Research On Feedback Control For A Class Of Uncertain Nonlinear Systems

Uncertain factors exist widespreadly in real systems, such as measurement drifts, parametric uncertain-ties, time-delays and stochastic disturbances, which inevitably affect systems’performance. Therefore, it is of great significance to investigate the feedback control problem for uncertain nonlinear systems from both theoretical and practical points of view. Based on the homogeneous system theory, Lyapunov stability theory and stochastic system theory, by adopting adding a power integrator technique, homogeneous domination approach and dynamic scaling gain method, this paper aims to address the state-feedback, output-feedback and adaptive feedback control problems for a class of uncertain generalized homogeneous nonlinear systems. The main contents are concluded as follows:First, the problem of designing a robust controller is addressed for the deterministic systems whose states cannot be precisely measured caused by the unknown drifts in the powers of the measurement functions. By adopting the concept of homogeneity with monotone degrees and revamping the technique of adding a power integrator, a new design procedure is introduced to recursively construct a generalized homogeneous controller with monotone degrees as well as a Lyapunov function with unknown parameters. The proposed robust controller is able to globally stabilize a family of nonlinear systems with different measurement drifts whose bounds can be determined by solving an optimization problem.Second, the feedback controller design schemes are discussed for the stochastic systems which are af-fected by time-delays, unknown parameters and some other uncertain factors.(1) The problem of universal output-feedback controller design is considered for the stochastic systems whose nonlinear terms satisfy lower-triangular linear growth conditions with unknown growth rates and time-delays. According to the universal control idea, a novel dynamic output-feedback controller is designed, whose dynamic gain is updated by the error signal between the system output and its estimate. Finally, based on the Lyapunov-Krasovskii functional and stochastic Barbalat’s lemma, it is proved that all the signals of the closed-loop system are strong bounded in probability and the system states converge to the origin almost surely.(2) With respect to the stochastic systems with unknown output gain and unknown nonlinear growth rates, a full-order homogeneous observer is constructed to estimate the unknown system states. Then, by combining the adding a power integrator technique and the adaptive control idea, an adaptive output-feedback controller is designed. It can be proved that the proposed output-feedback controller can regulate the system states to the origin almost surely according to the generalized stochastic Lyapunov stability theorem, which further removes the local Lipschitz condition on the stochastic nonlinear systems.(3) The problem of global finite-time control in probability is addressed for the stochastic systems whose drift and diffusion terms satisfy the lower-triangular homogeneous growth conditions. Based on the homo-geneous domination approach, a subtle nonsmooth observer and an output-feedback controller are proposed. Then, considering the stochastic systems with nonlinear parameterization, we employ the parameter separa- tion principle to set apart the nonlinear parameters from the nonlinear functions. With the help of the adding a power integrator technique and adaptive control method, a continuous adaptive state-feedback controller is obtained iteratively. Finally, according to the stochastic finite-time Lyapunov stability theorem, the system states can be regulated to the origin almost surely in a finite time.(4) In order to further relax the restrictions on system power orders and nonlinearities, the output-feedback stabilization problem is considered for a more general class of stochastic high-order nonlinear sys-tems with time-varying delays. On the basis of a subtle homogeneous observer and controller construction, and the homogeneous domination approach, the closed-loop system is globally asymptotically stable in proba-bility, by choosing an appropriate Lyapunov-Krasovskii functional. A numerical example is given to illustrate the effectiveness of the proposed design procedure.