Symbolic Models for Nonlinear Control Systems: Alternating Approximate Bisimulations

Symbolic models are abstract descriptions of continuous systems in which symbols represent aggregates of continuous states. In the last few years there has been a growing interest in the use of symbolic models as a tool for mitigating complexity in control design. In fact, symbolic models enable the use of well known algorithms in the context of supervisory control and algorithmic game theory, for controller synthesis. Since the 1990's many researchers faced the problem of identifying classes of dynamical and control systems that admit symbolic models. In this paper we make a further progress along this research line by focusing on control systems affected by disturbances. Our main contribution is to show that incrementally globally asymptotically stable nonlinear control systems with disturbances admit symbolic models. When specializing these results to linear systems, we show that these symbolic models can be easily constructed

Linear time logic control of linear systems with disturbances

The formal analysis and design of control systems is one of recent trends in control theory. In this area, in order to reduce the complexity and scale of control systems, finite abstractions of control systems are introduced and explored. In non-disturbance case, the controller of control systems is often generated from the controller of finite abstractions. Recently, Pola and Tabuada provide approximate finite abstractions for linear control systems with disturbance inputs. However, these finite abstractions and original linear systems do not always share the identical specifications, which obstructs designing controller (of linear systems) based on their finite abstractions. This paper tries to bridge such gap between linear systems and their finite abstractions.Comment: 32 pages, 4 figue