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George Pappas

University of Pennsylvania, Electrical and Systems Engineering, Faculty Member

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George J. Pappas is the Joseph Moore Professor and Chair of the Department of Electrical and Systems Engineering at the University of Pennsylvania. He also holds a secondary appointment in the Departments of Computer and Information Sciences, and Mechanical Engineering and Applied Mechanics. He is member of the GRASP Lab and the PRECISE Center. He has previously served as the Deputy Dean for Research in the School of Engineering and Applied Science. His research focuses on control theory and in particular, hybrid systems, embedded systems, hierarchical and distributed control systems, with applications to unmanned aerial vehicles, distributed robotics, green buildings, and biomolecular networks. He is a Fellow of IEEE, and has received various awards such as the Antonio Ruberti Young Researcher Prize, the George S. Axelby Award, the O. Hugo Schuck Best Paper Award, the National Science Foundation PECASE, and the George H. Heilmeier Faculty Excellence Award.

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Ellips Masehian

California State Polytechnic University at Pomona

Kansas State University

University of Cologne

Evangelos Papadopoulos

National Technical University of Athens

Armando Marques-Guedes

UNL - New University of Lisbon

Samit Chakrabarty

University of Leeds

Sharif University of Technology

Oxford Brookes University

Visvesvaraya Technological University

Dokuz Eylül University

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Papers by George Pappas

Approximate Bisimulations for Nonlinear Dynamical Systems

The notion of exact bisimulation equivalence for nondeterministic discrete systems has recently r... more The notion of exact bisimulation equivalence for nondeterministic discrete systems has recently resulted in notions of exact bisimulation equivalence for continuous and hybrid systems. In this paper, we establish the more robust notion of approximate bisimulation equivalence for nondeterministic nonlinear systems. This is achieved by requiring that a distance between system observations starts and remains, close, in the presence of nondeterministic system evolution. We show that approximate bisimulation relations can be characterized using a class of functions called bisimulation functions. For nondeterministic nonlinear systems, we show that conditions for the existence of bisimulation functions can be expressed in terms of Lyapunov-like inequalities, which for deterministic systems can be computed using recent sum-of-squares techniques. Our framework is illustrated on a safety verification example.

Hierarchical Synthesis of Hybrid Controllers from Temporal Logic Specifications

Springer eBooks, May 30, 2007

In this paper, the problem of synthesizing a hybrid controller for a specification expressed as a... more In this paper, the problem of synthesizing a hybrid controller for a specification expressed as a temporal logic formula φ is considered. We propose a hierarchical approach which consists of three steps. First, the plant to be controlled is abstracted to a fully actuated system. Using the notion of approximate simulation relation, we design a continuous interface allowing the plant to track the trajectories of its abstraction with a guaranteed precision δ. The second step, which is also the main contribution of this paper, consists in deriving a more robust specification φ from the temporal logic formula φ such that given a trajectory satisfying φ , any other trajectory remaining within distance δ satisfies φ. Third, we design a hybrid controller for the abstraction such that all its trajectories satisfy the robust specification φ . Then, the trajectories of the plant satisfy the original specification. An application to the control of a second order model of a planar robot in a polygonal environment is considered.

Approximate Bisimulation: A Bridge Between Computer Science and Control Theory

European Journal of Control, 2011

Fifty years ago, control and computing were part of a broader system science. After a long period... more Fifty years ago, control and computing were part of a broader system science. After a long period of separate development within each discipline, embedded and hybrid systems have challenged us to re-unite the, now sophisticated theories of continuous control and discrete computing on a broader system theoretic basis. In this paper, we present a framework of system approximation that applies to both discrete and continuous systems. We define a hierarchy of approximation metrics between two systems that quantify the quality of the approximation, and capture the established notions in computer science as zero sections. The central notions in this framework are that of approximate simulation and bisimulation relations and their functional characterizations called simulation and bisimulation functions and defined by Lyapunov-type inequalities. In particular, these functions can provide computable upper-bounds on the approximation metrics by solving a static game. Our approximation framework will be illustrated by showing some of its applications in various problems such as reachability analysis of continuous systems and hybrid systems, approximation of continuous and hybrid systems by discrete systems, hierarchical control design, and simulation-based approaches to verification of continuous and hybrid systems.

