Equivalence of switching linear systems by bisimulation

A general notion of hybrid bisimulation is proposed for the class of switching linear systems. Connections between the notions of bisimulation-based equivalence, state-space equivalence, algebraic and input–output equivalence are investigated. An algebraic characterization of hybrid bisimulation and an algorithmic procedure converging in a finite number of steps to the maximal hybrid bisimulation are derived. Hybrid state space reduction is performed by hybrid bisimulation between the hybrid system and itself. By specializing the results obtained on bisimulation, also characterizations of simulation and abstraction are derived. Connections between observability, bisimulation-based reduction and simulation-based abstraction are studied.\ud \u

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 paper, 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

A Process Algebra for Supervisory Coordination

A supervisory controller controls and coordinates the behavior of different components of a complex machine by observing their discrete behaviour. Supervisory control theory studies automated synthesis of controller models, known as supervisors, based on formal models of the machine components and a formalization of the requirements. Subsequently, code generation can be used to implement this supervisor in software, on a PLC, or embedded microprocessor. In this article, we take a closer look at the control loop that couples the supervisory controller and the machine. We model both event-based and state-based observations using process algebra and bisimulation-based semantics. The main application area of supervisory control that we consider is coordination, referred to as supervisory coordination, and we give an academic and an industrial example, discussing the process-theoretic concepts employed.Comment: In Proceedings PACO 2011, arXiv:1108.145

Towards Scalable Synthesis of Stochastic Control Systems

Formal control synthesis approaches over stochastic systems have received significant attention in the past few years, in view of their ability to provide provably correct controllers for complex logical specifications in an automated fashion. Examples of complex specifications of interest include properties expressed as formulae in linear temporal logic (LTL) or as automata on infinite strings. A general methodology to synthesize controllers for such properties resorts to symbolic abstractions of the given stochastic systems. Symbolic models are discrete abstractions of the given concrete systems with the property that a controller designed on the abstraction can be refined (or implemented) into a controller on the original system. Although the recent development of techniques for the construction of symbolic models has been quite encouraging, the general goal of formal synthesis over stochastic control systems is by no means solved. A fundamental issue with the existing techniques is the known "curse of dimensionality," which is due to the need to discretize state and input sets and that results in an exponential complexity over the number of state and input variables in the concrete system. In this work we propose a novel abstraction technique for incrementally stable stochastic control systems, which does not require state-space discretization but only input set discretization, and that can be potentially more efficient (and thus scalable) than existing approaches. We elucidate the effectiveness of the proposed approach by synthesizing a schedule for the coordination of two traffic lights under some safety and fairness requirements for a road traffic model. Further we argue that this 5-dimensional linear stochastic control system cannot be studied with existing approaches based on state-space discretization due to the very large number of generated discrete states.Comment: 22 pages, 3 figures. arXiv admin note: text overlap with arXiv:1407.273

Supervisory control of discrete event systems for bisimulation or simulation equivalence

The supervisory control of discrete event systems provides a framework for control of event-driven systems. Applications of supervisory control theory include protocol design for communication processes, control logic synthesis in manufacturing systems, and collision avoidance in human-computer interaction systems.;When designing a system at a certain level of abstraction, lower level details of the system and its specification are normally omitted to obtain higher level models that may be (non-deterministic) event-driven systems. Nondeterministic systems exhibit both branching and sequential behaviors and are captured using bisimulation equivalence (the traditional language equivalence only captures sequential behaviors). Simulation equivalence is more expressive than language equivalence but captures only the universal fragment of branching behaviors.;This dissertation presents supervisory control of discrete event systems for enforcing bisimulation equivalence or simulation equivalence with respect to given specifications. We show that in the general setting of nondeterministic systems and specifications, the complexity for bisimilarity enforcing control is doubly exponential and for similarity enforcing control remains polynomial solvable. So the choice of behavioral equivalence used depends on the application at hand and there is a trade-off between the expressivity and the complexity. We further show that the bisimilarity enforcing control problem becomes polynomially solvable when the system model is deterministic and there is complete observability of events. When the complete observability requirement is relaxed, the control existence problem remains polynomially solvable and the control synthesis problem becomes singly exponential. These complexities are similar to the ones for control under partial observation in completely deterministic setting Tsitsiklis (1989).;We introduce various notions of state-controllability (SC), state-recognizability (SR), state-achievability (SA), state-controllable-similar (SCS), state-controllability-bisimilar (SCB), and state-achievability-bisimilar (SAB) for deterministic system model. SC is a property of a controlled system under complete observation. Under partial observation, an additional property of a controlled system due to the partial observation is SR. The combined property of SC and SR is called SA. We show that properties of SC, SR and SA are not preserved under bisimulation equivalence and therefore cannot be served as a necessary condition for the existence of a bisimilarity enforcing supervisor. We introduce the notions of SCB and SAB, which are preserved under bisimulation, as part of the necessary and sufficient condition for the existence of a supervisor under complete and partial observation, respectively. We show that SC is not preserved under simulation equivalence and introduce SCS as a necessary and sufficient condition for the existence of a similarity enforcing supervisor under complete observation.;The aforementioned results use strict synchronous composition (SSC) of the system and supervisor as a mechanism of control. In SSC, it is required that individual systems synchronously execute all events. Prioritized synchronous composition (PSC) relaxed such synchronization requirements and this has been shown to enrich the control capability when the plant is non-deterministic. (The presence of nondeterminism in a plant model may cause the current state to be known with ambiguity, and allowing the flexibility of not synchronizing an event at all the candidate states that plant may have reached provides for additional benefits.) This dissertation introduces a notion of prioritized synchronous composition under mask (PSCM) to account for partial observation. We study the supervisory control when PSCM is adopted as a mechanism of interaction for both language and bisimulation equivalences. We show that the control & observation-compatibility requirements are removed of a supervisor. For control to achieve a language equivalence, the existence condition is given by achievability that is weaker than controllability and observability combined. (The weaker condition is required since we allow supervisors to be nondeterministic.) This suggests that the notion of PSCM is an appropriate generalization of PSC to account for partial observation

Controller Synthesis for Bisimulation Equivalence

Ph.DDOCTOR OF PHILOSOPH