Biblio

In this paper, we propose a compositional scheme for the construction of abstractions for networks of control systems by using the interconnection matrix and joint dissipativity-type properties of subsystems and their abstractions. In the proposed framework, the abstraction, itself a control system (possibly with a lower dimension), can be used as a substitution of the original system in the controller design process. Moreover, we provide a procedure for constructing abstractions of a class of nonlinear control systems by using the bounds on the slope of system nonlinearities. We illustrate the proposed results on a network of linear control systems by constructing its abstraction in a compositional way without requiring any condition on the number or gains of the subsystems. We use the abstraction as a substitute to synthesize a controller enforcing a certain linear temporal logic specification. This example particularly elucidates the effectiveness of dissipativity-type compositional reasoning for large-scale systems.

We consider a compositional construction of approximate abstractions of interconnected control systems. In our framework, an abstraction acts as a substitute in the controller design process and is itself a continuous control system. The abstraction is related to the concrete control system via a so-called simulation function: a Lyapunov-like function, which is used to establish a quantitative bound between the behavior of the approximate abstraction and the concrete system. In the first part of the paper, we provide a small gain type condition that facilitates the compositional construction of an abstraction of an interconnected control system together with a simulation function from the abstractions and simulation functions of the individual subsystems. In the second part of the paper, we restrict our attention to linear control system and characterize simulation functions in terms of controlled invariant, externally stabilizable subspaces. Based on those characterizations, we propose a particular scheme to construct abstractions for linear control systems. We illustrate the compositional construction of an abstraction on an interconnected system consisting of four linear subsystems. We use the abstraction as a substitute to synthesize a controller to enforce a certain linear temporal logic specification.

This paper is concerned with a compositional approach for constructing finite Markov decision processes of interconnected discrete-time stochastic control systems. The proposed approach leverages the interconnection topology and a notion of so-called stochastic storage functions describing joint dissipativity-type properties of subsystems and their abstractions. In the first part of the paper, we derive dissipativity-type compositional conditions for quantifying the error between the interconnection of stochastic control subsystems and that of their abstractions. In the second part of the paper, we propose an approach to construct finite Markov decision processes together with their corresponding stochastic storage functions for classes of discrete-time control systems satisfying some incremental passivablity property. Under this property, one can construct finite Markov decision processes by a suitable discretization of the input and state sets. Moreover, we show that for linear stochastic control systems, the aforementioned property can be readily checked by some matrix inequality. We apply our proposed results to the temperature regulation in a circular building by constructing compositionally a finite Markov decision process of a network containing 200 rooms in which the compositionality condition does not require any constraint on the number or gains of the subsystems. We employ the constructed finite Markov decision process as a substitute to synthesize policies regulating the temperature in each room for a bounded time horizon. We also illustrate the effectiveness of our results on an example of fully connected network.

This paper tackles the problem of constructing finite abstractions for formal controller synthesis with high dimensional systems. We develop a theory of abstraction for discrete time nonlinear systems that are equipped with variables acting as interfaces for other systems. Systems interact via an interconnection map which constrains the value of system interface variables. An abstraction of a high dimensional interconnected system is obtained by composing subsystem abstractions with an abstraction of the interconnection. System abstractions are modular in the sense that they can be rearranged, substituted, or reused in configurations that were unknown during the time of abstraction. Constructing the abstraction of the interconnection map can become computationally infeasible when there are many systems. We introduce intermediate variables which break the interconnection and the abstraction procedure apart into smaller problems. Examples showcase the abstraction of a 24-dimensional system through the composition of 24 individual systems, and the synthesis of a controller for a 6-dimensional system with a consensus objective.

Due to the growing performance requirements, embedded systems are increasingly more complex. Meanwhile, they are also expected to be reliable. Guaranteeing reliability on complex systems is very challenging. Consequently, there is a substantial need for designs that enable the use of unverified components such as real-time operating system (RTOS) without requiring their correctness to guarantee safety. In this work, we propose a novel approach to design a controller that enables the system to restart and remain safe during and after the restart. Complementing this controller with a switching logic allows the system to use complex, unverified controller to drive the system as long as it does not jeopardize safety. Such a design also tolerates faults that occur in the underlying software layers such as RTOS and middleware and recovers from them through system-level restarts that reinitialize the software (middleware, RTOS, and applications) from a read-only storage. Our approach is implementable using one commercial off-the-shelf (COTS) processing unit. To demonstrate the efficacy of our solution, we fully implement a controller for a 3 degree of freedom (3DOF) helicopter. We test the system by injecting various types of faults into the applications and RTOS and verify that the system remains safe.