classical Ho-Kalman algorithm. By proving a stability result for the Ho-Kalman algorithm and combining it with the sample complexity results for Markov parameters, we show how much data is needed to learn a balanced realization of the system up to a desired accuracy with high probability.

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arXiv2019

Optimal Input Design for Affine Model Discrimination with Applications in Intention-Aware Vehicles

This paper considers the optimal design of input signals for the purpose of discriminating among a finite number of affine models with uncontrolled inputs and noise. Each affine model represents a different system operating mode, corresponding to unobserved intents of other drivers or robots, or to fault types or attack strategies, etc. The input design problem aims to find optimal separating/discriminating (controlled) inputs such that the output trajectories of all the affine models are guaranteed to be distinguishable from each other, despite uncertainty in the initial condition and uncontrolled inputs as well as the presence of process and measurement noise. We propose a novel formulation to solve this problem, with an emphasis on guarantees for model discrimination and optimality, in contrast to a previously proposed conservative formulation using robust optimization. This new formulation can be recast as a bilevel optimization problem and further reformulated as a mixed-integer linear program (MILP). Moreover, our fairly general problem setting allows the incorporation of objectives and/or responsibilities among rational agents. For instance, each driver has to obey traffic rules, while simultaneously optimizing for safety, comfort and energy efficiency. Finally, we demonstrate the effectiveness of our approach for identifying the intention of other vehicles in several driving scenarios.

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arXiv2018

Multirobot Coordination with Counting Temporal Logics

In many multirobot applications, planning trajectories in a way to guarantee that the collective behavior of the robots satisfies a certain high-level specification is crucial. Motivated by this problem, we introduce counting temporal logics---formal languages that enable concise expression of multirobot task specifications over possibly infinite horizons. We first introduce a general logic called counting linear temporal logic plus (cLTL+), and propose an optimization-based method that generates individual trajectories such that satisfaction of a given cLTL+ formula is guaranteed when these trajectories are synchronously executed. We then introduce a fragment of cLTL+, called counting linear temporal logic (cLTL), and show that a solution to planning problem with cLTL constraints can be obtained more efficiently if all robots have identical dynamics. In the second part of the paper, we relax the synchrony assumption and discuss how to generate trajectories that can be asynchronously executed, while preserving the satisfaction of the desired cLTL+ specification. In particular, we show that when the asynchrony between robots is bounded, the method presented in this paper can be modified to generate robust trajectories. We demonstrate these ideas with an experiment and provide numerical results that showcase the scalability of the method.

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arXiv2018

Using control synthesis to generate corner cases: A case study on autonomous driving

This paper employs correct-by-construction control synthesis, in particular controlled invariant set computations, for falsification. Our hypothesis is that if it is possible to compute a "large enough" controlled invariant set either for the actual system model or some simplification of the system model, interesting corner cases for other control designs can be generated by sampling initial conditions from the boundary of this controlled invariant set. Moreover, if falsifying trajectories for a given control design can be found through such sampling, then the controlled invariant set can be used as a supervisor to ensure safe operation of the control design under consideration. In addition to interesting initial conditions, which are mostly related to safety violations in transients, we use solutions from a dual game, a reachability game for the safety specification, to find falsifying inputs. We also propose optimization-based heuristics for input generation for cases when the state is outside the winning set of the dual game. To demonstrate the proposed ideas, we consider case studies from basic autonomous driving functionality, in particular, adaptive cruise control and lane keeping. We show how the proposed technique can be used to find interesting falsifying trajectories for classical control designs like proportional controllers, proportional integral controllers and model predictive controllers, as well as an open source real-world autonomous driving package.

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arXiv2018

Control Synthesis for Permutation-Symmetric High-Dimensional Systems With Counting Constraints

General purpose correct-by-construction synthesis methods are limited to systems with low dimensionality or simple specifications. In this work we consider highly symmetrical counting problems and exploit the symmetry to synthesize provably correct controllers for systems with tens of thousands of states. The key ingredients of the solution are an aggregate abstraction procedure for mildly heterogeneous systems and a formulation of counting constraints as linear inequalities.

