Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userFinite Step Performance of First-order Methods Using Interpolation Conditions Without Function Evaluations
52
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We present a procedure to numerically compute finite step worst case performance guarantees on a given algorithm for the unconstrained optimization of strongly convex functions with Lipschitz continuous gradients. The solution method provided serves as an alternative approach to that derived by Taylor, Hendrickx, and Glineur in [Math. Prog. 161 (1-2), 2017]. The difference lies in the fact that our solution uses conditions for the interpolation of a set of points and gradient evaluations by the gradient of a function in the class of interest, whereas their solution uses conditions for the interpolation of a set of points, gradient evaluations, and function evaluations by a function in the class of interest. The motivation for this alternative solution is that, in many cases, neither the algorithm nor the performance metric of interest rely upon function evaluations. The primary development is a procedure to avoid suffering from the factorial growth in the number of these conditions with the size of the set to be interpolated when solving for the worst case performance.
rate research
Read More
Traffic Management in Advanced Aerial Mobility (AAM) inherits many elements of conventional Air Traffic Management (ATM), but brings new complexities and challenges of its own. One of its ways of guaranteeing separation is the use of airborne, stand-alone Detect-And-Avoid, an operational concept where each aircraft decides its avoidance maneuvers independently, observing right-of-way rules and, in specific implementations, some form of pairwise coordination. This is a fundamental safety element for autonomous aircraft but, according to our research, is not sufficient for high-density airspaces as envisioned for urban environments. In these environments, some way of explicit and strategic traffic coordination must be in place, as done for conventional ATM. For efficiency reasons, ATM is evolving to more flexible uses of the airspace, such that the use of dynamically allocated corridors is a rising concept for AAM. These strategic forms of traffic coordination are potentially highly efficient if the aircraft adhere to their trajectory contracts and there are no significant perturbations to the traffic. However, if significant perturbations occur, such as loss of data communication, or the sudden appearance of an intruder, a centralized system may not react appropriately in due time. In busy scenarios, even small deviations from plans may compound so rapidly as to result in large differences in the overall achieved scenario, resulting in congestions and convoluted conflicts. Therefore, it is worth studying traffic coordination techniques that work locally with shorter look-ahead times. To that end, we explore an airborne collaborative method for traffic coordination, which is capable of safely solving conflicts with multiple aircraft, stressing its capabilities throughout a large number of scenarios and comparing its performance with established methods.
In this paper, we propose a notion of high-order (zeroing) barrier functions that generalizes the concept of zeroing barrier functions and guarantees set forward invariance by checking their higher order derivatives. The proposed formulation guarantees asymptotic stability of the forward invariant set, which is highly favorable for robustness with respect to model perturbations. No forward completeness assumption is needed in our setting in contrast to existing high order barrier function methods. For the case of controlled dynamical systems, we relax the requirement of uniform relative degree and propose a singularity-free control scheme that yields a locally Lipschitz control signal and guarantees safety. Furthermore, the proposed formulation accounts for performance-critical control: it guarantees that a subset of the forward invariant set will admit any existing, bounded control law, while still ensuring forward invariance of the set. Finally, a non-trivial case study with rigid-body attitude dynamics and interconnected cell regions as the safe region is investigated.
New forms of on-demand transportation such as ride-hailing and connected autonomous vehicles are proliferating, yet are a challenging use case for electric vehicles (EV). This paper explores the feasibility of using deep reinforcement learning (DRL) to optimize a driving and charging policy for a ride-hailing EV agent, with the goal of reducing costs and emissions while increasing transportation service provided. We introduce a data-driven simulation of a ride-hailing EV agent that provides transportation service and charges energy at congested charging infrastructure. We then formulate a test case for the sequential driving and charging decision making problem of the agent and apply DRL to optimize the agents decision making policy. We evaluate the performance against hand-written policies and show that our agent learns to act competitively without any prior knowledge.
Interval approaches for the reachability analysis of initial value problems for sets of classical ordinary differential equations have been investigated and implemented by many researchers during the last decades. However, there exist numerous applications in computational science and engineering, where continuous-time system dynamics cannot be described adequately by integer-order differential equations. Especially in cases in which long-term memory effects are observed, fractional-order system representations are promising to describe the dynamics, on the one hand, with sufficient accuracy and, on the other hand, to limit the number of required state variables and parameters to a reasonable amount. Real-life applications for such fractional-order models can, among others, be found in the field of electrochemistry, where methods for impedance spectroscopy are typically used to identify fractional-order models for the charging/discharging behavior of batteries or for the dynamic relation between voltage and current in fuel cell systems if operated in a non-stationary state. This paper aims at presenting an iterative method for reachability analysis of fractional-order systems that is based on an interval arithmetic extension of Mittag-Leffler functions. An illustrating example, inspired by a low-order model of battery systems concludes this contribution.
In this paper, we propose a new automaton property of N-step nonblockingness for a given positive integer N. This property quantifies the standard nonblocking property by capturing the practical requirement that all tasks be completed within a bounded number of steps. Accordingly, we formulate a new N-step nonblocking supervisory control problem, and characterize its solvability in terms of a new concept of N-step language completability. It is proved that there exists a unique supremal N-step completable sublanguage of a given language, and we develop a generator-based algorithm to compute the supremal sublanguage. Finally, together with the supremal controllable sublanguage, we design an algorithm to compute a maximally permissive supervisory control solution to the new N-step nonblocking supervisory control problem.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
