State feedback stabilization for high-order stochastic nonlinear systems with zero dynamics

In this paper, for a class of high-order stochastic nonlinear systems with zero dynamics which are neither necessarily feedback linearizable nor affine in the control input, the problem of state feedback stabilization is investigated for the first time. Under some weaker assumptions, a smooth state feedback controller is designed, which ensures that the closed-loop system has an almost surely unique solution on [0,∞）, the equilibrium at the origin of the closed-loop system is globally asymptotically stable in probability, and all the states can be regulated to the origin almost surely. A simulation example demonstrates the control scheme.

Ill-conditioned stable inversion arising from singularly perturbed zero dynamics

The ill-conditioned stable inversion is studied for slightly nonminimum phase systems whose zero dynam- ics is singularly perturbed, that is, the relative degree is ill-defined. For these systems, we show that there exists an inherent limitation in the bandwidth of a reference trajectory to be tracked when a well-conditioned feedforward input via stable inversion is sought. We assert that, when the violation of this limitation occurs, the so-called reference trajectory redesign is called for. Our analysis results can provide an explicit assessment as well as useful guidance for the reference trajectory redesign if needed.

Construction of Control Lyapunov Functions for a Class of Nonlinear Systems

The construction of control Lyapunov functions for a class of nonlinear systems is considered. We develop a method by which a control Lyapunov function for the feedback linearizable part can be constructed systematically via Lyapunov equation. Moreover, by a control Lyapunov function of the feedback linearizable part and a Lyapunov function of the zero dynamics, a control Lyapunov function for the overall nonlinear system is established.

Output feedback stabilization for stochastic nonlinear systems in observer canonical form with stable zero-dynamics

In this paper, we study the problem of output feedback stabilization for stochastic nonlin-ear systems. We consider a class of stochastic nonlinear systems in observer canonical form with sta-ble zero-dynamics. We introduce a sequence of state transformations that transform the system into a lower triangular structure that is amenable for integrator backstepping design. Then we design the out-put-feedback controller and prove that the closed-loop system is bounded in probability. Furthermore, when the disturbance vector field vanishes at the origin, the closed-loop system is asymptotically stable in the large. With special care, the controller preserves the equilibrium of the nonlinear system. An ex-ample is included to illustrate the theoretical findings.

A Nonlinear Coordinated Approach to Enhance the Transient Stability of Wind Energy-Based Power Systems

This paper proposes a novel framework that enables the simultaneous coordination of the controllers of doubly fed induction generators(DFIGs) and synchronous generators(SGs).The proposed coordination approach is based on the zero dynamics method aims at enhancing the transient stability of multi-machine power systems under a wide range of operating conditions. The proposed approach was implemented to the IEEE39-bus power systems. Transient stability margin measured in terms of critical clearing time along with eigenvalue analysis and time domain simulations were considered in the performance assessment. The obtained results were also compared to those achieved using a conventional power system stabilizer/power oscillation(PSS/POD) technique and the interconnection and damping assignment passivity-based controller(IDA-PBC). The performance analysis confirmed the ability of the proposed approach to enhance damping and improve system’s transient stability margin under a wide range of operating conditions.

Nonlinear Control for Autonomous Underwater Glider Motion Based on Inverse System Method

Autonomous underwater gliders are highly effcient,buoyancy-driven,winged autonomous underwater vehicles. Their dynamics are multivariable nonlinear systems. In addition,the gliders are underactuated and diffcult to maneuver,and also dependent on their operational environment. To confront these problems and to design an effective controller,the inverse system method was used to decouple the original system into two independent single variable linear subsystems. The stability of the zero dynamics was analyzed,and an additional closed-loop controller for each linear subsystem was designed by sliding mode control method to form a type of composite controller. Simulation results demonstrate that the derived nonlinear controller is able to cope with the aforementioned problems simultaneously and satisfactorily.

Nonlinear Sampled-Data Systems with a Generalized Hold Polynomial-Function for Fast Sampling Rates

It is well-known that such non-conventional digital control schemes,such as generalized sampled-data hold functions,have clear advantages over the conventional single-rate digital control systems.However,they have theoretical negative aspects that deviation of the input can lead to intersample oscillations or intersample ripples.This paper investigates the zero dynamics of sampleddata models,as the sampling period tends to zero,composed of a new generalized hold polynomial function,a nonlinear continuous-time plant and a sampler in cascade.For a new design of generalized hold circuit,the authors give the approximate expression of the resulting sampled-data systems as power series with respect to a sampling period up to the some order term on the basis of the normal form representation for the nonlinear continuous-time systems,and remarkable improvements in the stability properties of discrete system zero dynamics may be achieved by using proper adj us tment.Of particular interest are the stability conditions of sampling zero dynamics in the case of a new hold proposed.Also,an insightful interpretation of the obtained sampled-data models can be made in terms of minimal intersample ripple by design,where the ordinary multirate sampled systems have a poor intersample behavior.It has shown that the intersample behavior arising from the multirate input polynomial function can be localised by appropriately selecting the design parameters based on the stability condition of the sampling zero dynamics.The results presen ted here generalize the well-known notion of sampling zero dynamics from the linear case to nonlinear systems.

Quadratic stabilization of switched nonlinear systems

In this paper, the problem of quadratic stabilization of multi-input multi-output switched nonlinear systems under an arbitrary switching law is investigated.When switched nonlinear systems have uniform normal form and the zero dynamics of uniform normal form is asymptotically stable under an arbitrary switching law, state feedbacks are designed and a common quadratic Lyapunov function of all the closed-loop subsystems is constructed to realize quadratic stabilizability of the class of switched nonlinear systems under an arbitrary switching law.The results of this paper are also applied to switched linear systems.