This paper addresses the design problem of practical (or satisfaction) output-feedback controls for stochastic strict-feedback nonlinear systems in observer canonical form with stable zerodynamics under long-term average tracking risk-sensitive cost criteria. The cost function adopted here is of the quadratic-integral type usually encountered in practice, rather than the quartic-integral one used to avoid difficulty in control design and performance analysis of the closed-loop system. A sequence of coordinate diffeomorphisms is introduced to separate the zero-dynamics from the entire system, so that the transformed system has an appropriate form suitable for integrator backstepping design. For any given risk-sensitivity parameter and desired cost value, by using the integrator backstepping methodology, an output-feedback control is constructively designed such that (a) the closed-loop system is bounded in probability and (b) the long-term average risk-sensitive cost is upper bounded by the desired value. In addition, this paper does not require the uniform boundedness of the gain functions of the system noise. Furthermore, an example is given to show the effectiveness of the theory.

In this paper, we investigate the stabilization control design problem of nonlinear stochastic SISO systems in strictfeedback form. By introducing a novel reduced-order observer, an output-feedback-based control is constructively designed, which renders the closed-loop system asymptotically stable in the large when the nonlinearities and stochastic disturbance equal zero at the equilibrium point of the open-loop system, and bounded in probability, otherwise. Besides, the obtained controller preserves the equilibrium point of the open-loop nonlinear system.

A minimal-order observer and output-feedback stabilization control are given for single-input multi-output stochastic nonlinear systems with unobservable states, unmodelled dynamics and stochastic disturbances. Based on the observer designed, the estimates of all observable states of the system are given, and the convergence of the estimation errors are analyzed. In addition, by using the integrator backstepping approach, an output-feedback stabilization control is constructively designed, and suf cient conditions are obtained under which the closed-loop system is asymptotically stable in the large or bounded in probability, respectively.

In this note, we study the problem of output-feedback control design for a class of strict feedback stochastic nonlinear systems. Under an infinite-horizon risk-sensitive cost criterion, the controller designed can guarantee an arbitrary small long-term average cost for arbitrary risk-sensitivity parameter and achieve boundedness in probability for the closed-loop system, using the integrator backstepping methodology. Furthermore, the controller preserves the equilibrium at the origin of the nonlinear system.

In this paper, the design problem of satisfaction output feedback controls for stochastic nonlinear systems in strict feedback form under long-term tracking risk-sensitive index is investigated. The index function adopted here is of quadratic form usually encountered in practice, rather than of quartic one used to beg the essential difficulty on controller design and performance analysis of the closed-loop systems. For any given risk-sensitive parameter and desired index value, by using the integrator backstepping method, an output feedback control is constructively designed so that the closed-loop system is bounded in probability and the risk-sensitive index is upper bounded by the desired value.

In this paper, we study the problem of output feedback stabilization for stochastic nonlinear systems. We consider a class of stochastic nonlinear systems in observer canonical form with stable 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 output-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 example is included to illustrate the theoretical findings.

对一类具有不可观测状态、未建模动态特性和随机干扰的单输入多输出随机非线性系统，给出了最小阶状态观测器和输出反馈镇定控制器的设计方法。基于所设计的最小阶状态观测器，给出了系统全部状态的估计，分析了状态估计误差的收敛性。进一步，结合Back-Stepping法，构造性地设计出了输出反馈镇定控制，给出了闭环系统全局渐近稳定和概率意义下有界稳定的充分条件。

在无限时区跟踪型风险灵敏度（risk-sensmve）指标下，研究了一类严格反馈随机非线性系统的满意输出反馈控制问题。所用指标函数为实际中常见的二次型函数，而非为回避控制器设计及闭环系统性能分析的本质困难而采用的四次型函数。对任意给定的风险灵敏度参数和期望指标值，利用积分反推（integratorbackstepping）方法构造性地给出了一个输出反馈控制器，使得闭环系统在概率意义下有界，并且风险灵敏度指标不大于所给的期望值。

考虑了一类具有稳定零动态观测器特征型随机非线性系统的输出反馈镇定问题应用一系列的状态变换，将系统转化为下三角结构以便于应用积分反推设计方法设计控制器设计了输出反馈控制器，证明了闭环系统的概率意义下的有界性当扰动向量场在原点处消逝时，闭环系统为概率意义下渐近稳定此控制器还满足非线性系统的平衡条件。

研究了一类严格反馈随机非线性系统的输出反馈设计问题。在无限时区风险灵敏度指标下，应用积分反推（integratorbackstepping）技术，设计了控制器。所设计的控制器能够保障对任意风险灵敏度系数具有任意小的指标，并且闭环系统为概率意义下有界的。特别地，所设计的控制器还能保证控制器的平衡条件。仿真例子验证了理论结果的正确性。