This article investigates the model predictive tracking control problem for nonlinear systems represented by Takagi-Sugeno (T-S) fuzzy models. First, in order to alleviate the online computational burden of the MPC algorithm, a simplified model-based predictive strategy is developed, where the nominal system is approximated by a known linear time-varying (LTV) model, enabling the online optimization to be formulated as a quadratic programming (QP) problem. Thereafter, to ensure recursive feasibility and bounded tracking errors under fuzzy approximation errors and bounded disturbances, a Lyapunov-based dynamically updated tracking error constraint is introduced. Furthermore, by converting the original ellipsoidal constraints into relaxed box constraints, computational complexity is further reduced without violating the Lyapunov-based guarantees, which is ensured by an auxiliary one-step optimizer incorporated in the online part of the proposed framework. Compared with existing results, the proposed approach maintains bounded tracking errors with relatively high computational efficiency. The effectiveness of the proposed MPC framework is then demonstrated through simulation results.

Automated library APIs testing is difficult as it requires exploring a vast space of parameter inputs that may involve objects with complex data types. Existing search based approaches, with limited knowledge of relations between object states and program branches, often suffer from the low efficiency issue, i.e., tending to generate invalid inputs. Symbolic execution based approaches can effectively identify such relations, but fail to scale to large programs. In this work, we present an LLM-based input space partitioning testing approach, LISP, for library APIs. The approach lever-ages LLMs to understand the code of a library API under test and perform input space partitioning based on its understanding and rich common knowledge. Specifically, we provide the signature and code of the API under test to LLMs, with the expectation of obtaining a text description of each input space partition of the API under test. Then, we generate inputs through employing the generated text description to sample inputs from each partition, ultimately resulting in test suites that systematically explore the program behavior of the API. We evaluate LISP on more than 2,205 library API meth-ods taken from 10 popular open-source Java libraries (e.g.,$a$p$a$che/commons-lang with 2.6k stars, guava with 48.8k stars on GitHub). Our experiment results show that LISP is effective in library API testing. It significantly outperforms state-of-the-art tool EvoSuite in terms of edge coverage. On average, LISP achieves 67.82 % branch coverage, surpassing EvoSuite by 1.21 times. In total, LISP triggers 404 exceptions or errors in the experiments, and discovers 13 previously unknown vulnerabilities during evaluation, which have been assigned CVE IDs.