Predictable timing on multicore systems requires careful management of shared resources such as the last-level cache and memory bandwidth. This paper presents MPORA, an uncertainty-aware dynamic resource allocation framework for multi-path, input-dependent real-time tasks on multicore platforms. MPORA models each job as a discrete-time dynamical system that captures execution dynamics and resource-dependent performance indicators. At runtime, MPORA monitors job execution states and predicts short-term instruction rates and remaining execution times under candidate allocations using predictive models trained offline. It then solves a receding-horizon optimization problem to compute resource allocations that maximize system-wide progress while meeting job deadlines. To address prediction uncertainty, MPORA integrates weighted conformal prediction into the optimization formulation, enabling uncertainty-aware deadline constraints. We implement MPORA as a Linux kernel module with microsecond-scale inference overhead. Experimental results on SPEC CPU benchmarks show that MPORA delivers accurate predictions under unseen inputs and distribution shifts with low overhead, while improving schedulability and response times over existing methods.

We study control design methods to endow hybrid systems under disturbances with safety guarantees as an inverse-optimality problem. First, we provide sufficient conditions to guarantee input-to-state safety of a hybrid system with disturbance inputs only. Next, given a nominal feedback law, we show that a hybrid system, with inputs and disturbances, can be rendered input-to-state controlled safe under the existence of a control barrier function (CBF) using pointwise min-norm safeguarding feedback laws. Finally, we demonstrate that every CBF is a meaningful value function for a two-player zero-sum hybrid game in the context of safety, and that every pointwise min-norm safeguarding feedback law is optimal for such a game, even though its design is independent of any cost functional. The main results are illustrated in an example.

In this paper, we propose a learning-based algorithm for hybrid systems with a twofold purpose: first, to design Lyapunov functions and, second, to upper bound the cost of solutions to the system. Via enforcing conditions at finitely many points of a set of interest and leveraging regularity properties of the maps defining the dynamics of the system and the stage costs associated to solutions, we extend the conditions to the entire set of interest. The method employs neural networks to learn a Lyapunov function and a value-like function to guarantee the extended pointwise conditions at all points in the set of interest and thus, guarantee practical asymptotic stability of a set or provide an upper bound on the cost of solutions, respectively. The approach is illustrated in a hybrid oscillator system.