Approximate Simulation Relations for Hybrid Systems

IFAC Proceedings Volumes, 2006

Approximate simulation relations have recently been introduced as a powerful tool for the approxi... more Approximate simulation relations have recently been introduced as a powerful tool for the approximation of discrete and continuous systems. In this paper, we extend this abstraction framework to hybrid systems. Using the notion of simulation functions, we develop a characterization of approximate simulation relations which can be used for hybrid systems approximation. For several classes of hybrid systems, this characterization leads to effective algorithms for the computation of approximate simulation relations. An application in the context of reachability analysis is shown.

Approximate Reduction of Dynamical Systems

The reduction of dynamical systems has a rich history, with many important applications related t... more The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction is typically performed in an "exact" manner-as is the case with mechanical systems with symmetry-which, unfortunately, limits the type of systems to which it can be applied. The goal of this paper is to consider a more general form of reduction, termed approximate reduction, in order to extend the class of systems that can be reduced. Using notions related to incremental stability, we give conditions on when a dynamical system can be projected to a lower dimensional space while providing hard bounds on the induced errors, i.e., when it is behaviorally similar to a dynamical system on a lower dimensional space. These concepts are illustrated on a series of examples.

Hierarchical Control using Approximate Simulation Relations

In this paper we present a new approach for hierarchical control based on the recent notions of a... more In this paper we present a new approach for hierarchical control based on the recent notions of approximate simulation relations and simulation functions. Given a complex system that need to be controlled, approximate simulation relations allow to characterize a simple approximation of the system, that can be used for the control design. The controller of this approximate system can be lifted to the complex system using an interface which is completely characterized by a simulation function. Then, the distance between the external trajectories of the complex system and the external trajectories of the approximation is guaranteed to remain bounded by a precision that can be evaluated from the simulation function. This makes our approach suitable for safety critical systems. We show an application to robot motion control.

MTL robust testing and verification for LPV systems

This paper deals with the robust Metric Temporal Logic (MTL) testing and verification of linear s... more This paper deals with the robust Metric Temporal Logic (MTL) testing and verification of linear systems with parametric uncertainties. This is a very general class of systems that includes not only Linear Time Invariant (LTI) systems with unknown constant parameters, but also Linear Time Varying (LTV) systems and certain classes of nonlinear systems through abstraction. The two main tools for the solution of this problem are the approximate bisimulation relations and a notion of robustness for temporal logic formulas.

Robustness of Temporal Logic Specifications

Lecture Notes in Computer Science, 2006

In this paper, we consider the robust interpretation of metric temporal logic (MTL) formulas over... more In this paper, we consider the robust interpretation of metric temporal logic (MTL) formulas over timed sequences of states. For systems whose states are equipped with nontrivial metrics, such as continuous, hybrid, or general metric transition systems, robustness is not only natural, but also a critical measure of system performance. In this paper, we define robust, multi-valued semantics for MTL formulas, which capture not only the usual Boolean satisfiability of the formula, but also topological information regarding the distance, ε, from unsatisfiability. We prove that any other timed trace which remains ε-close to the initial one also satisfies the same MTL specification with the usual Boolean semantics. We derive a computational procedure for determining an under-approximation to the robustness degree ε of the specification with respect to a given finite timed state sequence. Our approach can be used for robust system simulation and testing, as well as form the basis for simulation-based verification.

