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The time-marching strategy, which propagates the solution from one time step to the next, is a natural strategy for solving time-dependent differential equations on classical computers, as well as for solving the Hamiltonian simulation…
We consider problems originating in economics that may be solved automatically using mathematical software. We present and make freely available a new benchmark set of such problems. The problems have been shown to fall within the framework…
System identification through learning approaches is emerging as a promising strategy for understanding and simulating dynamical systems, which nevertheless faces considerable difficulty when confronted with power systems modeled by…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
We present a holistic data-driven approach to the problem of productivity increase on the example of a metallurgical pickling line. The proposed approach combines mathematical modeling as a base algorithm and a cooperative Multi-Agent…
This paper proposes an effective low-rank alternating direction doubling algorithm (R-ADDA) for computing numerical low-rank solutions to large-scale sparse continuous-time algebraic Riccati matrix equations. The method is based on the…
Quantum Annealing (QA) can efficiently solve combinatorial optimization problems whose objective functions are represented by Quadratic Unconstrained Binary Optimization (QUBO) formulations. For broader applicability of QA, quadratization…
A variational quantum algorithm for numerically solving partial differential equations (PDEs) on a quantum computer was proposed by Lubasch et al. In this paper, we generalize the method introduced by Lubasch et al. to cover a broader class…
We introduce a quantum algorithm for simulating the dynamics of electrical circuits consisting of resistors, inductors and capacitors (aka RLC circuits) along with power sources. Given oracle access to the connectivity of the circuit and…
In this paper, the reinforcement learning (RL)-based optimal control problem is studied for multiplicative-noise systems, where input delay is involved and partial system dynamics is unknown. To solve a variant of Riccati-ZXL equations,…
In this paper we consider a class of conjugate discrete-time Riccati equations, arising originally from the linear quadratic regulation problem for discrete-time antilinear systems. Under some mild assumptions and the framework of the…
The interplay between exploration and exploitation in competitive multi-agent learning is still far from being well understood. Motivated by this, we study smooth Q-learning, a prototypical learning model that explicitly captures the…
This paper applies a reinforcement learning (RL) method to solve infinite horizon continuous-time stochastic linear quadratic problems, where drift and diffusion terms in the dynamics may depend on both the state and control. Based on…
This paper presents a novel value iteration (VI) algorithm for finding the optimal control for a kind of infinite-horizon stochastic linear quadratic (SLQ) problem with unknown systems. First, an off-line algorithm is estabilished to obtain…
Simulation of realistic classical mechanical systems is of great importance to many areas of engineering such as robotics, dynamics of rotating machinery and control theory. In this work, we develop quantum algorithms to estimate quantities…
Individual agents in a multi-agent system (MAS) may have decoupled open-loop dynamics, but a cooperative control objective usually results in coupled closed-loop dynamics thereby making the control design computationally expensive. The…
In this paper, we address the problem of a two-player linear quadratic differential game with incomplete information, a scenario commonly encountered in multi-agent control, human-robot interaction (HRI), and approximation methods for…
Finding shape correspondences can be formulated as an NP-hard quadratic assignment problem (QAP) that becomes infeasible for shapes with high sampling density. A promising research direction is to tackle such quadratic optimization problems…
Adversarial continual learning is effective for continual learning problems because of the presence of feature alignment process generating task-invariant features having low susceptibility to the catastrophic forgetting problem.…
This paper discusses model order reduction of large sparse second-order index-3 differential algebraic equations (DAEs) by applying Iterative Rational Krylov Algorithm (IRKA). In general, such DAEs arise in constraint mechanics, multibody…