For a class of hybrid dynamical systems, we show that a recurrent neural network with hybrid dynamics, which we refer to as a hybrid dynamic recurrent neural network (HyRNN), can be constructed to approximate solutions to hybrid systems over bounded (hybrid) time horizons. Specifically, given a desired precision level, we show that a hybrid system with dynamics resembling those of recurrent neural networks for continuous-time and discrete-time systems can be designed so that, for each bounded hybrid time horizon, its solutions are close to the solutions to the given hybrid system. Through the use of universal approximation theorems, we show that the approximation result holds for traditional smooth activation functions, such as sigmoid and arctan, and that extensions to ReLU functions are possible, and characterize the complexity of the proposed HyRNN.

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.

Tight coupling between computation, communication, and control pervades the design and application of cyber-physical systems (CPSs). Due to the complexity of these systems, advanced design procedures that account for these tight interconnections are paramount to ensure the safe and reliable operation of control algorithms under computational constraints. This paper presents the Simulator for Hardware Architecture and Real-time Control (Sharc) to assist in the co-design of control algorithms and the computational hardware on which they are run. Sharc simulates the execution of a user-specified control algorithm on a given processor microarchitecture configuration, evaluating how computational constraints affect the dynamical properties of the closed-loop system. We illustrate the power of Sharc by examples of MPC applied to adaptive cruise control and the stabilization of an inverted pendulum. Sharc can be found at github.com/pwintz/sharc.

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.

Most proposals for securing control systems are heuristic in nature, and while they increase the protection of their target, the security guarantees they provide are unclear. This paper proposes a new way of modeling the security guarantees of a Cyber-Physical System (CPS) against arbitrary false command attacks. As our main case study, we use the most popular testbed for control systems security. We first propose a detailed formal model of this testbed and then show how the original configuration is vulnerable to a single-actuator attack. We then propose modifications to the control system and prove that our modified system is secure against arbitrary, single-actuator attacks.

In this paper, we formulate a two-player zero-sum game under dynamic constraints given in terms of hybrid dynamical systems. We present sufficient conditions with Hamilton-Jacobi-Isaacs-like equations to guarantee attaining a solution to the game. It is shown that when the players select the optimal strategy, the value function can be evaluated without the need of computing solutions. Under additional conditions, we show that the optimal feedback laws render a set of interest asymptotically stable. Using this framework, we address an optimal control problem under the presence of an adversarial action in which the decision-making agents have dynamics that might exhibit both continuous and discrete behavior. Applications of this problem, as presented here, include disturbance rejection and security scenarios, for which the effect of the worst-case adversarial action is minimized.

In this work, we formulate a two-player zero-sum game under dynamic constraints given in terms of hybrid dynamical systems. Find the full version in [8], including the main results and outlines of the corresponding proofs. We propose sufficient conditions to guarantee attaining a solution to the game. When the players select the optimal strategy, the value function can be evaluated without the need of computing solutions. Under additional conditions, the optimal feedback laws render a set of interest asymptotically stable. Using this framework, we address an optimal control problem under the presence of an adversarial action in which the decision-making agents have dynamics that might exhibit both continuous and discrete behavior.

In this paper, we introduce tools to verify the satisfaction of temporal logic specifications using the until operator for hybrid dynamical systems. Hybrid dynamical systems are given in terms of differential and difference inclusions, which capture the continuous and discrete dynamics (or events), respectively. For such systems, conditional invariance and eventual conditional invariance are employed to characterize dynamical properties associated with the until operators. Sufficient conditions for the satisfaction of temporal logic specifications involving the until operator are provided by guaranteeing properties of the data defining the systems and the existence of barrier functions or Lyapunov-like functions. Examples illustrate the results throughout the paper.

Motivated by the safety problem, several definitions of reachability maps, for hybrid dynamical systems, are introduced. It is well established that, under certain conditions, the solutions to continuous-time systems depend continuously with respect to initial conditions. In such setting, the reachability maps considered in this paper are locally Lipschitz (in the Lipschitz sense for set-valued maps) when the right-hand side of the continuous-time system is locally Lipschitz. However, guaranteeing similar properties for reachability maps for hybrid systems is much more challenging. Examples of hybrid systems for which the reachability maps do not depend nicely with respect to their arguments, in the Lipschitz sense, are introduced. With such pathological cases properly identified, sufficient conditions involving the data defining a hybrid system assuring Lipschitzness of the reachability maps are formulated. As an application, the proposed conditions are shown to be useful to significantly improve an existing converse theorem for safety given in terms of barrier functions. Namely, for a class of safe hybrid systems, we show that safety is equivalent to the existence of a locally Lipschitz barrier function. Examples throughout the paper illustrate the results.

Design support tools benefit from rich information about games' emergent behavior. Inventing successful AI players for particular games can help producing some of this information, but this is both labor intensive and limited in that it can generally only reveal that a solution exists and not say that no solution exists or that certain classes of solution exist. We show a generic method for posing and answering feasible-path, optimal-path, and reachable-space queries in action games, and we devise a measure of game level difficulty. We accomplish all this by encoding action videogame characters as hybrid dynamical systems, using Flappy Bird and Super Mario as case studies.

