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Symbolic models are becoming more and more popular in the research community working on hybrid systems because they provide a systematic approach to enforce logic specifications on purely continuous or hybrid systems while fulfilling the constraints at the hardware/software implementation level. This paper contributes to this research line and proposes symbolic models approximating possibly unstable time-delay systems with quantized measurements of the outputs. An application of the proposed results to the glucose control problems for the Artificial Pancreas is discussed in the paper.

There is an increasing demand for controller design techniques capable of addressing the complex requirements of todays embedded applications. This demand has sparked the interest in symbolic control where lower complexity models of control systems are used to cater for complex specifications given by temporal logics, regular languages, or automata. These specification mechanisms can be regarded as qualitative since they divide the trajectories of the plant into bad trajectories (those that need to be avoided) and good trajectories. However, many applications require also the optimization of quantitative measures of the trajectories retained by the controller, as specified by a cost or utility function. As a first step towards the synthesis of controllers reconciling both qualitative and quantitative specifications, we investigate in this paper the use of symbolic models for time-optimal controller synthesis. We consider systems related by approximate (alternating) simulation relations and show how such relations enable the transfer of time-optimality information between the systems. We then use this insight to synthesize approximately time-optimal controllers for a control system by working with a lower complexity symbolic model. The resulting approximately time-optimal controllers are equipped with upper and lower bounds for the time to reach a target, describing the quality of the controller. The results described in this paper were implemented in the Matlab Toolbox Pessoa which we used to workout several illustrative examples reported in this paper., 17 pages, 2 figures, journal

International audience; Attractivity specifications consist in driving the state of a system to a target region and to keep it in that region afterwards. In this paper, we develop an approach to controller synthesis for attractivity specifications based on iterative refinements of symbolic abstractions. We compute iteratively sequences of least-violating attractivity controllers and of associated attractors. The current controller is used to restrict possible control actions at the next iteration where a new abstraction is used following a local refinement applied inside the current attractor. The approach results in a nested sequence of attractors which are closer to the target region at each iteration. To illustrate the effectiveness of our approach, we show an application to a marine vessel system.

International audience; Although Model Predictive Control (MPC) has proven its e ciency in the process operation and it is known for its high performance, it also su ers from design limitation. One of the fundamental issues for such an optimization-based technique is the di culty to guarantee recursive feasibility in the absence of terminal constraints, or alternatively, the complexity of design when a certain basin of a raction or a controlled invariant set needs to be certi ed for the closed loop in the most general nonlinear se ing. Based on symbolic control techniques, this paper proposes a simple and guaranteed solution for such problems. As a main result, a Symbolically guided Model Predictive Control scheme is developed. is controller is an improved version of the generic MPC approach such that the recursive feasibility is guaranteed through appending time-varying terminal constraints, carefully designed using the symbolic control approach, to the optimization problem of the original MPC formulation.

International audience; In this paper, we provide a lazy control synthesis algorithm for monotone transition systems and directed safety specifications. Two classes of monotone transition systems are presented: state monotone transition systems and input-state monotone transition systems. For the first class of systems, a partial order is defined only on the state space, for the second, the input space is ordered as well. The introduced lazy synthesis approach is based on the efficient computation of predecessors. It benefits not only from a monotone property of transition systems but also from the ordered structure of the state (input) space and the fact, that directed safety specifications are considered. To enrich the class of the considered specifications, we also present an incremental controller synthesis framework, which allows us to deal with intersections of upper and lower-closed safety requirements. We then compare the proposed approach with the classical safety synthesis algorithm and illustrate the advantages, in terms of run-time and memory efficiency, on an adaptive cruise control problem.

International audience; In this paper, we introduce an approach for the data-driven abstraction of monotone dynamical systems. First, we introduce a set-valued simulating map, which over-approximates the dynamics of an unknown monotone system, using only a set of transitions generated by it. We establish the minimality of the introduced simulating map. Then, we show that the system, with this map as its transition relation, is equivalent (in the sense of alternating bisimulation) to a finite-state system. This equivalence enables the use of well-established symbolic control techniques to synthesize controllers. We show the effectiveness of the approach on a safety controller synthesis problem.