Approximate Bisimulations for Nonlinear

The notion of exact bisimulation equivalence for nondeterministic discrete systems has recently r... more The notion of exact bisimulation equivalence for nondeterministic discrete systems has recently resulted in notions of exact bisimulation equivalence for continuous and hybrid systems. In this paper, we establish the more robust notion of approximate bisimulation equivalence for nondeterministic nonlinear systems. This is achieved by requiring that a distance between system observations starts and remains, close, in the presence of nondeterministic system evolution. We show that approximate bisimulation relations can be characterized using a class of functions called bisimulation functions. For nondeterministic nonlinear systems, we show that conditions for the existence of bisimulation functions can be expressed in terms of Lyapunov-like inequalities, which for deterministic systems can be computed using recent sum-of-squares techniques. Our framework is illustrated on a safety verification example.

Approximate hierarchies of linear control systems

Recently, a hierarchical control approach based on the notion of approximate simulation relations... more Recently, a hierarchical control approach based on the notion of approximate simulation relations has been introduced. The proposed hierarchical control architecture consists of a precise model (the concrete system) of the plant to be controlled and of a rough model (the abstract system) of the plant that is used for control synthesis. In this paper, we consider the problem of computing approximate simulation relations for linear control systems. For stabilizable systems, we give an effective characterization of simulation functions (i.e. functions whose level sets define approximate simulation relations) and compute the associated interfaces which allow the refinement of the control inputs of the abstract system into control inputs of the concrete system. Then, we propose a procedure for the computation of abstractions of linear control systems that can be used in our hierachical control framework. Finally, as an example of application, we use our approach to synthesize hierarchical controllers of a class of high-order systems.

Model Checking LTL over Controllable Linear Systems Is Decidable

Lecture Notes in Computer Science, 2003

The use of algorithmic verification and synthesis tools for hybrid systems is currently limited t... more The use of algorithmic verification and synthesis tools for hybrid systems is currently limited to systems exhibiting simple continuous dynamics such as timed automata or rectangular hybrid systems. In this paper we enlarge the class of systems amenable to algorithmic analysis and synthesis by showing decidability of model checking Linear Temporal Logic (LTL) formulas over discrete time, controllable, linear systems. This result follows from the construction of a language equivalent, finite abstraction of a control system based on a set of finite observations which correspond to the atomic propositions appearing in a given LTL formula. Furthermore, the size of this abstraction is shown to be polynomial in the dimension of the control system and the number of observations. These results open the doors for verification and synthesis of continuous and hybrid control systems from LTL specifications.

Where's Waldo? Sensor-Based Temporal Logic Motion Planning

Proceedings, Apr 1, 2007

Given a robot model and a class of admissible environments, this paper provides a framework for a... more Given a robot model and a class of admissible environments, this paper provides a framework for automatically and verifiably composing controllers that satisfy high level task specifications expressed in suitable temporal logics. The desired task specifications can express complex robot behaviors such as search and rescue, coverage, and collision avoidance. In addition, our framework explicitly captures sensor specifications that depend on the environment with which the robot is interacting, resulting in a novel paradigm for sensor-based temporal logic motion planning. As one robot is part of the environment of another robot, our sensor-based framework very naturally captures multi-robot specifications. Our computational approach is based on first creating discrete controllers satisfying so-called General Reactivity(1) formulas. If feasible, the discrete controller is then used in order to guide the sensor-based composition of continuous controllers resulting in a hybrid controller satisfying the high level specification, but only if the environment is admissible.

Discrete abstractions of hybrid systems

Proceedings of the IEEE, Jul 1, 2000

A hybrid system is a dynamical system with both discrete and continuous state changes. For analys... more A hybrid system is a dynamical system with both discrete and continuous state changes. For analysis purposes, it is often useful to abstract a system in a way that preserves the properties being analyzed while hiding the details that are of no interest. We show that interesting classes of hybrid systems can be abstracted to purely discrete systems while preserving all properties that are definable in temporal logic. The classes that permit discrete abstractions fall into two categories. Either the continuous dynamics must be restricted, as is the case for timed and rectangular hybrid systems, or the discrete dynamics must be restricted, as is the case for o-minimal hybrid systems. In this paper, we survey and unify results from both areas.

