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Invariant tori, topological horseshoes, and their coexistence in piecewise smooth hybrid systems
This paper investigates the dynamics of tori and chaos in some classes of three-dimensional piecewise smooth hybrid systems, which consist of...
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Discrete adjoint method for variational integration of constrained ODEs and its application to optimal control of geometrically exact beam dynamics
Direct methods for the simulation of optimal control problems apply a specific discretization to the dynamics of the problem, and the discrete...
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On the Parallel Realization of Complex Rosenbrock ODEs Solution
The chapter proposes a research of a solver system for stiff systems of ordinary differential equations (SS ODEs) of moderate dimensionality...
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Positivity for Matrix Systems: A Case Study from Quantum Mechanics
We discuss an example from quantum physics of “positive system” in which the state (a density operator) is a square matrix constrained to be positive...
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Predicting Nonlinear Structural Dynamic Response of ODE Systems Using Constrained Gaussian Process Regression
Identification and characterization of a nonlinear structural dynamic system often involve inferring unknown parameters from experimental data....
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A relaxed coupling method for algebraically constrained mechanical systems
A coupling method is presented that aims at computing the dynamics of constrained mechanical systems connected by algebraic constraints. A relaxed...
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The Study of Linear and Nonlinear Fractional ODEs by Homotopy Analysis
In our work, we broaden the application of homotopy analysis method (HAM) to solve linear and nonlinear time fractional ordinary differential...
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Tracking Control for \(2\times 2\) Linear Heterodirectional Hyperbolic PDEs that Are Bidirectionally Coupled with Nonlinear ODEs
A solution-based approach to trajectory tracking control is presented for...
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State observer of multibody systems formulated using differential algebraic equations
Multibody dynamics comprises methodologies for the design and analysis of mechanical systems, with Kalman filters being the principal state...
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Dynamic Optimization of Switched Systems with Free Switching Sequences
After handling the difficulty of optimizing the input and switch times, in this chapter, we shall remove the restriction of the fixed switching...
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Control of Hybrid Nonlinear Systems
In this chapter, we develop hybrid nonlinear control methodologies for various classes of hybrid nonlinear processes. Initially, switched processes...
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First integrals and exact solutions of a class of nonlinear systems
Nonlinear nonconservative systems are not integrable for a general parametric choice, and it is difficult to obtain the first integral directly....
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Dynamical modelling of boom tower crane rigging systems: model selection for construction
Accurate dynamical models are imperative to the development of accurate monitoring and control systems, which are foundational to safety in...
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Parameter estimation and modeling of nonlinear dynamical systems based on Runge–Kutta physics-informed neural network
To identify the nonlinear behavior of dynamical systems subjected to external excitations such as earthquakes, explosions, and impacts, a novel...
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A Novel Method for Nonlinear Time-History Analysis of Structural Systems: Improved Newton–Cotes-Hermite-5P Method
Analyzing high-frequency systems in mechanics and structural dynamics is a challenging problem that can be difficult to handle by conventional...
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Application of genetic programming for model-free identification of nonlinear multi-physics systems
This study provides a general methodology based on genetic programming (GP) to identify nonlinear multi-physics systems. The proposed GP-based method...
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Basic Ingredients of Nonlinear Systems Dynamics
By and large, most real-world phenomena are dynamic, non-linear, and time-variable. Despite the fact that they appear mainly in the world of physics,...
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Model reduction for constrained mechanical systems via spectral submanifolds
Dynamical systems are often subject to algebraic constraints in conjunction with their governing ordinary differential equations. In particular,...
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Modeling and Simulation with Simulink
System simulation is the study of system performance based on the mathematical models and systems behavior of real systems. In particular, it refers...
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Joint sparse least squares via generalized fused lasso penalty for identifying nonlinear dynamical systems
This paper proposes a joint sparse least-square model that utilizes a generalized fused lasso penalty to jointly identify governing equations of...
