Zhaojing Wu

Tracking controller design for random nonlinear benchmark system

Abstract This paper considers a benchmark system consisting of a rolling ball and a moving car in the oscillating surroundings. By using the Lagrange law, the dynamic model without disturbance is first constructed, then according to the relative motion principle, random oscillation of surroundings is transformed into the random noises in the constructed Lagrange equation. The special structure of the quasi-lower triangle of Lagrange equation motivates us to pay more attention to the vectorial backstepping technique. By selecting an appropriate Lyapunov-like function, a tracking controller with tunable parameters is designed such that all signals of the closed-loop system are bounded and track error can be made arbitrarily small.

Adaptive output-feedback control for stochastic nonlinear systems with zero dynamics

A class of stochastic nonlinear systems with unknown bounded parameters and zero dynamics are considered in this paper. By a series of coordinate changes, the original system is re-parameterized, which is suit for using the reduced-order observer and 1-dimension adaptive law to reduce the dynamic order of closed-loop system. In adaptive backstepping design, the quadratic and the quartic Lyapunov functions are presented simultaneously to reduce the static order of nonlinearities. It is shown that all the solutions of the closed-loop system are regulated to an arbitrarily small neighborhood of the origin in probability. Due to the order reduction of the controller, the design scheme in this paper has more practical values. A simulation example demonstrates the control scheme.

Random Modeling and Control of Nonlinear Active Suspension

For a quarter car with nonlinear active suspension in rough road, the problem of random modeling and control is considered. According to the relative motion principle, the influence of rough road can be seen as that force is disturbed by the noise and a random model is constructed. By an appropriate transform, the model is transformed into a lower triangular system, which can be used as backstepping method. Then a controller is designed such that the mean square of the state converges to an arbitrarily small neighborhood of zero by tuning design parameters. The simulation results illustrate the effectiveness of the proposed scheme. Therefore, the active suspension system offers better riding comfort and vehicle handing to the passengers.

Stochastic position control for Permanent Magnet Synchronous Motor

This paper considers the problem of stochastic position control for Permanent Magnet Synchronous Motors( PMSM). The work of this paper is two-fold. Firstly, by adding the winer process to the voltage and adding the markov process to the load torque, a more realistic model of PMSM is proposed. Secondly, by using the backstepping design technique, the closed-loop system has a unique solution that is bounded in probability and L4-norm of the tracking error converges to an arbitrarily small neighborhood of the origin in probability.

Stochastic control of semi-active suspension system

In this paper, for automobile semi-active suspension in rough road, the problems of random modeling and control are considered. First, dynamics model is constructed assuming the road being flat. According to the dynamic-static method and the relative-motion principle, the road irregularities is transformed to disturbance to the control. Thus, the random dynamic model of the system is established. Second, the system is transformed into a lower triangular system by an appropriate transform. Using backstepping method and Lyapunov theory, a controller is designed such that the closed-loop system is noise-to-state stability in probability(NSS-P) and the mean square of the state converges to an arbitrarily small neighborhood of zero, which means that the passengers feel much comfortable. Finally, the simulation experiment is carried out by Matlab. The simulation results show the effectiveness of the control strategy.

Tracking controller design for random nonlinear TORA system

This paper considers a TORA system consists of a rolling ball and a moving car in the oscillating surroundings. By using the Lagrangian law, the dynamic model without disturbance is constructed. According to the relative motion principle, stochastic oscillations of surroundings are transformed into the random noises in the constructed Lagrange equation. The special structure of the quasi lower triangle of Lagrange equation motivates us pay more attentions to find a vectorial backstepping controller. By selecting an appropriate Lyapunov-like function, a backstepping controller with tunable parameters is designed such that all signals of the closed-loop system are bounded and track error can be made arbitrarily small.

Output feedback control based on augmented observer for random system

In this paper, for a class of nonlinear systems with stationary processes and modeling errors, an observer-based backstepping controller is designed. The main work consists of three aspects. First, an augmented observer is constructed to estimate the unmeasurable states and the modeling errors; Second, an output-feedback controller is designed by using the integrator backstepping approach; Third, it is proved that the output can be regulated to an arbitrarily small neighborhood of the origin and all the other signals in the closed-loop system are bounded in probability. A simulation example is presented to demonstrate reasonability and efficiency of the proposed method.

Adaptive tracking control for a class of random nonlinear systems

Different with nonlinear systems described by Itó integral (or differential) equations, the model in form of RDSs with uncertain parameters is researched in this paper. Compared with the traditional methods of stochastic backstepping control, which focus the attentions on Hessian terms caused by Brown motions, an adaptive backstepping control scheme is designed to perform the task of output-tracking, by adopting separation technique. It is proved that the tracking error can be made arbitrarily small and all other signals are bounded in probability. A numerical simulation example is presented to explain the reasonability of the proposed method.

Stabilization of random nonlinear systems with unmodeled dynamics

A class of nonlinear systems described by random differential equations (RDEs) in the presence of unmodeled dynamics are considered in this paper. Under the assumption of unmodeled dynamics having enough stability margin, a feedback stabilization controller is consecutively designed by backstepping method and separation technique. The method of ordinary differential equations is used to analyze the stability of the closed-loop system. It is shown that the closed-loop system is noise-to-state stable in probability (NSS-P) and the system can be stabilized in some sense. Finally, a simulation example is used to illustrate the validity of our results.

Stability of a class of stochastic switched systems with time delays

In this paper, the problem of stochastic switched systems with time delay is investigated. To study the existence of the solution to the switched system with time delay by means of Itos formula, it is critical to show switching moments as stopping times. For switching law caused by overlapping active regions, the solution of the switched system is constructed and a stability criterion of the equilibrium is presented. The significance of the work in this paper is that all the results depend on some easily-verified assumptions that are as elegant as those in the deterministic case.