Differentially Private Filtering

arXiv (Cornell University), Jul 18, 2012

Hybrid control in air traffic management systems

In a new collaborative project involving the

A next generation architecture for air traffic management systems

Differential privacy in control and network systems

As intelligent automation and large-scale distributed monitoring and control systems become more ... more As intelligent automation and large-scale distributed monitoring and control systems become more widespread, concerns are growing about the way these systems collect and make use of privacy-sensitive data obtained from individuals. This tutorial paper gives a systems and control perspective on the topic of privacy preserving data analysis, with a particular emphasis on the processing of dynamic data as well as data exchanged in networks. Specifically, we consider mechanisms enforcing differential privacy, a state-ofthe-art definition of privacy initially introduced to analyze large, static datasets, and whose guarantees hold against adversaries with arbitrary side information. We discuss in particular how to perform tasks such as signal estimation, consensus and distributed optimization between multiple agents under differential privacy constraints.

IEEE Robotics & Automation Magazine, Mar 1, 2008

Semidecidable controller synthesis for classes of linear hybrid systems

A problem of great interest in the control of hybrid systems is the design of least restrictive c... more A problem of great interest in the control of hybrid systems is the design of least restrictive controllers for reachability specifications. Controller design typically uses game theoretic methods to compute the region of the state space for which there exists a control such that for all disturbances, an unsafe set is not reached. In general, the computation of the controllers requires the steady state solution of a Hamilton-Jacobi partial differential equation which is very difficult to compute, if it exists. In this paper, we show that for special classes of hybrid systems where the continuous vector fields are linear, the controller synthesis problem is semi-decidable: There exists a computational algorithm which, if it terminates in a finite number of steps, will exactly compute the least restrictive controller. This result is achieved by a very interesting interaction of results from mathematical logic and o p timal control.

Decidable Controller Synthesis for Classes of Linear Systems

Lecture Notes in Computer Science, 2000

A problem of great interest in the control of hybrid systems is the design of least restrictive c... more A problem of great interest in the control of hybrid systems is the design of least restrictive controllers for reachability specifications. Controller design typically uses game theoretic methods which compute the region of the state space for which there exists a control such that for all disturbances, an unsafe set is not reached. In general, the computation of the controllers requires the steady state solution of a Hamilton-Jacobi-Isaacs partial differential equation which is very difficult to compute, if it exists. In this paper, we show that for classes of linear systems, the controller synthesis problem is decidable: There exists a computational algorithm which, after a finite number of steps, will exactly compute the least restrictive controller. This result is achieved by a very interesting interaction of results from mathematical logic and optimal control.

Approximate Bisimulations for Nonlinear Dynamical Systems

The notion of exact bisimulation equivalence for nondeterministic discrete systems has recently r... more The notion of exact bisimulation equivalence for nondeterministic discrete systems has recently resulted in notions of exact bisimulation equivalence for continuous and hybrid systems. In this paper, we establish the more robust notion of approximate bisimulation equivalence for nondeterministic nonlinear systems. This is achieved by requiring that a distance between system observations starts and remains, close, in the presence of nondeterministic system evolution. We show that approximate bisimulation relations can be characterized using a class of functions called bisimulation functions. For nondeterministic nonlinear systems, we show that conditions for the existence of bisimulation functions can be expressed in terms of Lyapunov-like inequalities, which for deterministic systems can be computed using recent sum-of-squares techniques. Our framework is illustrated on a safety verification example.

