Synthesizing Switching Controllers for Hybrid Systems by Continuous Invariant Generation

We extend a template-based approach for synthesizing switching controllers for semi-algebraic hybrid systems, in which all expressions are polynomials. This is achieved by combining a QE (quantifier elimination)-based method for generating continuous invariants with a qualitative approach for predefining templates. Our synthesis method is relatively complete with regard to a given family of predefined templates. Using qualitative analysis, we discuss heuristics to reduce the numbers of parameters appearing in the templates. To avoid too much human interaction in choosing templates as well as the high computational complexity caused by QE, we further investigate applications of the SOS (sum-of-squares) relaxation approach and the template polyhedra approach in continuous invariant generation, which are both well supported by efficient numerical solvers

Exact Asymptotic Stability Analysis and Region-of-Attraction Estimation for Nonlinear Systems

We address the problem of asymptotic stability and region-of-attraction analysis of nonlinear dynamical systems. A hybrid symbolic-numeric method is presented to compute exact Lyapunov functions and exact estimates of regions of attraction of nonlinear systems efficiently. A numerical Lyapunov function and an estimate of region of attraction can be obtained by solving an (bilinear) SOS programming via BMI solver, then the modified Newton refinement and rational vector recovery techniques are applied to obtain exact Lyapunov functions and verified estimates of regions of attraction with rational coefficients. Experiments on some benchmarks are given to illustrate the efficiency of our algorithm

Search-based inference of polynomial metamorphic relations

Metamorphic testing (MT) is an effective methodology for testing those so-called 'non-testable' programs (e.g., scientific programs), where it is sometimes very difficult for testers to know whether the outputs are correct. In metamorphic testing, metamorphic relations (MRs) (which specify how particular changes to the input of the program under test would change the output) play an essential role. However, testers may typically have to obtain MRs manually. In this paper, we propose a search-based approach to automatic inference of polynomial MRs for a program under test. In particular, we use a set of parameters to represent a particular class of MRs, which we refer to as polynomial MRs, and turn the problem of inferring MRs into a problem of searching for suitable values of the parameters. We then dynamically analyze multiple executions of the program, and use particle swarm optimization to solve the search problem. To improve the quality of inferred MRs, we further use MR filtering to remove some inferred MRs. We also conducted three empirical studies to evaluate our approach using four scientific libraries (including 189 scientific functions). From our empirical results, our approach is able to infer many high-quality MRs in acceptable time (i.e., from 9.87 seconds to 1231.16 seconds), which are effective in detecting faults with no false detection. ? 2014 ACM.EI