Periodically Controlled Hybrid Systems: Verifying A Controller for An Autonomous Vehicle

This paper introduces Periodically Controlled Hybrid Automata (PCHA) for describing a class of hybrid control systems. In a PCHA, control actions occur roughly periodically while internal and input actions, may occur in the interim changing the discrete-state or the setpoint. Based on periodicity and subtangential conditions, a new sufficient condition for verifying invariance of PCHAs is presented. This technique is used in verifying safety of the planner-controller subsystem of an autonomous ground vehicle, and in deriving geometric properties of planner generated paths that can be followed safely by the controller under environmental uncertainties

Design and implimentation of a supervisory safety controller for a 3DOF helicopter

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2004.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 79-80).This research effort presents the design and implementation of a supervisory controller for a 3DOF helicopter. This safety critical system is used in undergraduate laboratories in the Department of Aeronautics and Astronautics at MIT. There already exists a framework for designing a supervisory safety controller for motions about one axis. It is based on an analytical description of the safety region in state space. However, this framework cannot be easily extended to more complicated systems such as a 3DOF helicopter. In this thesis we present a different approach which uses a real-time simulation of linearized plant dynamics with a feedback law to ensure the system's safety. We describe the development of the system model, the design and implementation of the supervisory safety controller, integration of the safety controller as part of a remote laboratory and its evaluation based on its performance during laboratory exercises.by Mariya A. Ishutkina.S.M

Safety Verification of Model Helicopter Controller using Hybrid Input/Output Automata

This paper presents an application of the Hybrid I/O Automaton modelling framework [9] to a realistic hybrid system verification problem. A supervisory pitch controller for ensuring the safety of a model helicopter system is designed and verified. The supervisor periodically observes the plant state and takes over control from the user when the latter is capable of taking the plant to an unsafe state. The design of the supervisor is limited by the actuator bandwidth, the sensor inaccuracies and the sampling rates. Safety is proved by inductively reasoning over the executions of the composed system automaton. The paper also presents a set of language constructs for specifying hybrid I/O automata

A finite state machine framework for robust analysis and control of hybrid systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2006.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 107-115).Hybrid systems, describing interactions between analog and discrete dynamics, are pervasive in engineered systems and pose unique, challenging performance verification and control synthesis problems. Existing approaches either lead to computationally intensive and sometimes undecidable problems, or make use of highly specialized discrete abstractions with questionable robustness properties. The thesis addresses some of these challenges by developing a systematic, computationally tractable approach for design and certification of systems with discrete, finite-valued actuation and sensing. This approach is inspired by classical robust control, and is based on the use of finite state machines as nominal models of the hybrid systems. The development does not assume a particular algebraic or topological structure on the signal sets. The thesis adopts an input/output view of systems, proposes specific classes of inequality constraints to describe performance objectives, and presents corresponding 'small gain' type arguments for robust performance verification. A notion of approximation that is compatible with the goal of controller synthesis is defined. An approximation architecture that is capable of handling unstable systems is also proposed.(cont.) Constructive algorithms for generating finite state machine approximations of the hybrid systems of interest, and for efficiently computing a-posteriori bounds on the approximation error are presented. Analysis of finite state machine models, which reduces to searching for an appropriate storage function, is also shown to be related to the problem of checking for the existence of negative cost cycles in a network, thus allowing for a verification algorithm with polynomial worst-case complexity. Synthesis of robust control laws is shown to reduce to solving a discrete, infinite horizon min-max problem. The resulting controllers consist of a finite state machine state observer for the hybrid system and a memoryless full state feedback switching control law. The use of this framework is demonstrated through a simple benchmark example, the problem of stabilizing a double integrator using switched gain feedback and binary sensing. Finally, some extensions to incremental performance objectives and robustness measures are presented.by Danielle C. Tarraf.Ph.D

A verification framework for hybrid systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.Includes bibliographical references (p. 193-205) and index.Combining; discrete state transitions with differential equations, Hybrid system models provide an expressive formalism for describing software systems that interact with a physical environment. Automatically checking properties, such as invariance and stability, is extremely hard for general hybrid models, and therefore current research focuses on models with restricted expressive power. In this thesis we take a complementary approach by developing proof techniques that are not necessarily automatic, but are applicable to a general class of hybrid systems. Three components of this thesis, namely, (i) semantics for ordinary and probabilistic hybrid models, (ii) methods for proving invariance, stability, and abstraction, and (iii) software tools supporting (i) and (ii), are integrated within a common mathematical framework. (i) For specifying nonprobabilistic hybrid models, we present Structured Hybrid I/O Automata (SHIOAs) which adds control theory-inspired structures, namely state models, to the existing Hybrid I/O Automata, thereby facilitating description of continuous behavior. We introduce a generalization of SHIOAs which allows both nondeterministic and stochastic transitions and develop the trace-based semantics for this framework. (ii) We present two techniques for establishing lower-bounds on average dwell time (ADT) for SHIOA models. This provides a sufficient condition of establishing stability for SHIOAs with stable state models. A new simulation-based technique which is sound for proving ADT-equivalence of SHIOAs is proposed. We develop notions of approximate implementation and corresponding proof techniques for Probabilistic I/O Automata. Specifically, a PIOA A is an E-approximate implementation of B, if every trace distribution of A is c-close to some trace distribution of B-closeness being measured by a metric on the space of trace distributions.(cont.) We present a new class of real-valued simulation functions for proving c-approximate implementations, and demonstrate their utility in quantitatively reasoning about probabilistic safety and termination. (iii) We introduce a specification language for SHIOAs and a theorem prover interface for this language. The latter consists of a translator to typed high order logic and a set of PVS-strategies that partially automate the above verification techniques within the PVS theorem prover.by Sayan Mitra.Ph.D