Stochastic Strict-feedback Systems Research Articles

Adaptive NN Control of Input-Delayed Stochastic Nonlinear Systems With States and Input Quantization

In this article, the adaptive neural control problem is studied for the input-delayed stochastic nonlinear system that has both states and input quantization. The main difficulty is to deal with the discontinuity of the virtual control laws caused by states quantization, and to compensate the influence of the input quantization by building the relation between the control input and quantized input. Moreover, this paper considers a sector bounded quantizer and proposes a new adaptive neural network (NN) control algorithm to handle the problem of quantization errors cannot be automatically bounded. For the unknown function in stochastic strict-feedback systems, the radial basis function neural network (RBFNN) is utilized to approximate it. The Pade approximation technique is employed to tackle the issue of input delay. All the closed-loop signals can maintain semi-globally uniformly ultimately bounded (SGUUB) in probability under the constructed controller and quantizer. Lastly, the efficiency of the developed control method is evaluated by a simulation experiment.

Adaptive-gain observer-based stabilization of stochastic strict-feedback systems with sensor uncertainty

We study the adaptive output-feedback stabilization problem of stochastic strict-feedback systems with sensor uncertainty. Specifically, we consider the simultaneous presence of sensor uncertainty, unknown growth rate and stochastic disturbance, which has not been treated heretofore. By developing a new stochastic adaptive dual-domination approach, an adaptive observer and an output-feedback controller are designed, in which two gains are suitably selected to dominate the unknown sensor sensitivity and unknown growth rate, respectively. By using the nonnegative semimartingale convergence theorem, it is proved that the closed-loop system has an almost surely unique solution on [0,+∞) and that regulation to the equilibrium at the origin of the closed-loop system is achieved almost surely. Finally, two simulation examples are given to illustrate the control design.

Asymptotic Fuzzy Tracking Control for a Class of Stochastic Strict-Feedback Systems

This paper presents an asymptotic tracking control design method for stochastic strict-feedback systems via fuzzy logic systems. In the existing results, stochastic controls are usually limited to be bounded in probability. However, how to realize the asymptotic tracking control for stochastic strict-feedback systems remains a control dilemma. This paper achieves the asymptotic tracking control by proposing a novel gain suppressing inequality approach. Specifically, the three-part construction is performed to achieve such control objective for stochastic systems. First, the novel gain suppressing inequality technique is developed to lay the foundation for carrying out the Lyapunov stability analysis. Second, the developed inequality technique is integrated with each step of the backstepping-based adaptive control design procedure. Third, analyses are provided to realize the asymptotic tracking control of stochastic strict-feedback systems.

Adaptive neural control for a class of stochastic nonlinear systems by backstepping approach

This paper addresses adaptive neural control for a class of stochastic nonlinear systems which are not in strict-feedback form. Based on the structural characteristics of radial basis function (RBF) neural networks (NNs), a backstepping design approach is extended from stochastic strict-feedback systems to a class of more general stochastic nonlinear systems. In the control design procedure, RBF NNs are used to approximate unknown nonlinear functions and the backstepping technique is utilized to construct the desired controller. The proposed adaptive neural controller guarantees that all the closed-loop signals are bounded and the tracking error converges to a sufficiently small neighborhood of the origin. Two simulation examples are used to illustrate the effectiveness of the proposed approach.

Direct adaptive neural control for strict-feedback stochastic nonlinear systems

This note considers the problem of direct adaptive neural control for a class of nonlinear single-input/single-output (SISO) strict-feedback stochastic systems. The variable separation technique is introduced to decompose the coefficient functions of the diffusion term. Radical basis function (RBF) neural networks are used to approximate unknown and desired control signals, then a novel direct adaptive neural controller is constructed via backstepping. The proposed adaptive neural controller guarantees that all the signals in the closed-loop system remain bounded in probability. A main advantage of the proposed controller is that it contains only one adaptive parameter needed to be updated online. Simulation results demonstrate the effectiveness of the proposed approach.

Decentralized risk-sensitive controller design for strict-feedback systems

This paper studies decentralized control of uncertain systems. The class of systems focused on is a set of stochastic strict-feedback systems which interact through their outputs, and performance is measured with respect to a risk sensitive cost criterion. The unknown nonlinear interconnection terms are assumed to be bounded by some known functions of the outputs of the subsystems, multiplied by some unknown parameters. The controllers designed for each subsystem have access only to the information available with regard to the respective subsystem, and they achieve an arbitrarily small value for the risk-sensitive cost for the overall system. Under this completely decentralized control scheme, all closed-loop signals remain bounded in probability.

Stabilization of stochastic nonlinear systems driven by noise of unknown covariance

This paper poses and solves a new problem of stochastic (nonlinear) disturbance attenuation where the task is to make the system solution bounded by a monotone function of the supremum of the covariance of the noise. This is a natural stochastic counterpart of the problem of input-to-state stabilization in the sense of Sontag (1989). Our development starts with a set of new global stochastic Lyapunov theorems. For an exemplary class of stochastic strict-feedback systems with vanishing nonlinearities, where the equilibrium is preserved in the presence of noise, we develop an adaptive stabilization scheme (based on tuning functions) that requires no a priori knowledge of a bound on the covariance. Next, we introduce a control Lyapunov function formula for stochastic disturbance attenuation. Finally, we address optimality and solve a differential game problem with the control and the noise covariance as opposing players; for strict-feedback systems the resulting Isaacs equation has a closed-form solution.