arXiv subjects

Pushpak Jagtap

Publications and source records attributed to Pushpak Jagtap.

86 records · Page 5Linked to original sources

arXiv2022

Distributed Consensus of Stochastic Multi-agent Systems with Prescribed Performance Constraints

This paper focuses on the problem of distributed consensus control of multi-agent systems while considering two main practical concerns (i) stochastic noise in the agent dynamics and (ii) predefined performance constraints over evolutions of multi-agent systems. In particular, we consider that each agent is driven by a stochastic differential equation with state-dependent noise which makes the considered problem more challenging compared to non-stochastic agents. The work provides sufficient conditions under which the proposed timevarying distributed control laws ensure consensus in expectation and almost sure consensus of stochastic multi-agent systems while satisfying prescribed performance constraints over evolutions of the systems in the sense of the qth moment. Finally, we demonstrate the effectiveness of the proposed results with a numerical example.

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arXiv2021

Verification of Switched Stochastic Systems via Barrier Certificates

The paper presents a methodology for temporal logic verification of continuous-time switched stochastic systems. Our goal is to find the lower bound on the probability that a complex temporal property is satisfied over a finite time horizon. The required temporal properties of the system are expressed using a fragment of linear temporal logic, called safe-LTL with respect to finite traces. Our approach combines automata-based verification and the use of barrier certificates. It relies on decomposing the automaton associated with the negation of specification into a sequence of simpler reachability tasks and compute upper bounds for these reachability probabilities by means of common or multiple barrier certificates. Theoretical results are illustrated by applying a counter-example guided inductive synthesis framework to find barrier certificates.

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arXiv2021

Synthesis of Partially Observed Jump-Diffusion Systems via Control Barrier Functions

In this paper, we study formal synthesis of control policies for partially observed jump-diffusion systems against complex logic specifications. Given a state estimator, we utilize a discretization-free approach for formal synthesis of control policies by using a notation of control barrier functions without requiring any knowledge of the estimation accuracy. Our goal is to synthesize an offline control policy providing (potentially maximizing) a lower bound on the probability that the trajectories of the partially observed jump-diffusion system satisfy some complex specifications expressed by deterministic finite automata. Finally, we illustrate the effectiveness of the proposed results by synthesizing a policy for a jet engine example.

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arXiv2020

Compositional Abstraction-based Synthesis for Interconnected Systems: An Approximate Composition Approach

In this paper, we focus on mitigating the computational complexity in abstraction-based controller synthesis for interconnected control systems. To do so, we provide a compositional framework for the construction of abstractions for interconnected systems and a bottom-up controller synthesis scheme. In particular, we propose a notion of approximate composition which makes it possible to compute an abstraction of the global interconnected system from the abstractions (possibly of different types) of its components. Finally, by leveraging our notion of approximate composition, we propose a bottom-up approach for the synthesis of controllers enforcing decomposable safety specifications. The effectiveness of the proposed results is demonstrated using two case studies (viz., DC microgrid and traffic network) by comparing them with different abstraction and controller synthesis schemes.

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arXiv2020

Control Barrier Functions for Unknown Nonlinear Systems using Gaussian Processes

This paper focuses on the controller synthesis for unknown, nonlinear systems while ensuring safety constraints. Our approach consists of two steps, a learning step that uses Gaussian processes and a controller synthesis step that is based on control barrier functions. In the learning step, we use a data-driven approach utilizing Gaussian processes to learn the unknown control affine nonlinear dynamics together with a statistical bound on the accuracy of the learned model. In the second controller synthesis steps, we develop a systematic approach to compute control barrier functions that explicitly take into consideration the uncertainty of the learned model. The control barrier function not only results in a safe controller by construction but also provides a rigorous lower bound on the probability of satisfaction of the safety specification. Finally, we illustrate the effectiveness of the proposed results by synthesizing a safety controller for a jet engine example.

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arXiv2020

Formal Synthesis of Stochastic Systems via Control Barrier Certificates

This paper focuses on synthesizing control policies for discrete-time stochastic control systems together with a lower bound on the probability that the systems satisfy the complex temporal properties. The desired properties of the system are expressed as linear temporal logic (LTL) specifications over finite traces. In particular, our approach decomposes the given specification into simpler reachability tasks based on its automata representation. We then propose the use of so-called \emph{control barrier certificate} to solve those simpler reachability tasks along with computing the corresponding controllers and probability bounds. Finally, we combine those controllers to obtain a hybrid control policy solving the considered problem. Under some assumptions, we also provide two systematic approaches for uncountable and finite input sets to search for control barrier certificates. We demonstrate the effectiveness of the proposed approach on a room temperature control and lane-keeping of a vehicle modeled as a four-dimensional single-track kinematic model. We compare our results with the discretization-based methods in the literature.

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arXiv2020

Numerical Estimation of Invariance Entropy for Nonlinear Control Systems

For a closed-loop control system with a digital channel between the sensor and the controller, the notion of invariance entropy quantifies the smallest average rate of information transmission above which a given compact subset of the state space can be made invariant. In this work, we present for the first time an algorithm to numerically compute upper bounds of invariance entropy. With three examples, for which the exact value of the invariance entropy is known to us or can be estimated by other means, we demonstrate that the upper bound obtained by our algorithm is of the same order of magnitude as the actual value. Additionally, our algorithm provides a static coder-controller scheme corresponding to the obtained data-rate bound.