International audience; In this paper, we present an abstraction-based approach to robust safety controller synthesis for continuous-time nonlinear systems. To reduce the computational complexity associated with symbolic control approaches, we develop a lazy controller synthesis algorithm, which iteratively explores states on the boundary of controllable domain while avoiding exploration of internal states, supposing that they are safely controllable a priory. A closedloop safety controller for the original problem is then defined as follows: we use the abstract controller to push the system from a boundary state back towards the interior, while for inner states, any admissible input is valid. We then compare the proposed approach with the classical safety synthesis algorithm and illustrate the advantages, in terms of run-time and memory efficiency, on an adaptive cruise control problem.

International audience; 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.

International audience; Abstraction-based synthesis techniques are limited to systems with moderate size. Thus to contribute towards scalability of these techniques, in this paper we propose a compositional abstraction-based synthesis for cascade interconnected discrete-time control systems. Given a cascade interconnection of several components, we provide results on the compositional construction of finite abstractions based on the notion of approximate cascade composition. Then, we provide a compositional controller synthesis for cascade interconnection. Finally, we demonstrate the applicability and effectiveness of the results using a numerical example and compare it with different abstraction and controller synthesis schemes.

International audience; 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.

This paper presents a compositional approach to specification-guided abstraction refinement for control synthesis of a nonlinear system associated with a method to over-approximate its reachable sets. Given an initial coarse partition of the state space, the control specification is given as a sequence of the cells of this partition to visit at each sampling time. The dynamics are decomposed into subsystems where some states and inputs are not observed, some states are observed but not controlled and where assume-guarantee obligations are used on the uncontrolled states of each subsystem. A finite abstraction is created for each subsystem through a refinement procedure starting from a coarse partition of the state space, then proceeding backwards on the specification sequence to iteratively split the elements of the partition whose coarseness prevents the satisfaction of the specification. Each refined abstraction is associated with a controller and it is proved that combining these local controllers can enforce the specification on the original system. The efficiency of the proposed approach compared to other abstraction methods is illustrated in a numerical example. QC 20171213

The problem of efficiently steering dynamical systems by generating input plans is considered. Plans are considered which consist of finite-length words constructed on an alphabet of input symbols, which could be, e.g., transmitted through a limited capacity channel to a remote system, where they can be decoded in suitable control actions. Efficiency is considered in terms of the computational complexity of plans, and in terms of their description length (in number of bits). We show that, by suitable choice of the control encoding, finite plans can be efficiently built for a wide class of dynamical systems, computing arbitrarily close approximations of a desired equilibrium in polynomial time. The paper also investigates how the efficiency of planning is affected by the choice of inputs, and provides some results as to optimal performance in terms of accuracy and range.

In this paper we address the problem of generating input plans to steer complex dynamical systems in an obstacle-free environment. Plans considered admit a finite description length and are constructed by words on an alphabet of input symbols, which could be e.g. transmitted through a limited capacity channel to a remote system, where they can be decoded in suitable control actions. We show that, by suitable choice of the control encoding, finite plans can be efficiently built for a wide class of dynamical systems, computing arbitrarily close approximations of a desired equilibrium in polynomial time. Moreover, we illustrate by simulations the power of the proposed method, solving the steering problem for an example in the class of underactuated systems, which have attracted wide attention in the recent literature

Complex dynamical systems can be steered by using symbolic input plans. These plans must have a finite descriptive length, and can be expressed by means of words chosen in an alphabet of symbols. In this way, such plans can be sent through a limited capacity channel to a remote system, where they are decoded in suitable control actions. The choice of this symbols is essential to efficiently encode steering plans. To this aim, in this paper, we state the problem of finding symbols maximizing the interval of points reachable by the system along paths with constrained length. We focus on the problem with two symbols, and compare the results with those produced by plans not accounting for the length constraint. Moreover, the behavior of a simple helicopter, steered by both kinds of plans, has been simulated, in order to illustrate the power of the overall control system, and to emphasize the improvements introduced by the new plans.

International audience; In this paper, we present a novel approach for the abstraction of monotone systems with bounded disturbances. The approach is data-driven and uses a given set of samples of the (unknown) dynamics of the system to compute an abstraction defined on partitions of the state and input spaces. The proposed method is efficient as its computational complexity is linear in the number of samples and in the size of the partitions. Moreover, the abstraction is shown to be minimally conservative in the absence of disturbances. We show that the resulting symbolic model is itself a monotone transition system and is related to the original system by an alternating simulation relation. We present some numerical experiments to show the effectiveness of the approach and to show how the choice of the partitions or the number of samples affects the quality of the approximation.