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arXiv2018

A Robust Algorithm for Online Switched System Identification

In this paper, we consider the problem of online identification of Switched AutoRegressive eXogenous (SARX) systems, where the goal is to estimate the parameters of each subsystem and identify the switching sequence as data are obtained in a streaming fashion. Previous works in this area are sensitive to initialization and lack theoretical guarantees. We overcome these drawbacks with our two-step algorithm: (i) every time we receive new data, we first assign this data to one candidate subsystem based on a novel robust criterion that incorporates both the residual error and an upper bound of subsystem estimation error, and (ii) we use a randomized algorithm to update the parameter estimate of chosen candidate. We provide a theoretical guarantee on the local convergence of our algorithm. Though our theory only guarantees convergence with a good initialization, simulation results show that even with random initialization, our algorithm still has excellent performance. Finally, we show, through simulations, that our algorithm outperforms existing methods and exhibits robust performance.

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arXiv2018

Nonuniform abstractions, refinement and controller synthesis with novel BDD encodings

This paper presents a control synthesis algorithm for dynamical systems to satisfy specifications given in a fragment of linear temporal logic. It is based on an abstraction-refinement scheme with nonuniform partitions of the state space. A novel encoding of the resulting transition system is proposed that uses binary decision diagrams for efficiency. We discuss several factors affecting scalability and present some benchmark results demonstrating the effectiveness of the new encodings. These ideas are also being implemented on a publicly available prototype tool, ARCS, that we briefly introduce in the paper.

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arXiv2018

On sufficient conditions for mixed monotonicity

Mixed monotone systems form an important class of nonlinear systems that have recently received attention in the abstraction-based control design area. Slightly different definitions exist in the literature, and it remains a challenge to verify mixed monotonicity of a system in general. In this paper, we first clarify the relation between different existing definitions of mixed monotone systems, and then give two sufficient conditions for mixed monotone functions defined on Euclidean space. These sufficient conditions are more general than the ones from the existing control literature, and they suggest that mixed monotonicity is a very generic property. Some discussions are provided on the computational usefulness of the proposed sufficient conditions.

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arXiv2017

Guaranteed Model-Based Fault Detection in Cyber-Physical Systems: A Model Invalidation Approach

This paper presents a sound and complete fault detection approach for cyber-physical systems represented by hidden-mode switched affine models with time varying parametric uncertainty. The fault detection approach builds upon techniques from model invalidation. In particular, a set-membership approach is taken where the noisy input-output data is compared to the set of behaviors of a nominal model. As we show, this set-membership check can be reduced to the feasibility of a mixed-integer linear programming (MILP) problem, which can be solved efficiently by leveraging the state-of-the-art MILP solvers. In the second part of the paper, given a system model and a fault model, the concept of T-detectability is introduced. If a pair of system and fault models satisfies T-detectability property for a finite T, this allows the model invalidation algorithm to be implemented in a receding horizon manner, without compromising detection guarantees. In addition, the concept of weak-detectability is introduced which extends the proposed approach to a more expressive class of fault models that capture language constraints on the mode sequences. Finally, the efficiency of the approach is illustrated with numerical examples motivated by smart building radiant systems.

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arXiv2017

Guaranteed Fault Detection and Isolation for Switched Affine Models

This paper considers the problem of fault detection and isolation (FDI) for switched affine models. We first study the model invalidation problem and its application to guaranteed fault detection. Novel and intuitive optimization-based formulations are proposed for model invalidation and T-distinguishability problems, which we demonstrate to be computationally more efficient than an earlier formulation that required a complicated change of variables. Moreover, we introduce a distinguishability index as a measure of separation between the system and fault models, which offers a practical method for finding the smallest receding time horizon that is required for fault detection, and for finding potential design recommendations for ensuring T-distinguishability. Then, we extend our fault detection guarantees to the problem of fault isolation with multiple fault models, i.e., the identification of the type and location of faults, by introducing the concept of I-isolability. An efficient way to implement the FDI scheme is also proposed, whose run-time does not grow with the number of fault models that are considered. Moreover, we derive bounds on detection and isolation delays and present an adaptive scheme for reducing isolation delays. Finally, the effectiveness of the proposed method is illustrated using several examples, including an HVAC system model with multiple faults.