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arXiv2020

dtControl: Decision Tree Learning Algorithms for Controller Representation

Decision tree learning is a popular classification technique most commonly used in machine learning applications. Recent work has shown that decision trees can be used to represent provably-correct controllers concisely. Compared to representations using lookup tables or binary decision diagrams, decision trees are smaller and more explainable. We present dtControl, an easily extensible tool for representing memoryless controllers as decision trees. We give a comprehensive evaluation of various decision tree learning algorithms applied to 10 case studies arising out of correct-by-construction controller synthesis. These algorithms include two new techniques, one for using arbitrary linear binary classifiers in the decision tree learning, and one novel approach for determinizing controllers during the decision tree construction. In particular the latter turns out to be extremely efficient, yielding decision trees with a single-digit number of decision nodes on 5 of the case studies.

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arXiv2020

Compositional Construction of Control Barrier Functions for Interconnected Control Systems

In this paper, we provide a compositional framework for synthesizing hybrid controllers for interconnected discrete-time control systems enforcing specifications expressed by co-Buchi automata. In particular, we first decompose the given specification to simpler reachability tasks based on automata representing the complements of original co-Buchi automata. Then, we provide a systematic approach to solve those simpler reachability tasks by computing corresponding control barrier functions. We show that such control barrier functions can be constructed compositionally by assuming some small-gain type conditions and composing so-called local control barrier functions computed for subsystems. We provide two systematic techniques to search for local control barrier functions for subsystems based on the sum-of-squares optimization program and counter-example guided inductive synthesis approach. Finally, we illustrate the effectiveness of our results through two large-scale case studies.

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arXiv2019

Symbolic Models for Retarded Jump-Diffusion Systems

In this paper, we provide for the first time an automated, correct-by-construction, controller synthesis scheme for a class of infinite dimensional stochastic systems, namely, retarded jump-diffusion systems. First, we construct finite abstractions approximately bisimilar to non-probabilistic retarded systems corresponding to the original systems having some stability property, namely, incremental input-to-state stability. Then, we provide a result on quantifying the distance between output trajectory of the obtained finite abstraction and that of the original retarded jump-diffusion system in a probabilistic setting. Using the proposed result, one can refine the control policy synthesized using finite abstractions to the original systems while providing guarantee on the probability of satisfaction of high-level requirements. Moreover, we provide sufficient conditions for the proposed notion of incremental stability in terms of the existence of incremental Lyapunov functions which reduce to some matrix inequalities for the linear systems. Finally, the effectiveness of the proposed results is illustrated by synthesizing a controller regulating the temperatures in a ten-room building modelled as a delayed jump-diffusion system.

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arXiv2018

Software Fault Tolerance for Cyber-Physical Systems via Full System Restart

The paper addresses the issue of reliability of complex embedded control systems in the safety-critical environment. In this paper, we propose a novel approach to design controller that (i) guarantees the safety of nonlinear physical systems, (ii) enables safe system restart during runtime, and (iii) allows the use of complex, unverified controllers (e.g., neural networks) that drive the physical systems towards complex specifications. We use abstraction-based controller synthesis approach to design a formally verified controller that provides application and system-level fault tolerance along with safety guarantee. Moreover, our approach is implementable using commercial-off-the-shelf (COTS) processing unit. To demonstrate the efficacy of our solution and to verify the safety of the system under various types of faults injected in applications and in the underlying real-time operating system (RTOS), we implemented the proposed controller for the inverted pendulum and three degree-of-freedom (3-DOF) helicopter.

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arXiv2018

Complex Laplacian based Distributed Control for Multi-Agent Network

The work done in this paper, proposes a complex Laplacian-based distributed control scheme for convergence in the multi-agent network. The proposed scheme has been designated as cascade formulation. The proposed technique exploits the traditional method of organizing large scattered networks into smaller interconnected clusters to optimize information flow within the network. The complex Laplacian-based approach results in a hierarchical structure, with formation of a meta-cluster leading other clusters in the network. The proposed formulation enables flexibility to constrain the eigen spectra of the overall closed-loop dynamics, ensuring desired convergence rate and control input intensity. The sufficient conditions ensuring globally stable formation for proposed formulation are also asserted. Robustness of the proposed formulation to uncertainties like loss in communication links and actuator failure has also been discussed. The effectiveness of the proposed approach is illustrated by simulating a finitely large network of thirty vehicles.

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arXiv2018

Temporal Logic Verification of Stochastic Systems Using Barrier Certificates

This paper presents a methodology for temporal logic verification of discrete-time stochastic systems. Our goal is to find a lower bound on the probability that a complex temporal property is satisfied by finite traces of the system. Desired temporal properties of the system are expressed using a fragment of linear temporal logic, called safe LTL over finite traces. We propose to use barrier certificates for computations of such lower bounds, which is computationally much more efficient than the existing discretization-based approaches. The new approach is discretization-free and does not suffer from the curse of dimensionality caused by discretizing state sets. The proposed approach relies on decomposing the negation of the specification into a union of sequential reachabilities and then using barrier certificates to compute upper bounds for these reachability probabilities. We demonstrate the effectiveness of the proposed approach on case studies with linear and polynomial dynamics.

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arXiv2017

Backstepping Design for Incremental Stability of Stochastic Hamiltonian Systems with Jumps

Incremental stability is a property of dynamical systems ensuring the uniform asymptotic stability of each trajectory rather than a fixed equilibrium point or trajectory. Here, we introduce a notion of incremental stability for stochastic control systems and provide its description in terms of existence of a notion of so-called incremental Lyapunov functions. Moreover, we provide a backstepping controller design scheme providing controllers along with corresponding incremental Lyapunov functions rendering a class of stochastic control systems, namely, stochastic Hamiltonian systems with jumps, incrementally stable. To illustrate the effectiveness of the proposed approach, we design a controller making a spring pendulum system in a noisy environment incrementally stable.

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