This paper investigates characterizations of safety in terms of barrier functions for hybrid systems modeled by hybrid inclusions. After introducing an adequate definition of safety for hybrid inclusions, sufficient conditions using continuously differentiable as well as lower semicontinuous barrier functions are proposed. Furthermore, the lack of existence of autonomous and continuous barrier functions certifying safety, guides us to propose, inspired by converse Lyapunov theorems for only stability, nonautonomous barrier functions and conditions that are shown to be both necessary as well as sufficient, provided that mild regularity conditions on the system's dynamics holds.

By this poster, we aim at presenting in a comprehensive manner our new results on safety characterization using barrier functions in the general context of hybrid systems. Roughly speaking, a dynamical system is said to be safe when the solutions starting from a given initial set never reach a given unsafe set. Barrier functions in this context constitute a qualitative methodological tool that avoid the computation of the system's solutions yet to determine if the safety property holds. According to literature, a barrier function candidate with respect to a given initial and unsafe sets is nonpositive on the initial set and strictly positive on the unsafe set. Such a barrier candidate becomes a certificate of safety provided that it satisfies some variational properties involving the system's dynamics at least in a specific region around its zero-sublevel set.

We propose tools for the study of robust stabilizability and the design of robustly stabilizing feedback laws for a wide class of hybrid systems given in terms of hybrid inclusions with inputs and disturbances. We introduce notions of robust uniform global stabilizability and stabilization that capture the case when disturbances can be fully rejected, practically rejected, and when they induce a residual set that can be stabilized. Robust control Lyapunov functions are em- ployed to determine when stabilizing static state-feedback laws are available and also to synthesize robustly stabilizing feedback laws with minimum pointwise norm. Sufficient conditions on the data of the hybrid system as well as on the control Lyapunov function are proposed for the said properties to hold. An example illustrates the results throughout the paper.

This paper describes hybrid model predictive controllers that switch between two predictor functions based on the uncontrollable divergence metric. The uncontrollable divergence metric relates the computational capabilities of the model predictive controller, to the error of the system due to model mismatch of the predictor function during computation of the solution. The contribution of this paper is in its treatment of the model predictive controller to permit optimization to take multiple timesteps to occur, but still rely on the uncontrollable divergence metric. The results demonstrate the approach for control of a vertical takeoff-and-landing aerial vehicle.

In this paper, we tackle the problem of trajectory tracking for a particular class of underactuated vehicles with full torque actuation and a single force direction (thrust) that is fixed relative to a body attached frame. Additionally, we consider that thrust reversal is not available. We present the design of a hybrid controller that, under some given assumptions, is able to globally asymptotically stabilize the vehicle to a reference position trajectory while minimizing the angle to the desired attitude trajectory. This objective is achieved robustly and globally, in the sense that small perturbations do not lead to instability and it is achieved regardless of the initial state of the vehicle. The algorithm is tested in a experimental setup, using a small scale quadrotor vehicle and the VICON motion capture system.

This paper describes the Hybrid Equations (HyEQ) Toolbox implemented in Matlab/Simulink for the simulation of hy- brid dynamical systems. This toolbox is capable of comput- ing approximations of trajectories to hybrid systems given in terms of differential and difference equations with con- straints, called hybrid equations. The toolbox is suitable for the simulation of hybrid systems with different type of trajectories, including those that are Zeno and that have multiple jumps at the same instant. It is also capable of simulating hybrid systems without inputs, with inputs, as well as interconnections of hybrid systems. The structure, components, and usage of the simulation scripts within the toolbox are described. Examples are included to illustrate the main capabilities of the toolbox.

A novel solution to the problem of controlling a one degree-of-freedom ball juggling system that explicitly models friction is proposed. A hybrid controller is designed to steer the ball to track a specific reference trajectory. The juggling system consists of a nearly-smooth vertical shaft with a piston-actuated bouncing ball. The hybrid controller is capable of tracking a periodic reference trajectory. A practical (finite-time) tracking property is established using hybrid systems theory, while juggling experiments are presented to validate the hybrid control algorithm. Key to these experimental results are: 1) the use of a filtered zero-crossing impact detection algorithm; 2) a Savitzky-Golay filter for smooth piston position and velocity; 3) a custom external PID controller; and 4) the estimation of the apparatus parameters via system ID methods.

We study the problem of designing controllers to track state trajectories for plants with jumps in the state that are given by constrained differential equations capturing the continuous dynamics and constrained difference equations (or inclusions) capturing the discrete dynamics. The reference trajectories consist of signals having intervals of flow and instantaneous jumps, and are generated via a known hybrid exosystem. The class of controllers considered are hybrid and are designed to guarantee that the jump times of the plant coincide with those of the given reference trajectories. By recasting the tracking problem as the stabilization of a set and using asymptotic stability tools for time invariant hybrid systems, we derive sufficient conditions for the closed-loop system that guarantee tracking of reference trajectories.