Adaptive state-feedback stabilization for a large class of high-order stochastic nonlinear systems

Under the more general conditions on the power order and the nonlinear functions, this paper investigates the problem of adaptive state-feedback stabilization for a class of high-order stochastic nonlinear systems with time-varying control coefficients. Based on the backstepping design method and homogeneous domination technique, the closed-loop system can be proved to be globally stable in probability and the states can be regulated to the origin almost surely. The efficiency of the state-feedback controller is demonstrated by a simulation example.     

Adaptive state-feedback stabilization for a class of high-order nonlinear uncertain systems

For high-order nonlinear uncertain systems, there have been a lot of investigations under a strong assumption that the lower bounds of the unknown control coefficients should be exactly known. In this paper, this assumption is removed and a unified approach is developed to systematically construct a state-feedback adaptive stabilizing control law for a class of high-order nonlinear uncertain systems with unknown control coefficients. By using the method of the so-called adding a power integrator merging with adaptive technique, a recursive design procedure is provided to achieve a smooth adaptive state-feedback control law, which guarantees that the closed-loop system is globally uniformly stable while the original system states globally asymptotically converge to zero. Finally, a simulation example is given to illustrate the correctness of the theoretical results.     

Adaptive control of nonlinear systems with nonlinear parameterization

An adaptive feedback regulation scheme is proposed for a class of single input nonlinear systems, with nonlinear parameterizations. A proof of local regulation is given. The results are validated through a simulation study.     

Adaptive global stabilization of nonholonomic systems with strong nonlinear drifts

A new input-to-state scaling scheme is first introduced to transform a class of nonholonomic systems in a chained form with strong nonlinear drifts and unknown constant parameters into a strict feedback form. The backstepping technique is then applied to design a global adaptive stabilization controller. A switching strategy based on the control input magnitude rather than the time is derived to get around the phenomenon of uncontrollability. Simulation examples validate the effectiveness of the proposed controller.     

Adaptive stabilization of multi-input nonlinear systems

Universal stabilizers are presented for two classes of nonlinear systems, linear in their multiple control inputs: (I) a class of pth order controlled differential inclusions on R″ with full state available for feedback, and (II) a class of nonlinearly perturbed linear systems with restricted state availability. The stabilizers are of a discontinuous feedback form (embedded in a set-valued map), and incorporate adaptive matrix-valued gain functions which exploit the existence of finite spectrum-unmixing sets associated with the systems under consideration. The analysis draws on an extension, to differential inclusions, of LaSalle's invariance principle for ordinary differential equations.     

一类高阶次随机非线性系统的输出反馈镇定

针对一类高阶次随机非线性系统,研究其输出反馈镇定问题．通过选择有效的观测器和李雅普诺夫函数,所设计的光滑输出反馈控制器保证了闭环系统的平衡点是依概率全局渐近稳定的,输出几乎处处调节到零．数值仿真验证了控制方案的有效性．     

Adaptive estimation of discrete-time systems with nonlinear parameterization

This paper concerns adaptive estimation of dynamic systems which are nonlinearly parameterized. A majority of adaptive algorithms employ a gradient approach to determine the direction of adjustment, which ensures stable estimation when parameters occur linearly. These algorithms, however, do not suffice for estimation in systems with nonlinear parameterization. We introduce in this paper a new algorithm for such systems and show that it leads to globally stable estimation by employing a different regression vector and selecting a suitable step size. Both concave/convex parameterizations as well as general nonlinear parameterizations are considered. Stable estimation in the presence of both nonlinear parameters and linear parameters which may appear multiplicatively is established. For the case of concave/convex parameterizations, parameter convergence is shown to result under certain conditions of persistent excitation.     

Finite-time state-feedback control for a class of stochastic high-order nonlinear systems

This paper discusses the problem of global finite-time stabilization in probability for a class of stochastic high-order nonlinear systems whose drift and diffusion terms satisfy lower-triangular growth conditions. By adopting adding one power integrator technique and constructing twice continuous differential Lyapunov functions, a continuous state-feedback controller is recursively designed. Based on stochastic finite-time stability theorem, it is proved that the solution of the closed-loop system is finite-time stable in probability. Several simulation examples are given to illustrate the effectiveness of the proposed design procedure.     

Output-feedback stabilization for stochastic high-order nonlinear systems with time-varying delay

This paper investigates output-feedback control for a class of stochastic high-order nonlinear systems with time-varying delay for the first time. By introducing the adding a power integrator technique in the stochastic systems and a rescaling transformation, and choosing an appropriate Lyapunov-Krasoviskii functional, an output-feedback controller is constructed to render the closed-loop system globally asymptotically stable in probability and the output can be regulated to the origin almost surely. A simulation example is provided to show the effectiveness of the designed controller.     

Adaptive stabilization of time-delay feedforward nonlinear systems

In this paper, we consider the adaptive stabilization problem for feedforward nonlinear systems with time delays. An adaptive stabilizer is proposed. Our stabilizer takes a nested saturation feedback, and a set of switching logics is designed to tune online the saturation levels in a piecewise constant or switching manner. It has been shown that under our proposed control, all closed-loop states are bounded and asymptotic regulation is achieved.     

