On The Complexity of Bounded Time Reachability for Piecewise Affine Systems
نویسندگان
چکیده
Reachability for piecewise affine systems is known to be undecidable, starting from dimension 2. In this paper we investigate the exact complexity of several decidable variants of reachability and control questions for piecewise affine systems. We show in particular that the region to region bounded time versions leads to NP -complete or co-NP -complete problems, starting from dimension 2.
منابع مشابه
Enlarging Domain of Attraction for a Special Class of Continuous-time Quadratic Lyapunov Function Piecewise Affine Systems based on Discontinuous Piecewise
This paper presents a new approach to estimate and to enlarge the domain of attraction for a planar continuous-time piecewise affine system. Various continuous Lyapunov functions have been proposed to estimate and to enlarge the system’s domain of attraction. In the proposed method with a new vision and with the aids of a discontinuous piecewise quadratic Lyapunov function, the domain of attrac...
متن کاملReachability analysis of continuous-time piecewise affine systems
This paper proposes an algorithm for the characterization of reachable sets of states for continuous-time piecewise affine systems. Given a model of the system and a bounded set of possible initial states, the algorithm employs a linear matrix inequality approach to compute both upper and lower bounds on reachable regions. Rather than performing computations in the state-space, this method uses...
متن کاملReconfiguration in Hierarchical Control of Piecewise-Affine Systems
The In this paper the problem of reconfiguration in hierarchical control of piecewise-affine systems in discrete time is considered as the choice of input constraints applied to the low-level control. It is shown how such reconfiguration can provide fault-tolerance to actuator faults while reducing the computational complexity of low-level control. The approach is based on partitioning the stat...
متن کاملAdaptive Consensus Control for a Class of Non-affine MIMO Strict-Feedback Multi-Agent Systems with Time Delay
In this paper, the design of a distributed adaptive controller for a class of unknown non-affine MIMO strict-feedback multi agent systems with time delay has been performed under a directed graph. The controller design is based on dynamic surface control method. In the design process, radial basis function neural networks (RBFNNs) were employed to approximate the unknown nonlinear functions. S...
متن کاملReachability and Robust Control of PWA Systems with Parameter Variations and Bounded Disturbance
This paper considers discrete-time, uncertain PWA (piecewise affine) systems affected by parameter variations and bounded disturbances, where reachability technique based on polyhedral approach is developed and the robust control problems are investigated. Checking attainability and calculating the state space regions for which a robust control is assured despite the possible disturbance and th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014