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We present an abstraction and refinement methodology for the automated controller synthesis to enforce general predefined specifications. The designed controllers require quantized (or symbolic) state information only and can be interfaced with the system via a static quantizer. Both features are particularly important with regard to any practical implementation of the designed controllers and, as we prove, are characterized by the existence of a feedback refinement relation between plant and abstraction. Feedback refinement relations are a novel concept introduced in this paper. Our work builds on a general notion of system with set-valued dynamics and possibly non-deterministic quantizers to permit the synthesis of controllers that robustly, and provably, enforce the specification in the presence of various types of uncertainties and disturbances. We identify a class of abstractions that is canonical in a well-defined sense, and provide a method to efficiently compute canonical abstractions. We demonstrate the practicality of our approach on two examples. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper describes an approach to the control of continuous systems through the use of symbolic models describing the system behavior only at a finite number of points in the state space. These symbolic models can be seen as abstract representations of the continuous dynamics enabling the use of algorithmic controller design methods. We identify a class of linear control systems for which the loss of information incurred by working with symbolic subsystems can be compensated by feedback. We also show how to transform symbolic controllers designed for a symbolic subsystem mb controllers for the original system. The resulting controllers combine symbolic controller dynamics with continuous feedback control laws and can thus be seen as hybrid systems. Furthermore, if the symbolic controller already accounts for software/hardware requirements, the hybrid controller is guaranteed to enforce the desired specifications by construction thereby reducing the need for formal verification. [ABSTRACT FROM AUTHOR]