Adaptive control of a class of nonlinear systems with convex/concave parameterization

This paper deals with adaptive control of a class of second-order nonlinear systems with a triangular structure and convex/concave parameterization. In Annaswamy et al. (Automatica 33(11) (1998) 1975–1995) it was shown that nonlinearly parameterized systems that satisfy certain matching conditions can be adaptively controlled in a stable manner. In this paper, we relax these matching conditions and include additional dynamics between the nonlinearities and the control input. Global boundedness and convergence to within a desired precision is established. No overparameterization of the adaptive controller is required.     

Further results on adaptive state-feedback stabilization for stochastic high-order nonlinear systems

This paper aims to relax the results in Xie and Tian (2009) from the following two aspects: completely removing the power order restriction and largely relaxing the growth conditions of nonlinear functions. By using the backstepping design method and homogeneous domination technique, this paper investigates the problem of adaptive state-feedback stabilization for a class of stochastic high-order nonlinear systems with nonlinear parameterization. The closed-loop system can be proved to be globally stable in probability and the states can be regulated to the origin almost surely. The efficiency of the adaptive state-feedback controller is demonstrated by a simulation example.     

Adaptive stabilization of a class of uncertain switched nonlinear systems with backstepping control

In this paper, we focus on the problem of adaptive stabilization for a class of uncertain switched nonlinear systems, whose non-switching part consists of feedback linearizable dynamics. The main result is that we propose adaptive controllers such that the considered switched systems with unknown parameters can be stabilized under arbitrary switching signals. First, we design the adaptive state feedback controller based on tuning the estimations of the bounds on switching parameters in the transformed system, instead of estimating the switching parameters directly. Next, by incorporating some augmented design parameters, the adaptive output feedback controller is designed. The proposed approach allows us to construct a common Lyapunov function and thus the closed-loop system can be stabilized without the restriction on dwell-time, which is needed in most of the existing results considering output feedback control. A numerical example and computer simulations are provided to validate the proposed controllers.     

Delay-dependent stabilization of stochastic interval delay systems with nonlinear disturbances

In this paper, a delay-dependent approach is developed to deal with the robust stabilization problem for a class of stochastic time-delay interval systems with nonlinear disturbances. The system matrices are assumed to be uncertain within given intervals, the time delays appear in both the system states and the nonlinear disturbances, and the stochastic perturbation is in the form of a Brownian motion. The purpose of the addressed stochastic stabilization problem is to design a memoryless state feedback controller such that, for all admissible interval uncertainties and nonlinear disturbances, the closed-loop system is asymptotically stable in the mean square, where the stability criteria are dependent on the length of the time delay and therefore less conservative. By using Itô's differential formula and the Lyapunov stability theory, sufficient conditions are first derived for ensuring the stability of the stochastic interval delay systems. Then, the controller gain is characterized in terms of the solution to a delay-dependent linear matrix inequality (LMI), which can be easily solved by using available software packages. A numerical example is exploited to demonstrate the effectiveness of the proposed design procedure.     

Further results on state feedback stabilization of stochastic high-order nonlinear systems

In this paper,a combined homogeneous domination and sign function design approach is presented to state feedback control for a class of stochastic high-order nonlinear systems with time-varying delay.The use of the combined approach relaxes the restriction on nonlinear functions and makes the closed-loop system globally asymptotically stable in probability.     

Finite-time output feedback stabilization of high-order uncertain nonlinear systems

This paper studies the problem of finite-time output feedback stabilization for a class of high-order nonlinear systems with the unknown output function and control coefficients. Under the weaker assumption that output function is only continuous, by using homogeneous domination method together with adding a power integrator method, introducing a new analysis method, the maximal open sector Ω of output function is given. As long as output function belongs to any closed sector included in Ω, an output feedback controller can be developed to guarantee global finite-time stability of the closed-loop system.     

Global stabilization of nonlinear cascade systems

We present sufficient conditions for the global stabilizability of two cascade connected nonlinear systems. These are based on general results concerning global asymptotic stability of triangular systems which are proved in the last section. For polynomial systems, in particular, the stabilizing feedback is given explicitly.     

Output-feedback stabilization of stochastic nonlinear systems driven by noise of unknown covariance

We address the class of stochastic output-feedback nonlinear systems driven by noise whose covariance is time varying and bounded but the bound is not known a priori. This problem is analogous to deterministic disturbance attenuation problems. We first design a controller which guarantees that the solutions converge (in probability) to a residual set proportional to the unknown bound on the covariance. Then, for the case of a vanishing noise vector field, we design an adaptive controller which, besides global stability in probability, guarantees regulation of the state of the plant to zero with probability one.     

Adaptive observer-based control for a class of nonlinear stochastic systems

In this paper, the adaptive state estimation and state-feedback stabilization problems for a class of nonlinear stochastic systems with unknown constant parameters are studied. The sequential design methods are proposed to construct the adaptive controllers. Adaptive state and parameter estimators are designed by using a stochastic Lyapunov method and the separation theory of the design for the state-feedback gain and observer gain, which guarantees that the closed-loop system is asymptotically stable in the mean-square sense. Sufficient conditions for the existence of parameters estimator are given in terms of linear matrix inequalities. Finally, the numerical examples are provided to illustrate the feasibility of the proposed theoretical results.     

Adaptive backstepping with a high-order tuner

The paper proposes a new type of adaptive backstepping design. At each step of the design procedure a virtual control directly counteracts the transients of adjustable parameters, while the time derivatives of these parameters up to the desired order are generated by a special adaptation law (high-order tuner) defined at the final step. Thus, the proposed approach combines adaptive backstepping with high-order tuners. The resultant control law does not involve tuning functions and, at the same time, is free of overparametrization.