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arXiv2017

Weak Adaptive Submodularity and Group-Based Active Diagnosis with Applications to State Estimation with Persistent Sensor Faults

In this paper, we consider adaptive decision-making problems for stochastic state estimation with partial observations. First, we introduce the concept of weak adaptive submodularity, a generalization of adaptive submodularity, which has found great success in solving challenging adaptive state estimation problems. Then, for the problem of active diagnosis, i.e., discrete state estimation via active sensing, we show that an adaptive greedy policy has a near-optimal performance guarantee when the reward function possesses this property. We further show that the reward function for group-based active diagnosis, which arises in applications such as medical diagnosis and state estimation with persistent sensor faults, is also weakly adaptive submodular. Finally, in experiments of state estimation for an aircraft electrical system with persistent sensor faults, we observe that an adaptive greedy policy performs equally well as an exhaustive search.

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arXiv2016

SAT-based Distributed Reactive Control Protocol Synthesis for Boolean Networks

This paper considers the synthesis of distributed reactive control protocols for a Boolean network in a distributed manner. We start with a directed acyclic graph representing a network of Boolean subsystems and a global contract, given as an assumption-guarantee pair. Assumption captures the environment behavior, and guarantee is the requirements to be satisfied by the system. Local assumption-guarantee contracts, together with local control protocols ensuring these local contracts, are computed recursively for each subsystem based on the partial order structure induced by the directed acyclic graph. By construction, implementing these local control protocols together guarantees the satisfaction of the global assumption-guarantee contract. Moreover, local control protocol synthesis reduces to quantified satisfiability (QSAT) problems in this setting. We also discuss structural properties of the network that affect the completeness of the proposed algorithm. As an application, we show how an aircraft electric power system can be represented as a Boolean network, and we synthesize distributed control protocols from a global assumption-guarantee contract. The assumptions capture possible failures of the system components, and the guarantees capture safety requirements related to power distribution.

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arXiv2015

Synthesis of separable controlled invariant sets for modular local control design

Many correct-by-construction control synthesis methods suffer from the curse of dimensionality. Motivated by this challenge, we seek to reduce a correct-by-construction control synthesis problem to subproblems of more modest dimension. As a step towards this goal, in this paper we consider the problem of synthesizing decoupled robustly controlled invariant sets for dynamically coupled linear subsystems with state and input constraints. Our approach, which gives sufficient conditions for decoupled invariance, is based on optimization over linear matrix inequalities which are obtained using slack variable identities. We illustrate the applicability of our method on several examples, including one where we solve local control synthesis problems in a compositional manner.

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arXiv2015

Passivity Degradation In Discrete Control Implementations: An Approximate Bisimulation Approach

In this paper, we present some preliminary results for compositional analysis of heterogeneous systems containing both discrete state models and continuous systems using consistent notions of dissipativity and passivity. We study the following problem: given a physical plant model and a continuous feedback controller designed using traditional control techniques, how is the closed-loop passivity affected when the continuous controller is replaced by a discrete (i.e., symbolic) implementation within this framework? Specifically, we give quantitative results on performance degradation when the discrete control implementation is approximately bisimilar to the continuous controller, and based on them, we provide conditions that guarantee the boundedness property of the closed-loop system.

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arXiv2015

Computing finite abstractions with robustness margins via local reachable set over-approximation

This paper proposes a method to compute finite abstractions that can be used for synthesizing robust hybrid control strategies for nonlinear systems. Most existing methods for computing finite abstractions utilize some global, analytical function to provide bounds on the reachable sets of nonlinear systems, which can be conservative and lead to spurious transitions in the abstract systems. This problem is even more pronounced in the presence of imperfect measurements and modelling uncertainties, where control synthesis can easily become infeasible due to added spurious transitions. To mitigate this problem, we propose to compute finite abstractions with robustness margins by over-approximating the local reachable sets of nonlinear systems. We do so by linearizing the nonlinear dynamics into linear affine systems and keeping track of the linearization error. It is shown that this approach provides tighter approximations and several numerical examples are used to illustrate of effectiveness of the proposed methods.

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