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.