Hongsheng Xi

Adaptive output-feedback tracking of stochastic nonlinear systems

We address the adaptive stabilization and tracking problems for a class of output feedback canonical systems driven by Wiener noises of unknown covariance. Filtered transformation and backstepping techniques are employed in the stochastic control design. We obtain two adaptive controllers that guarantee the global stability in probability for vanishing perturbations or the input-to-state stability in probability for nonvanishing perturbations respectively. The tracking error can converge to a small residual set around the origin in the sense of mean quartic value.

The guaranteed estimation performance filter for discrete-time descriptor systems with uncertain noise

This paper deals with the problem of a robust filter design for discrete-time descriptor systems with uncertain noise. The problem addressed is the construction of a perturbating upper bound on uncertain noise covariances so as to guarantee that the deviation of the estimate error performance index remains within the precision prescribed in actual problems. Furthermore, the worst performance in the uncertain case can be minimized by a minimax robust filter.

Adaptive Stabilization for Stochastic Parametric-Strict-Feedback Systems with Wiener Noises of Unknown Covariance

An adaptive control design for a class of stochastic parametric-strict-feedback systems is given. The disturbance considered herein is Wiener noise of unknown covariance, which is represented as a simplified unknown parameter. By using stochastic Lyapunov method and backstepping techniques, an adaptive controller was obtained that guaranteed the global asymptotic stabilization in probability.

Robust Kalman filter of continuous-time Markov jump linear systems based on state estimation performance

Robust Kalman filtering problem for a class of continuous-time Markov jump linear systems with uncertain second-order statistical properties is investigated. Uncertainty is modeled by allowing process and observation noises spectral density matrices to vary arbitrarily within given classes. The upper bounds of the perturbation to the noise covariance matrices are given based on the estimation error performance, and a steady-state estimator is therefore adopted under the worst situation. Not only can this method minimize the worst performance function of the uncertainty, but the error performance can be guaranteed to be within a given bound. Finally the developed theory is illustrated by a numerical example.

Finding Optimal Observation-Based Policies for Constrained POMDPs Under the Expected Average Reward Criterion

In this technical note, constrained partially observable Markov decision processes with discrete state and action spaces under the average reward criterion are studied from a sensitivity point of view. By analyzing the derivatives of performance criteria, we develop a simulation-based optimization algorithm to find the optimal observation-based policy on the basis of a single sample path. This algorithm does not need any overly strict assumption and can be applied to the general ergodic Markov systems with the imperfect state information. The performance is proved to converge to the optimum with probability 1. One numerical example is provided to illustrate the applicability of the algorithm.

Stability robustness analysis of state-space models for uncertain Linear time-varying systems

The stability robustness of linear-variant systems in the time domain is considered using the Lyapunov approach and the maximum singular values of a time-variant matrix. Bounds on linear time-varying perturbations that maintain the stability of a uniformly asymptotically stable linear time-variant system are obtained for both unstructured and structured independent perturbations. Bounds are also derived assuming that various elements of the system matrix are perturbed dependently. The result for the structural perturbation case is extended to the stability analysis of time-variant interval matrices.

Finding Optimal Polices for Wideband Spectrum Sensing Based on Constrained POMDP Framework

This paper considers the problem of opportunistically accessing a wide range of frequency band in which multiple subbands may be occupied. A major obstacle to utilizing such wideband spectrum is that performing Nyquist sampling on the wideband signal is either infeasible or too expensive. We propose an adaptive energy-constrained sensing scheme based on sub-Nyquist sampling and stochastic control theory. In contrast to the existing sub-Nyquist approaches, we select the subband that has high probability to be idle based on the sub-Nyquist samples and spectrum prediction, without reconstructing the wideband signal. The sensing process is formulated as a constrained partially observable Markov decision process to exploit the statistical characteristics of the wideband signal, and a simulation-based gradient algorithm is proposed to compute the optimal adaptive sensing policy. The algorithm is shown to converge to the optimal solution with probability one. Simulation results show that with low computational complexity, the adaptive sensing policy performs well even in the crowded spectrum with low SNR.

Centralized Optimization for Dec-POMDPs Under the Expected Average Reward Criterion

In this paper, the decentralized partially observable Markov decision process (Dec-POMDP) systems with discrete state and action spaces are studied from a gradient point of view. Dec-POMDPs have recently emerged as a promising approach to optimizing multiagent decision making in the partially observable stochastic environment. However, the decentralized nature of the Dec-POMDP framework results in a lack of shared belief state, which makes the decision maker impossible to estimate the system state based on local information. In contrast to the belief-based policy, this paper focuses on optimizing the decentralized observation-based policy, which is easily to be applied and does not have the sharing problem. By analyzing the gradient of the objective function, we have developed a centralized stochastic gradient policy iteration algorithm to find the optimal policy on the basis of gradient estimates from a single sample path. This algorithm does not need any specific assumption and can be applied to most practical Dec-POMDP problems. One numerical example is provided to demonstrate the effectiveness of the algorithm.

Adaptive multicoset sampling for wideband spectrum sensing based on POMDP framework

In this paper, we consider the problem of opportunistically accessing a wide range of frequency band in which multiple subbands may be occupied. A major obstacle of utilizing such wideband spectrum is that it is either infeasible or too expansive to perform Nyquist sampling on the wideband signal. In this paper, we propose an adaptive sensing scheme based on a sub-Nyquist sampling method called multicoset sampling, which is similar to the polyphase implementation of Nyquist sampling, but requires less A/D converters. In contrast to the traditional sub-Nyquist sampling approaches where all subbands are considered to design the sampling filters, we develop a method that adaptively selects part of wideband spectrum to do sub-Nyquist sampling, by exploiting its statistical properties. Therefore, the computational overhead for reconstructing the wideband signal from the sub-Nyquist samples can be significantly reduced. Simulation results are provided to demonstrate the effectiveness of the proposed adaptive wideband sensing method.

A POMDP approach to adaptive wideband spectrum sensing based on sub-Nyquist sampling

This poster considers the problem of opportunistically accessing a wide range of frequency band. A major obstacle is that it is infeasible to perform Nyquist sampling on the wideband signal. We propose an adaptive sensing scheme based on a sub-Nyquist sampling method, which is similar to the polyphase implementation of Nyquist sampling, but requires less A/D converters. This method adaptively selects part of wideband spectrum to do sub-Nyquist sampling, by exploiting its statistical properties. The computational overhead can be significantly reduced.