Hierarchical Synthesis of Hybrid Controllers from Temporal Logic Specifications

Springer eBooks, May 30, 2007

In this paper, the problem of synthesizing a hybrid controller for a specification expressed as a... more In this paper, the problem of synthesizing a hybrid controller for a specification expressed as a temporal logic formula φ is considered. We propose a hierarchical approach which consists of three steps. First, the plant to be controlled is abstracted to a fully actuated system. Using the notion of approximate simulation relation, we design a continuous interface allowing the plant to track the trajectories of its abstraction with a guaranteed precision δ. The second step, which is also the main contribution of this paper, consists in deriving a more robust specification φ from the temporal logic formula φ such that given a trajectory satisfying φ , any other trajectory remaining within distance δ satisfies φ. Third, we design a hybrid controller for the abstraction such that all its trajectories satisfy the robust specification φ . Then, the trajectories of the plant satisfy the original specification. An application to the control of a second order model of a planar robot in a polygonal environment is considered.

Approximate Bisimulation: A Bridge Between Computer Science and Control Theory

European Journal of Control, 2011

Fifty years ago, control and computing were part of a broader system science. After a long period... more Fifty years ago, control and computing were part of a broader system science. After a long period of separate development within each discipline, embedded and hybrid systems have challenged us to re-unite the, now sophisticated theories of continuous control and discrete computing on a broader system theoretic basis. In this paper, we present a framework of system approximation that applies to both discrete and continuous systems. We define a hierarchy of approximation metrics between two systems that quantify the quality of the approximation, and capture the established notions in computer science as zero sections. The central notions in this framework are that of approximate simulation and bisimulation relations and their functional characterizations called simulation and bisimulation functions and defined by Lyapunov-type inequalities. In particular, these functions can provide computable upper-bounds on the approximation metrics by solving a static game. Our approximation framework will be illustrated by showing some of its applications in various problems such as reachability analysis of continuous systems and hybrid systems, approximation of continuous and hybrid systems by discrete systems, hierarchical control design, and simulation-based approaches to verification of continuous and hybrid systems.

Approximate Simulation Relations for Hybrid Systems

IFAC Proceedings Volumes, 2006

Approximate simulation relations have recently been introduced as a powerful tool for the approxi... more Approximate simulation relations have recently been introduced as a powerful tool for the approximation of discrete and continuous systems. In this paper, we extend this abstraction framework to hybrid systems. Using the notion of simulation functions, we develop a characterization of approximate simulation relations which can be used for hybrid systems approximation. For several classes of hybrid systems, this characterization leads to effective algorithms for the computation of approximate simulation relations. An application in the context of reachability analysis is shown.

Approximate Reduction of Dynamical Systems

The reduction of dynamical systems has a rich history, with many important applications related t... more The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction is typically performed in an "exact" manner-as is the case with mechanical systems with symmetry-which, unfortunately, limits the type of systems to which it can be applied. The goal of this paper is to consider a more general form of reduction, termed approximate reduction, in order to extend the class of systems that can be reduced. Using notions related to incremental stability, we give conditions on when a dynamical system can be projected to a lower dimensional space while providing hard bounds on the induced errors, i.e., when it is behaviorally similar to a dynamical system on a lower dimensional space. These concepts are illustrated on a series of examples.

Hierarchical Control using Approximate Simulation Relations

In this paper we present a new approach for hierarchical control based on the recent notions of a... more In this paper we present a new approach for hierarchical control based on the recent notions of approximate simulation relations and simulation functions. Given a complex system that need to be controlled, approximate simulation relations allow to characterize a simple approximation of the system, that can be used for the control design. The controller of this approximate system can be lifted to the complex system using an interface which is completely characterized by a simulation function. Then, the distance between the external trajectories of the complex system and the external trajectories of the approximation is guaranteed to remain bounded by a precision that can be evaluated from the simulation function. This makes our approach suitable for safety critical systems. We show an application to robot motion control.

MTL robust testing and verification for LPV systems

This paper deals with the robust Metric Temporal Logic (MTL) testing and verification of linear s... more This paper deals with the robust Metric Temporal Logic (MTL) testing and verification of linear systems with parametric uncertainties. This is a very general class of systems that includes not only Linear Time Invariant (LTI) systems with unknown constant parameters, but also Linear Time Varying (LTV) systems and certain classes of nonlinear systems through abstraction. The two main tools for the solution of this problem are the approximate bisimulation relations and a notion of robustness for temporal logic formulas.

