Bore-Kuen Lee

The applications of stochastic regulation H ∞ control to HIV therapy

In this study, a nonlinear stochastic differential equation model is used to describe the interactions of the immune system with human immunodeficiency virus (HIV) under intrinsic parametric fluctuation and the extrinsic modular disturbance. A robust H∞ regulation control is proposed for chemotherapy in an early treatment setting of HIV to achieve a desired steady state under intrinsic parametric fluctuations and external disturbances. The effect of intrinsic parametric fluctuations and external disturbances on the regulation error is minimized to achieve the optimal H∞ robust regulation. In order to avoid solving the Hamilton-Jacobi inequality (HJI) for H∞, robust regulation of HIV therapy. The fuzzy dynamic model is employed to interpolate several linear stochastic differential equations to approximate 11. nonlinear stochastic equation model to simplify the design procedure of H. robust regulation control. Based on fuzzy interpolation, we use a set of linear matrix inequalities (LMIs) to replace the HJI so that the Η∞ robust regulation control of HIV therapy can be designed via the help of robust control tool box of matlab. Finally, a simulation example is given to illustrate the design procedure and to confirm the performance of the proposed stochastic 11 robust regulation control for HIV therapy.

Observer base linear quadratic regulation with estimated state feedback control

For the continuous infinite horizon time-invariant linear quadratic regulator problem (LQR), in the paper, the optimal state feedback controller based on the estimated state of the observer can be decoupled by the proposed approach which resulting one continuous time algebraic Riccati equation (CARE) for the controller design and one matrix equality equation (MEE) for the observer design. A coupling term related the CARE of the controller is found to be existed in the MEE of the observer. Unlike the separate principle to design the controller and observer separately without any coupling term, the design of the observer should consider the coupling term related to the CARE of the controller. The coupling problem between the controller and the observer usually exists in the linear matrix inequality (LMI) approach, and it is the main problem to be solved. The two-stage scheme is popular in the LMI approach, and the proposed method is similar to it, but adopting equality instead of inequality.

Long-Range Prediction for Real-Time MPEG Video Traffic: An

A novel prediction scheme is proposed for real-time MPEG video to predict the burst and long-range dependent traffic. The trend and periodic characteristics of MPEG video traffic are fully captured by a proposed stochastic state-space dynamic model. Then a recursive Hinfin filtering algorithm is proposed to estimate traffic for long-range prediction. Simulation results based on real MPEG traffic data show that the proposed scheme has superior performance and lower complexity than some adaptive neural network methods, such as TDNN, NARX, and Elman neural networks.

H_{\infty}

This paper mainly outlines the model of the invented spherical robot using Omni wheels to drive a spherical wheel. The dynamical model is derived based on Euler Lagrange approach. Therefore, based on the derived model, the variable structure control (VSC) is presented in which the sliding mode control (SMC) is adopted to achieve a constant speed at a vertical balance altitude. Simulations of the proposed control algorithm have been conducted based on two pre-determined sliding surfaces with adjustable parameters to discuss the effective time to enter the sliding surface and the convergence.

Filter Approach

Abstract For diverse multiple access communication systems based on frame slotted aloha (FSA) protocol, it is important to analyze collision probability for the system performance evaluation. As shown in the literature, for general settings, it is difficult to derive an exact and closed-form solution for collision probability without approximation. Recently, an exact solution based on generic analytical approach (GAA) [31] has been proposed, yet its numerical computation will become difficult when the number of slots is larger than 16. In this paper, we develop an exact closed-form formula (ECFF) for collision probability that can not only overcome the computational deficiency of GAA in the presence of a large number of slots, but also reduce the computation complexity of collision probability. Surprisingly, by introducing a differentiation operator to form a hybrid recursive equation and applying various algebraic properties of Laplace transform and Z transform, the final collision probability can be represented by a compact double summation. Accuracy of the ECFF and comparison with the GAA have been studied by Monte Carlo simulation.

Constant speed VSC of a spherical robot driven by Omni wheels

The target of the paper is a spherical robot using Omni wheels to drive a spherical wheel, and its position control based on the cascade sliding model control (CSMC) has been studied. The structure of the CSMC is cascade combination of states of this dynamic model and a series of sliding surfaces. Because the CSMC is easy to result in a constant speed of spherical wheel, a constant without any switching cascade sliding model control, denoted as CSMCl, has been proposed to solve the undesired constant speed problem. The positive constant coefficients without any switching can release the body convergent rate, so the constant speed problem can be avoided to achieve the position control.

An Exact Closed-Form Formula of Collision Probability in Diverse Multiple Access Communication Systems with Frame Slotted Aloha Protocol

In the field of adaptive fuzzy control, there has been a severe deficiency by assuming the premise variables will usually stay within the universe of discourse in the derivation of stability of the adaptive control system. To overcome this deficiency, we develop a switching adaptive control scheme using only essential qualitative information of the plant to attain asymptotical stability of the adaptive control system for a typical first-order nonlinear system without imposing the mentioned severe assumption. The switching adaptive control system consists of an adaptive VSS controller for coarse control, an adaptive fuzzy controller for fine control, and a hysteresis switching mechanism. An adaptive VSS control scheme is proposed to force the state to enter the universe of discourse in finite time. While the premise variable is within the universe of discourse, an adaptive fuzzy control is proposed to learn the capability to stabilize the plant. At the boundary of the universe of discourse, a hysteresis switching scheme between the two controllers will be proposed. We show that after finite times of switching, the premise variables of the fuzzy system will remain within the universe of discourse and stability of the closed-loop system can be attained by applying Lyapunov direct method.

Cascade sliding mode control of a spherical wheel robot driven by Omni wheels

In the conventional adaptive control field, parameter tuning law based on σ-modification has been widely used to construct an adaptive controller. However, using the (σ-modification parameter tuning law, usually only the UUB stability can be attained for the adaptive control system. In this study, we simplify the parameter tuning law and the adaptive VSS control law to construct the proposed adaptive VSS control systems for typical first-order systems. Even though the σ-modification term in the parameter tuning law and the stabilizing control term in the adaptive control law are omitted, we shall show that asymptotical stability of the state and boundedness of the parameter estimates can be guaranteed. Particularly, in the proposed adaptive control schemes, only the structural information of the plant is needed. Several simulation examples are given to verify the proposed adaptive control algorithms.

A switching adaptive VSS/fuzzy control

In this paper, H∞ dynamic output feedback control for discrete-time nonlinear stochastic T-S fuzzy model with state-dependent noise is attacked. We consider the fuzzy T-S models has has stochastic uncertainties, i.e., state-dependent noise, in the system matrix, input matrix, and output matrix. First, when the premise variables in the fuzzy plant model are available, an H∞ fuzzy dynamic output feedback controller, which uses the same premise variables as the T-S fuzzy model, is proposed for regulation of the controlled system to meet the H∞ control performance specification. Next, when the premise variables for building the fuzzy plant model are not available, a fuzzy H, observer-based state feedback controller, in which the premise variables are the estimated version of the premise variables in the T-S fuzzy model, is proposed. For the two cases, we conduct sufficient conditions described by linear matrix inequalities (LMI) to ensure stability of the closed-loop system. Performance of the proposed fuzzy controller is verified by simulation study.

On adaptive VSS control

Estimator which guarantee Hinfin robustness performance for the considered nonlinear stochastic systems can be obtained by solving bilinear matrix inequalities. Then, to solve the bilinear matrix inequalities, a two-stage method is adopted to separately obtain the controller gain matrices and the estimator gain matrices by solving two sets of linear matrix inequalities. An example is given to verify the derived results.