Finite-Time Control for Nonlinear Time-Delay Hamiltonian Systems
Summary
Finite-time control for nonlinear time-delay Hamiltonian systems seeks to drive a physical or engineered system from an arbitrary initial condition to a desired equilibrium in a guaranteed finite interval, even in the presence of input or state delays. Under the port-controlled Hamiltonian formalism, energy-based models describe interconnections, dissipation and storage in mechanical, electrical or fluidic systems. Time delays—arising from signal transmission, computation or actuator dynamics—can undermine stability and degrade performance if not properly accounted for. Recent strategies leverage Lyapunov–Krasovskii functionals, passivity-based interconnection and damping assignment, sliding-mode techniques and homogeneous system theory to construct explicit control laws. Adaptive and robust schemes further compensate for parametric uncertainties, external disturbances and input saturations. A subclass known as predefined-time control ensures convergence within a user-specified horizon regardless of initial conditions. Key applications include networked robotic manipulators under communication delays, renewable-energy converters in wide-area power systems and environmental processes such as pollution dispersion control. By uniting rigorous mathematical guarantees with energy-shaping insights, finite-time controllers offer rapid response, enhanced disturbance rejection and resilience in complex, delayed Hamiltonian frameworks.
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Finite-Time Control for Nonlinear Time-Delay Hamiltonian Systems publication trend
The graph below shows the total number of articles in finite-time control for nonlinear time-delay hamiltonian systems across all publications each year (not limited to Nature Index journals).
Technical terms
Hamiltonian system: A mathematical model describing energy storage and exchange in conservative or dissipative physical systems, defined by a Hamiltonian (total energy) function.
Port-controlled Hamiltonian (PCH) system: An interconnection framework that represents subsystems and their energy ports, facilitating passivity-based control design through energy shaping.
Finite-time control: A control strategy that ensures system trajectories reach the desired equilibrium in a strictly bounded time rather than asymptotically.
Time-delay: A lag between cause and effect in a system’s state or input, often due to transmission, measurement or actuator dynamics.
Lyapunov–Krasovskii functional: An extension of Lyapunov functions incorporating integral terms to account for the influence of time delays on system stability.
References
- Adaptive predefined-time robust control for nonlinear time-delay systems with different power Hamiltonian functions. AIMS Mathematics (2023).
- Finite-time stabilization and H∞ control of Port-controlled Hamiltonian systems with disturbances and saturation. PLOS ONE (2021).
- Stability of port-Hamiltonian systems with mixed time delays subject to input saturation. Nonlinear Analysis Modelling and Control (2023).
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