Reachability Analysis Of Linear Systems Research Articles

Reachability analysis of linear systems

Reachability analysis of linear systems

Reachability Analysis of Large Linear Systems With Uncertain Inputs in the Krylov Subspace

One often wishes for the ability to formally analyze large-scale systems---typically, however, one can either formally analyze a rather small system or informally analyze a large-scale system. This work tries to further close this performance gap for reachability analysis of linear systems. Reachability analysis can capture the whole set of possible solutions of a dynamic system and is thus used to prove that unsafe states are never reached; this requires full consideration of arbitrarily varying uncertain inputs, since sensor noise or disturbances usually do not follow any patterns. We use Krylov methods in this work to compute reachable sets for large-scale linear systems. While Krylov methods have been used before in reachability analysis, we overcome the previous limitation that inputs must be (piecewise) constant. As a result, we can compute reachable sets of systems with several thousand state variables for bounded, but arbitrarily varying inputs.

Reachability Analysis of Linear Systems with Stepwise Constant Inputs

Reachability analysis is one major approach for safety verification of continuous and hybrid dynamical systems. In this paper we present a new approach to calculate the reachable states of linear systems with uncertain inputs under the assumption that the inputs are stepwise constant. The original system S with inputs is transformed into a system S′ without inputs such that the reachability problem of S can be reformulated as a problem that involves only S′ and thus the inputs need no longer to be considered. Finally, we show that this approach is in accordance with existing ones.

Reachability analysis of linear systems using support functions

This work is concerned with the algorithmic reachability analysis of continuous-time linear systems with constrained initial states and inputs. We propose an approach for computing an over-approximation of the set of states reachable on a bounded time interval. The main contribution over previous works is that it allows us to consider systems whose sets of initial states and inputs are given by arbitrary compact convex sets represented by their support functions. We actually compute two over-approximations of the reachable set. The first one is given by the union of convex sets with computable support functions. As the representation of convex sets by their support function is not suitable for some tasks, we derive from this first over-approximation a second one given by the union of polyhedrons. The overall computational complexity of our approach is comparable to the complexity of the most competitive available specialized algorithms for reachability analysis of linear systems using zonotopes or ellipsoids. The effectiveness of our approach is demonstrated on several examples.

Efficient Reachability Analysis for Linear Systems using Support Functions

This work is concerned with the algorithmic reachability analysis of linear systems with constrained initial states and inputs. In this paper, we present a new approach for the computation of tight polyhedral over-approximations of the reachable sets of a linear system. The main contribution over our previous work is that it makes it possible to consider systems whose sets of initial states and inputs are given by arbitrary compact convex sets represented by their support functions. We first consider the discrete-time setting and then we show how our algorithm can be extended to handle continuous-time linear systems. Finally, the effectiveness of our approach is demonstrated through several examples.

Effective synthesis of switching controllers for linear systems

In this paper, we suggest a novel methodology for synthesizing switching controllers for continuous and hybrid systems whose dynamics are defined by linear differential equations. We formulate the synthesis problem as finding the conditions upon which a controller should switch the behavior of the system from one "mode" to another in order to avoid a set of bad states and propose an abstract algorithm that solves the problem by an iterative computation of reachable states. We have implemented a concrete version of the algorithm, which uses a new approximation scheme for reachability analysis of linear systems.