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Stochastic differential equations (SDEs) are a ubiquitous modeling framework that finds applications in physics, biology, engineering, social science, and finance. Due to the availability of large-scale data sets, there is growing interest…
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The identification of a nonlinear dynamic model is an open topic in control theory, especially from sparse input-output measurements. A fundamental challenge of this problem is that very few to zero prior knowledge is available on both the…
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By one of the most fundamental principles in physics, a dynamical system will exhibit those motions which extremise an action functional. This leads to the formation of the Euler-Lagrange equations, which serve as a model of how the system…
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We introduce a novel class of score-based diffusion processes that operate directly in the representation space of Lie groups. Leveraging the framework of Generalized Score Matching, we derive a class of Langevin dynamics that decomposes as…
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Adaptive tracking control for rigid body dynamics is of critical importance in control and robotics, particularly for addressing uncertainties or variations in system model parameters. However, most existing adaptive control methods are…
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Nonlinear systems of affine control inputs overarch many sensor fusion instances. Analyzing whether a state variable in such a nonlinear system can be estimated (i.e., observability) informs better estimator design. Among the research on…
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Many safety-critical scientific and engineering systems evolve according to differential-algebraic equations (DAEs), where dynamical behavior is constrained by physical laws and admissibility conditions. In practice, these systems operate…
When the system is linear, why should learning be nonlinear? Linear dynamical systems, the analytical backbone of control theory, signal processing and circuit analysis, have exact closed-form solutions via the state transition matrix. Yet…
This paper investigates the qualitative behavior of a system of ordinary differential equations (ODEs) defined by a matrix operator derived from the algebraic structure of the Alpha Group. The system depends on a rotational parameter that…
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