Robustness of Temporal Logic Specifications

Lecture Notes in Computer Science, 2006

In this paper, we consider the robust interpretation of metric temporal logic (MTL) formulas over... more In this paper, we consider the robust interpretation of metric temporal logic (MTL) formulas over timed sequences of states. For systems whose states are equipped with nontrivial metrics, such as continuous, hybrid, or general metric transition systems, robustness is not only natural, but also a critical measure of system performance. In this paper, we define robust, multi-valued semantics for MTL formulas, which capture not only the usual Boolean satisfiability of the formula, but also topological information regarding the distance, ε, from unsatisfiability. We prove that any other timed trace which remains ε-close to the initial one also satisfies the same MTL specification with the usual Boolean semantics. We derive a computational procedure for determining an under-approximation to the robustness degree ε of the specification with respect to a given finite timed state sequence. Our approach can be used for robust system simulation and testing, as well as form the basis for simulation-based verification.

Approximate Bisimulations for Nonlinear

The notion of exact bisimulation equivalence for nondeterministic discrete systems has recently r... more The notion of exact bisimulation equivalence for nondeterministic discrete systems has recently resulted in notions of exact bisimulation equivalence for continuous and hybrid systems. In this paper, we establish the more robust notion of approximate bisimulation equivalence for nondeterministic nonlinear systems. This is achieved by requiring that a distance between system observations starts and remains, close, in the presence of nondeterministic system evolution. We show that approximate bisimulation relations can be characterized using a class of functions called bisimulation functions. For nondeterministic nonlinear systems, we show that conditions for the existence of bisimulation functions can be expressed in terms of Lyapunov-like inequalities, which for deterministic systems can be computed using recent sum-of-squares techniques. Our framework is illustrated on a safety verification example.

Approximate hierarchies of linear control systems

Recently, a hierarchical control approach based on the notion of approximate simulation relations... more Recently, a hierarchical control approach based on the notion of approximate simulation relations has been introduced. The proposed hierarchical control architecture consists of a precise model (the concrete system) of the plant to be controlled and of a rough model (the abstract system) of the plant that is used for control synthesis. In this paper, we consider the problem of computing approximate simulation relations for linear control systems. For stabilizable systems, we give an effective characterization of simulation functions (i.e. functions whose level sets define approximate simulation relations) and compute the associated interfaces which allow the refinement of the control inputs of the abstract system into control inputs of the concrete system. Then, we propose a procedure for the computation of abstractions of linear control systems that can be used in our hierachical control framework. Finally, as an example of application, we use our approach to synthesize hierarchical controllers of a class of high-order systems.

Model Checking LTL over Controllable Linear Systems Is Decidable

Lecture Notes in Computer Science, 2003

The use of algorithmic verification and synthesis tools for hybrid systems is currently limited t... more The use of algorithmic verification and synthesis tools for hybrid systems is currently limited to systems exhibiting simple continuous dynamics such as timed automata or rectangular hybrid systems. In this paper we enlarge the class of systems amenable to algorithmic analysis and synthesis by showing decidability of model checking Linear Temporal Logic (LTL) formulas over discrete time, controllable, linear systems. This result follows from the construction of a language equivalent, finite abstraction of a control system based on a set of finite observations which correspond to the atomic propositions appearing in a given LTL formula. Furthermore, the size of this abstraction is shown to be polynomial in the dimension of the control system and the number of observations. These results open the doors for verification and synthesis of continuous and hybrid control systems from LTL specifications.

