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To solve the control problem of time-varying state-scale nonlinear systems whose initial state is not affected by settling time, fixed-time convergence algorithms are proposed for first-order systems and higher-order systems in this paper. First, a scalar model is used to illustrate how the time-varying feedback parameter can guarantee that the system achieves asymptotic stability while achieving finite-time convergence, and it is proved that the settling time obtained in this paper is only related to the prescribed boundary. This allows us to design the settling time with an appropriate parameter based on the prescribed boundary. To exhibit the effectiveness and extensibility of the proposed algorithm for first-order scalar systems, the results are subsequently extended to general higher-order systems based on the backstepping method. By introducing numerical simulation results, this paper verifies that the proposed algorithm will make the system achieve asymptotic stability and its output can converge to a given boundary, regardless of the system's initial states. [ABSTRACT FROM AUTHOR]

We focus on the control and the synthesis of secure timed systems which are modelled as timed automata. The security property that the system must satisfy is anon-interferenceproperty. Intuitively, non-interference ensures the absence of any causal dependency from a high-level domain to a lower level domain. Various notions of non-interference have been defined in the literature, and in this paper, we focus onstrong non-deterministic non-interference(SNNI) and two (bi)simulation-based variants thereof (cosimulation-based SNNI and bisimulation-based SNNI). These properties and their extensions have been mostly studied in the context of discrete event systems, while it is now well-known that time is an important attack vector against secure systems. At the same time, there is an obvious interest in going beyond simple verification to control problems: to be able to automatically make systems secure. We consider non-interference properties in the challenging setting of control of dense-time systems specified bytimed automataand we study the two following problems: (1) check whether it is possible to find a sub-system so that it is non-interferent; if yes, (2) compute a (largest) sub-system which is non-interferent. We exhibit decidable sub-classes for these problems, assess their theoretical complexities and provide effective algorithms based on the classical framework of timed games. [ABSTRACT FROM AUTHOR]