The LQ control problem for Markovian jumps linear systems with horizon defined by stopping times

This paper deals with a stochastic optimal control problem involving discrete-time jump Markov linear systems. The jumps or changes between the system operation modes evolve according to an underlying Markov chain. In the model studied, the problem horizon is defined by a stopping time τ which represents either, the occurrence of a fix number N of failures or repairs (TN), or the occurrence of a crucial failure event (τΔ), after which the system is brought to a halt for maintenance. In addition, an intermediary mixed case for which T represents the minimum between TN and τΔ is also considered. These stopping times coincide with some of the jump times of the Markov state and the information available allows the reconfiguration of the control action at each jump time, in the form of a linear feedback gain. The solution for the linear quadratic problem with complete Markov state observation is presented. The solution is given in terms of recursions of a set of algebraic Riccati equations (ARE) or a coupled set of algebraic Riccati equation (CARE).

Optimal mean-variance control for discrete-time linear systems with Markovian jumps and multiplicative noises

In this paper, we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noises under two criteria. The first one is an unconstrained mean-variance trade-off performance criterion along the time, and the second one is a minimum variance criterion along the time with constraints on the expected output. We present explicit conditions for the existence of an optimal control strategy for the problems, generalizing previous results in the literature. We conclude the paper by presenting a numerical example of a multi-period portfolio selection problem with regime switching in which it is desired to minimize the sum of the variances of the portfolio along the time under the restriction of keeping the expected value of the portfolio greater than some minimum values specified by the investor. (C) 2011 Elsevier Ltd. All rights reserved.

LQ optimal and risk-sensitive control for vehicle suspensions

This paper is concerned with time-domain optimal control of active suspensions. The optimal control problem formulation has been generalised by incorporating both road disturbances (ride quality) and a representation of driver inputs (handling quality) into the optimal control formulation. A regular optimal control problem as well as a risk-sensitive exponential optimal control performance index is considered. Emphasis has been given to practical considerations including the issue of state estimation in the presence of load disturbances (driver inputs). © 2012 IEEE.

Linear quadratic and tumour control probability modelling in external beam radiotherapy

The standard linear-quadratic (LQ) survival model for external beam radiotherapy is reviewed with particular emphasis on studying how different schedules of radiation treatment planning may be affected by different tumour repopulation kinetics. The LQ model is further examined in the context of tumour control probability (TCP) models. The application of the Zaider and Minerbo non-Poissonian TCP model incorporating the effect of cellular repopulation is reviewed. In particular the recent development of a cell cycle model within the original Zaider and Minerbo TCP formalism is highlighted. Application of this TCP cell-cycle model in clinical treatment plans is explored and analysed.

Body-centric modelling, identification, and acceleration tracking control of a quadrotor UAV

This paper presents the mathematical development of a body-centric nonlinear dynamic model of a quadrotor UAV that is suitable for the development of biologically inspired navigation strategies. Analytical approximations are used to find an initial guess of the parameters of the nonlinear model, then parameter estimation methods are used to refine the model parameters using the data obtained from onboard sensors during flight. Due to the unstable nature of the quadrotor model, the identification process is performed with the system in closed-loop control of attitude angles. The obtained model parameters are validated using real unseen experimental data. Based on the identified model, a Linear-Quadratic (LQ) optimal tracker is designed to stabilize the quadrotor and facilitate its translational control by tracking body accelerations. The LQ tracker is tested on an experimental quadrotor UAV and the obtained results are a further means to validate the quality of the estimated model. The unique formulation of the control problem in the body frame makes the controller better suited for bio-inspired navigation and guidance strategies than conventional attitude or position based control systems that can be found in the existing literature.

Improved low-voltage-ride-through capability of fixed-speed wind turbines using decentralised control of STATCOM with energy storage system

The design and implementation of a new control scheme for reactive power compensation, voltage regulation and transient stability enhancement for wind turbines equipped with fixed-speed induction generators (IGs) in large interconnected power systems is presented in this study. The low-voltage-ride-through (LVRT) capability is provided by extending the range of the operation of the controlled system to include typical post-fault conditions. A systematic procedure is proposed to design decentralised multi-variable controllers for large interconnected power systems using the linear quadratic (LQ) output-feedback control design method and the controller design procedure is formulated as an optimisation problem involving rank-constrained linear matrix inequality (LMI). In this study, it is shown that a static synchronous compensator (STATCOM) with energy storage system (ESS), controlled via robust control technique, is an effective device for improving the LVRT capability of fixed-speed wind turbines.

A second order control-volume finite-element least-squares strategy for simulating diffusion in strongly anisotropic media

An unstructured mesh �nite volume discretisation method for simulating di�usion in anisotropic media in two-dimensional space is discussed. This technique is considered as an extension of the fully implicit hybrid control-volume �nite-element method and it retains the local continuity of the ux at the control volume faces. A least squares function recon- struction technique together with a new ux decomposition strategy is used to obtain an accurate ux approximation at the control volume face, ensuring that the overall accuracy of the spatial discretisation maintains second order. This paper highlights that the new technique coincides with the traditional shape function technique when the correction term is neglected and that it signi�cantly increases the accuracy of the previous linear scheme on coarse meshes when applied to media that exhibit very strong to extreme anisotropy ratios. It is concluded that the method can be used on both regular and irregular meshes, and appears independent of the mesh quality.