Control of Stochastic Nonlinear Switched Systems using Fuzzy Law

The problem about controller design for stochastic nonlinear switched systems with delay is considered. Stochastic switched nonlinear system is a kind of nonlinear system which integrates switching and nonlinear fuzzy characteristics and can fully reflect stochastic factors. First, the mathematical model of stochastic nonlinear switched systems with time delay and disturbance is given. Second, the corresponding controller is designed for the proposed model. Then, we use the multi-Lyapunov method to establish the closed-loop system on the basis of our designed controller, and give the necessary and sufficient conditions for the stability of the system. The switching law is designed to ensure the stability of subsystems activated by switching time. Finally, through the simulation software, we can see that the stability condition we obtained can make the studied system stable.

Robust tracking control of robot manipulators with friction and variable loads without velocity measurement: A switched control strategy

This article addresses the adaptive-based robust output feedback tracking control for robot manipulators with friction and alternating unknown loads. A switched nonlinear system is first established to model the friction and parameter variations, caused by the load change. Under arbitrary load changings, an adaptive [Formula: see text] tracking control strategy is proposed to ensure link position tracking, in the presence of uncertainties and external disturbances. Then, for bounded external disturbances, a novel robust adaptive output tracking control strategy is developed, which guarantees all the closed-loop signals are bounded and tracking error is driven to zero. Unlike some previous studies, the proposed algorithms do not require velocity measurements, and the unknown switched parameters and disturbances are neither required to be periodic nor to have known bounds. A simulation study is also given to demonstrate the analytically proved properties of the proposed schemes.

Incremental passivity and stabilization for switched nonlinear systems

This paper studies the problems of incremental passivity, incremental passification and incremental stabilization for a switched nonlinear system. First, an incremental passivity concept for switched nonlinear systems is proposed. Each subsystem is only required to be incrementally passive, when it is active. The energy change of each inactive subsystem is charaterized. Then, a sufficient condition for such a system to be incrementally passive is given. Second, a state-dependent switching law and state feedback controllers are designed to render a system with relative degree one incrementally passive. Third, we show that an incrementally passive switched nonlinear system can be incrementally stabilized under some constraints on the energy change of inactive subsystems. In particular, a recursive feedback incremental passification design technique is adopted to achieve the incremental stability for a switched nonlinear system with any same relative degree by designing a set of feedback controllers and a state-dependent switching law, constructively. Finally, two examples are provided to verify the effectiveness of the proposed theory.

Variable-Structure Near-Space Vehicles with Time-Varying State Constraints Attitude Control Based on Switched Nonlinear System

This study is concerned with the attitude control problem of variable-structure near-space vehicles (VSNSVs) with time-varying state constraints based on switched nonlinear system. The full states of vehicles are constrained in the bounded sets with asymmetric time-varying boundaries. Firstly, considering modeling uncertainties and external disturbances, an extended state observer (ESO), including two distinct linear regions, is proposed with the advantage of avoiding the peaking value problem. The disturbance observer is utilized to estimate the total disturbances of the attitude angle and angular rate subsystems, which are described in switched nonlinear systems. Then, based on the estimation values, the asymmetric time-varying barrier Lyapunov function (BLF) is employed to construct the active disturbance rejection controller, which can ensure the full state constraints are not violated. Furthermore, to resolve the ‘explosion of complexity’ problem in backstepping control, a modified dynamic surface control is proposed. Rigorous stability analysis is given to prove that all signals of the closed-loop system are bounded. Numerical simulations are carried out to demonstrate the effectiveness of the proposed control scheme.