Beyond the Traditional Analyses and Resource Management in Real-Time Systems

The difficulties in estimating the Worst-Case Execution Time (WCET) of applications make the use of modern computing architectures limited in real-time systems. Critical embedded systems require the tasks of hard real-time applications to meet their deadlines, and formal proofs on the validity of this condition are usually required by certification authorities. In the last decade, researchers proposed the use of probabilistic measurement-based methods to estimate the WCET instead of traditional static methods. In this chapter, we summarize recent theoretical and quantitative results on the use of probabilistic approaches to estimate the WCET presented in the PhD thesis of the author, including possible exploitation scenarios, open challenges, and future directions.

An active set solver for constrained $ H_\infty $ optimal control problems with state and input constraints

<p style='text-indent:20px;'>This paper proposes an active set solver for <inline-formula><tex-math id="M2">\begin{document}$ H_\infty $\end{document}</tex-math></inline-formula> min-max optimal control problems involving linear discrete-time systems with linearly constrained states, controls and additive disturbances. The proposed solver combines Riccati recursion with dynamic programming. To deal with possible degeneracy (i.e. violations of the linear independence constraint qualification), constraint transformations are introduced that allow the surplus equality constraints on the state at each stage to be moved to the previous stage together with their Lagrange multipliers. In this way, degeneracy for a feasible active set can be determined by checking whether there exists an equality constraint on the initial state over the prediction horizon. For situations when the active set is degenerate and all active constraints indexed by it are non-redundant, a vertex exploration strategy is developed to seek a non-degenerate active set. If the sampled state resides in a robust control invariant set and certain second-order sufficient conditions are satisfied at each stage, then a bounded <inline-formula><tex-math id="M3">\begin{document}$ l_2 $\end{document}</tex-math></inline-formula> gain from the disturbance to controlled output can be guaranteed for the closed-loop system under some standard assumptions. Theoretical analysis and numerical simulations show that the computational complexity per iteration of the proposed solver depends linearly on the prediction horizon.</p>