Many techniques for verifying invariance properties are limited to systems of moderate size. In this paper, we propose an approach based on assume-guarantee contracts and compositional reasoning for verifying invariance properties of a broad class of discrete-time and continuous-time systems consisting of interconnected components. The notion of assumeguarantee contracts makes it possible to divide responsibilities among the system components: a contract specifies an invariance property that a component must fulfill under some assumptions on the behavior of its environment (i.e. of the other components). We define weak and strong semantics of assumeguarantee contracts for both discrete-time and continuous-time systems. We then establish a certain number of results for compositional reasoning, which allow us to show that a global invariance property of the whole system is satisfied when all components satisfy their own contract. Interestingly, we show that the weak satisfaction of the contract is sufficient to deal with cascade compositions, while strong satisfaction is needed to reason about feedback composition. Specific results for systems described by differential inclusions are then developed. Throughout the paper, the main results are illustrated using simple examples.

This paper deals with the synthesis of symbolic controllers for interconnected sampled-data systems where each component has its own sampling period. A compositional approach based on continuous-time assume-guarantee contracts is used. We provide sufficient conditions guaranteeing for a sampled-data system, satisfaction of an assume-guarantee contract and completeness of trajectories. Then, compositional results can be used to reason about interconnection of multiperiodic sampled-data systems. We then show how discrete abstractions and symbolic control techniques can be applied to enforce the satisfaction of contracts and ensure completeness of trajectories. Finally, theoretical results are applied to a vehicle platooning problem on a circular road, which show the effectiveness of our approach.

This paper presents a symbolic control approach to the design of distributed safety controllers for a class of continuous-time nonlinear systems. More precisely, we consider systems made of components where each component is equipped with a sampled-data controller with its own sampling period, resulting globally in a distributed multiperiodic sampled-data system. Moreover, controllers receive partial information on the state of the other components. We propose a component-based approach to controller synthesis, which relies on the use of abstractions and continuous-time assume-guarantee contracts. The abstractions describe the dynamics of the system from the point of view of each component based on the information structure, while assume-guarantee contracts specify guarantees that a component must satisfy if assumptions on the other components are met. We show that our approach makes it possible to decompose a global safety control problem into local ones that can be solved independently. We then show how symbolic control techniques can be used to synthesize controllers that enforce the local control objectives. Illustrative applications in building automation and vehicle platooning are shown.

In this paper we address the problem of voltage stability and power sharing in DC microgrids with time-varying power demand. By exploiting the monotonicity property enjoyed by the system, and under the assumption of full observability of the bus voltages, we design a centralized, abstractionbased symbolic controller that, once refined into a controller for the original system, ensures the required specifications. Whereas load voltages cannot be measured, we propose an appropriate decomposition of the system, such that the control problem can be reformulated in terms of assume-guarantee contracts to be satisfied by the observable and unobservable components. A constructive procedure to determine suitable contracts is further investigated and the obtained results are validated with two numerical examples.

Many techniques for verifying properties of continuous-time systems are limited to systems of moderate size. In this paper, we propose an approach based on assume-guarantee contracts and compositional reasoning for verifying properties of a broad class of continuous-time systems consisting of interconnected components. The notion of assume-guarantee contracts makes it possible to divide responsibilities among the system components: a contract specifies the property that a component must fulfill under some assumptions on the behavior of its environment (i.e. of the other components). We define weak and strong semantics of assume-guarantee contracts.c We then establish a certain number of results for compositional reasoning, which allow us to show that a global assume-guarantee contract of the whole system is satisfied when all components satisfy their own contracts. We show that the weak satisfaction of the contract is sufficient to deal with interconnections described by a directed acyclic graph, while strong satisfaction is needed to reason about general interconnections containing cycles. Specific results for systems described by differential inclusions and invariance assume-guarantee contracts are then developed. Finally, we show how the proposed assume-guarantee framework can recast different versions of the small-gain theorem as a particular case. Throughout the paper, the main results are illustrated using simple examples.

Methods for computing approximately bisimilar symbolic models for incrementally stable switched systems are often based on discretization of time and space, where the value of time and space sampling parameters must be carefully chosen in order to achieve a desired precision. These approaches can result in symbolic models that have a very large number of transitions, especially when the time sampling, and thus the space sampling parameters are small. In this paper, we present an approach to the computation of symbolic models for switched systems with dwell-time constraints using multirate time sampling, where the period of symbolic transitions is a multiple of the control (i.e. switching) period. We show that all the multirate symbolic models, resulting from the proposed construction, are approximately bisimilar to the original incrementally stable switched system with the precision depending on the sampling parameters, and the sampling factor between transition and control periods. The main contribution of the paper is the explicit determination of the optimal sampling factor, which minimizes the number of transitions in the class of proposed symbolic models for a prescribed precision. Interestingly, we prove that this optimal sampling factor is mainly determined by the state space dimension and the number of modes of the switched system. Finally, an illustration of the proposed approach is shown on an example, which shows the benefit of multirate symbolic models in reducing the computational cost of abstraction-based controller synthesis.

In this paper, we investigate novel self-triggered controllers for nonlinear control systems with reachability and safety specifications. To synthesize the self-triggered controller, we leverage the notion of symbolic models, or abstractions, which represent abstracted expressions of control systems. The symbolic models will be constructed through the concepts of approximate alternating simulation relations, based on which, and by employing a reachability game, the self-triggered controller is synthesized. We illustrate the effectiveness of the proposed approach through numerical simulations.

In this paper, we consider the problem of symbolic model design for the class of incrementally stable switched systems. Contrarily to the existing results in the literature where switching is considered as periodically controlled, in this paper, we consider aperiodic time sampling resulting either from uncertain or event-based sampling mechanisms. Firstly, we establish sufficient conditions ensuring that usual symbolic models computed using periodic time-sampling remain approximately bisimilar to a switched system when the sampling period is uncertain and belongs to a given interval; estimates on the bounds of the interval are provided. Secondly, we propose a new method to compute symbolic models related by feedback refinement relations to incrementally stable switched systems, using an event-based approximation scheme. For a given precision, these event-based models are guaranteed to enable transitions of shorter duration and are likely to allow for more reactiveness in controller design. Finally, an example is proposed in order to illustrate the proposed results and simulations are performed for a Boost dc-dc converter structure.