In this paper, we consider bifurcation analysis of nonlinear uncertain dynamical systems. A concept of robust bifurcation analysis is proposed. To this end, we give robust stability and robust instability conditions for uncertain feedback systems. Then, we propose a novel method for robust bifurcation analysis of systems with dynamic uncertainties. Finally, we carry out bifurcation analysis of an uncertain gene regulatory network model as an example.
This paper considers a problem to transfer a trajectory from one zero dynamics submanifold to another one in finite time, for a time-invariant nonlinear system. In general, it is preferred to keep a trajectory on a zero dynamics submanifold when partial feedback linearization is applied to. Hence, this paper proposes a method to keep a trajectory on zero dynamics submanifold during the transfer by using time-varying zero dynamics submanifold. Main contribution is to develop the condition for time-varying linearizing coordinate to connect two zero dynamics submanifolds with the same dimension. The validity of the controller based on the proposed method is verified via numerical simulations of mono-rotor unmanned aerial vehicle (UAV) system and Acrobot system.
In this paper, we deal with physical experiments of tracking control for the trident snake robot with the transverse function(TF) approach. The TF approach was originally proposed by Morin and Samson (2002) that is supposed to applicable to the systems evolving on Lie groups with left-invaliant control vector fields. The control objective is to practically stabilize any given reference trajectory in the space of planar rigid motions (SE(2)) while avoiding mechanical singularities. In the authors’ previous works, the tracking control of the trident snake robot with this approach was validated in terms of improvements of control smoothness and stability by several simulations. However, experimental verification is not conducted yet. In this paper, therefore, the usability of TF approach is examined by several experiments.
In this paper, we consider the optimal servo design problems of the systems with input norm constraints. We propose a new method to design nonlinear optimal servo controllers satisfying the input norm constraints. This method is based on solving Hamilton-Jacobi equations via center-stable manifold theory. We verify the effectiveness of the proposed method by a computer simulation by using Permanent Magnet Synchronous Motor.
This paper derives a passivity defined in the neighborhood of a non-degenerate critical point of energy functions of systems on compact manifolds from which analytical solutions cannot be always derived, e.g., systems of nonlinear partial differential equations, but the energy can be regarded as a Morse function. We first show that the change in energy of the systems defined on a closed domain in the neighborhood can be transformed into an energy flow defined on a boundary of the domain in terms of the boundary integrability of Stokes theorem. Next, this boundary power balance is detailed by using the index of the critical points; therefore, it can be considered as the extended passivity.
This paper presents a nonlinear model, involving load-dependent parameters, of a McKibben pneumatic artificial muscle system that includes a proportional directional control valve, and also proposes a partially heuristic but reasonable procedure for identifying nine key parameters characterizing transient and steady state behaviors of the system. And then, this paper validates the obtained model and illustrates how it can simulate the real under several loads, comparing with experimental data.
This paper considers a boundary stabilization problem of systems described by boundary coupled two one-dimensional parabolic partial differential equations based on the backstepping method. Unlike the conventional backstepping framework, we propose a state transformation that contains the state of the unforced subsystem partially. It is proved that this transformation is well-defined and converts the original system into an exponentially stable system together with an associated state feedback control law under a condition that ensures the stability of the unforced subsystem. The original system with this control law inherits the stability of the transfomed one. The effectiveness of the obtained control law is demonstrated numerically.
This paper discusses passivity-based boundary controls of flexible beams with large deformations in terms of a distributed parameter port-Hamiltonian system. Distributed parameter systems have been mainly studied from the viewpoint of analytical methods. However, analytical solutions cannot be always derived from nonlinear distributed parameter systems such as the flexible beam. A distributed parameter port-Hamiltonian system is a standard control representation that can be applied to such a complex system without model reductions. The passivity-based boundary controls consist of boundary damping assignment and boundary energy shaping. Inputs and outputs for the controls are systematically derived from the system representation. Finally, we illustrate numerical results of the controls for stabilizing the flexible beam and shaping its potential energy.