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Recently, alternating transition systems are adopted to describe control systems with disturbances and their finite abstract systems. In order to capture the equivalence relation between these systems, a notion of alternating approximate…
This paper formulates and studies the concepts of approximate (alternating) bisimulation relations characterizing equivalence relations between interconnected systems and their abstractions. These equivalence relations guarantee that the…
Controller synthesis techniques for continuous systems with respect to temporal logic specifications typically use a finite-state symbolic abstraction of the system. Constructing this abstraction for the entire system is computationally…
Controller synthesis techniques for continuous systems with respect to temporal logic specifications typically use a finite-state symbolic abstraction of the system model. Constructing this abstraction for the entire system is…
In this paper, we consider the problem of synthesizing low-complexity controllers for incrementally stable switched systems. For that purpose, we establish a new approximation result for the computation of symbolic models that are…
In this paper, we introduce a compositional method for the construction of finite abstractions of interconnected discrete-time switched systems. Particularly, we use a notion of so-called alternating simulation function as a relation…
In this paper, we consider the problem of controller design using approximately bisimilar abstractions with an emphasis on safety and reachability specifications. We propose abstraction-based approaches to solve both classes of problems. We…
Translating continuous control system models into finite automata allows us to use powerful discrete tools to synthesize controllers for complex specifications. The abstraction construction step is unfortunately hamstrung by high runtime…
The objective of this paper is to solve the controller synthesis problem for bisimulation equivalence in a wide variety of scenarios including discrete-event systems, nonlinear control systems, behavioral systems, hybrid systems and many…
In this paper, we introduce a compositional scheme for the construction of finite abstractions (a.k.a. symbolic models) of interconnected discrete-time control systems. The compositional scheme is based on small-gain type reasoning. In…
We construct compositional continuous approximations for an interconnection of infinitely many discrete-time switched systems. An approximation (known as abstraction) is itself a continuous-space system, which can be used as a replacement…
Previous approaches to constructing abstractions for control systems rely on geometric conditions or, in the case of an interconnected control system, a condition on the interconnection topology. Since these conditions are not always…
We present lazy abstraction-based controller synthesis (ABCS) for continuous-time nonlinear dynamical systems against reach-avoid and safety specifications. State-of-the-art multi-layered ABCS pre-computes multiple finite-state abstractions…
In this manuscript, we investigate symbolic abstractions that capture the behavior of piecewise-affine systems under input constraints and bounded external noise. This is accomplished by considering local affine feedback controllers that…
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…
The problem of finding a finite state symbolic model which is bisimilar to a hybrid dynamical system (HDS) and has the minimum number of states is considered. The considered class of HDS allows for discrete-valued inputs that only affect…
Automated synthesis of reactive control protocols from temporal logic specifications has recently attracted considerable attention in various applications in, for example, robotic motion planning, network management, and hardware design. An…
At the intersection of dynamical systems, control theory, and formal methods lies the construction of symbolic abstractions: these typically represent simpler, finite-state models whose behavior mimics that of an underlying concrete system…
Finite-state models of control systems were proposed by several researchers as a convenient mechanism to synthesize controllers enforcing complex specifications. Most techniques for the construction of such symbolic models have two main…
One central issue in the formal design and analysis of reactive systems is the notion of refinement that asks whether all behaviors of the implementation is allowed by the specification. The local interpretation of behavior leads to the…