Where's Waldo? Sensor-Based Temporal Logic Motion Planning

Proceedings, Apr 1, 2007

Given a robot model and a class of admissible environments, this paper provides a framework for a... more Given a robot model and a class of admissible environments, this paper provides a framework for automatically and verifiably composing controllers that satisfy high level task specifications expressed in suitable temporal logics. The desired task specifications can express complex robot behaviors such as search and rescue, coverage, and collision avoidance. In addition, our framework explicitly captures sensor specifications that depend on the environment with which the robot is interacting, resulting in a novel paradigm for sensor-based temporal logic motion planning. As one robot is part of the environment of another robot, our sensor-based framework very naturally captures multi-robot specifications. Our computational approach is based on first creating discrete controllers satisfying so-called General Reactivity(1) formulas. If feasible, the discrete controller is then used in order to guide the sensor-based composition of continuous controllers resulting in a hybrid controller satisfying the high level specification, but only if the environment is admissible.

Discrete abstractions of hybrid systems

Proceedings of the IEEE, Jul 1, 2000

A hybrid system is a dynamical system with both discrete and continuous state changes. For analys... more A hybrid system is a dynamical system with both discrete and continuous state changes. For analysis purposes, it is often useful to abstract a system in a way that preserves the properties being analyzed while hiding the details that are of no interest. We show that interesting classes of hybrid systems can be abstracted to purely discrete systems while preserving all properties that are definable in temporal logic. The classes that permit discrete abstractions fall into two categories. Either the continuous dynamics must be restricted, as is the case for timed and rectangular hybrid systems, or the discrete dynamics must be restricted, as is the case for o-minimal hybrid systems. In this paper, we survey and unify results from both areas.

Differentially Private Filtering

arXiv (Cornell University), Jul 18, 2012

Hybrid control in air traffic management systems

In a new collaborative project involving the

A next generation architecture for air traffic management systems

Differential privacy in control and network systems

As intelligent automation and large-scale distributed monitoring and control systems become more ... more As intelligent automation and large-scale distributed monitoring and control systems become more widespread, concerns are growing about the way these systems collect and make use of privacy-sensitive data obtained from individuals. This tutorial paper gives a systems and control perspective on the topic of privacy preserving data analysis, with a particular emphasis on the processing of dynamic data as well as data exchanged in networks. Specifically, we consider mechanisms enforcing differential privacy, a state-ofthe-art definition of privacy initially introduced to analyze large, static datasets, and whose guarantees hold against adversaries with arbitrary side information. We discuss in particular how to perform tasks such as signal estimation, consensus and distributed optimization between multiple agents under differential privacy constraints.

IEEE Robotics & Automation Magazine, Mar 1, 2008

Semidecidable controller synthesis for classes of linear hybrid systems

A problem of great interest in the control of hybrid systems is the design of least restrictive c... more A problem of great interest in the control of hybrid systems is the design of least restrictive controllers for reachability specifications. Controller design typically uses game theoretic methods to compute the region of the state space for which there exists a control such that for all disturbances, an unsafe set is not reached. In general, the computation of the controllers requires the steady state solution of a Hamilton-Jacobi partial differential equation which is very difficult to compute, if it exists. In this paper, we show that for special classes of hybrid systems where the continuous vector fields are linear, the controller synthesis problem is semi-decidable: There exists a computational algorithm which, if it terminates in a finite number of steps, will exactly compute the least restrictive controller. This result is achieved by a very interesting interaction of results from mathematical logic and o p timal control.

Decidable Controller Synthesis for Classes of Linear Systems

Lecture Notes in Computer Science, 2000

A problem of great interest in the control of hybrid systems is the design of least restrictive c... more A problem of great interest in the control of hybrid systems is the design of least restrictive controllers for reachability specifications. Controller design typically uses game theoretic methods which compute the region of the state space for which there exists a control such that for all disturbances, an unsafe set is not reached. In general, the computation of the controllers requires the steady state solution of a Hamilton-Jacobi-Isaacs partial differential equation which is very difficult to compute, if it exists. In this paper, we show that for classes of linear systems, the controller synthesis problem is decidable: There exists a computational algorithm which, after a finite number of steps, will exactly compute the least restrictive controller. This result is achieved by a very interesting interaction of results from mathematical logic and optimal control.