An Exploration on Adaptive Iterative Learning Control for a Class of Commensurate High-order Uncertain Nonlinear Fractional Order Systems

This paper explores the adaptive iterative learning control method in the control of fractional order systems for the first time. An adaptive iterative learning control(AILC) scheme is presented for a class of commensurate high-order uncertain nonlinear fractional order systems in the presence of disturbance.To facilitate the controller design, a sliding mode surface of tracking errors is designed by using sufficient conditions of linear fractional order systems. To relax the assumption of the identical initial condition in iterative learning control(ILC), a new boundary layer function is proposed by employing MittagLeffler function. The uncertainty in the system is compensated for by utilizing radial basis function neural network. Fractional order differential type updating laws and difference type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. The hyperbolic tangent function and a convergent series sequence are used to design robust control term for neural network approximation error and bounded disturbance, simultaneously guaranteeing the learning convergence along iteration. The system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapnov-like composite energy function(CEF)containing new integral type Lyapunov function, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.

Bifurcation of piecewise-linear nonlinear vibration system of vehicle suspension

A kinetic model of the piecewise-linear nonlinear suspension system that consists of a dominant spring and an assistant spring is established. Bifurcation of the resonance solution to a suspension system with two degrees of freedom is investigated with the singularity theory. Transition sets of the system and 40 groups of bifurcation diagrams are obtained. The local bifurcation is found, and shows the overall character- istics of bifurcation. Based on the. relationship between parameters and the topological bifurcation solutions, motion characteristics with different parameters are obtained. The results provides a theoretical basis for the optimal control of vehicle suspension system parameters.

Safety Verification of Semi-Algebraic Dynamical Systems via Inductive Invariant

To verify the safety of nonlinear dynamical systems based on inductive invariants, key issues include defining the most complete inductive condition and discovering an inductive invariant that satisfies the specified inductive condition. In this paper, to lay a solid foundation for future research into the safety verification of semi- algebraic dynamical systems, we first establish a formal framework for evaluating the quality of continuous inductive conditions. In addition, we propose a new complete and computable inductive condition for verifying the safety of semi-algebraic dynamical systems. Compared with the existing complete and computable inductive condition, this new inductive condition can be easily adapted to achieve a set of sufficient inductive conditions with different level of conservativeness and computational complexity, which provides us with a means to trade off between the verification power and complexity. These inductive conditions can be solved by quantifier elimination and SMT solvers.

Universal Adaptive Observerfor Nonlinear Time varying Deterministic Systems

Designing adaptive observers for MIMO nonlinear time varying deterministic systems is an open problem .Inthis papera novelsolutiontothis problem is given byuse ofa “strongtrackingfilter(STF)”.First,the STFis outlined,then sometechnicalpoints ofview to usethe STFas an adaptive observer are discussed .Finally, two typicalexamples are presentedtoillustrate the effectiveness ofthe proposed approach.