Keith J. Burnham

On stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters

In this paper, we investigate the stochastic stabilization problem for a class of bilinear continuous time-delay uncertain systems with Markovian jumping parameters. Specifically, the stochastic bilinear jump system under study involves unknown state time-delay, parameter uncertainties, and unknown nonlinear deterministic disturbances. The jumping parameters considered here form a continuous-time discrete-state homogeneous Markov process. The whole system may be regarded as a stochastic bilinear hybrid system that includes both time-evolving and event-driven mechanisms. Our attention is focused on the design of a robust state-feedback controller such that, for all admissible uncertainties as well as nonlinear disturbances, the closed-loop system is stochastically exponentially stable in the mean square, independent of the time delay. Sufficient conditions are established to guarantee the existence of desired robust controllers, which are given in terms of the solutions to a set of either linear matrix inequalities (LMIs), or coupled quadratic matrix inequalities. The developed theory is illustrated by numerical simulation.

Dual extended Kalman filter for vehicle state and parameter estimation

The article demonstrates the implementation of a model-based vehicle estimator, which can be used for combined estimation of vehicle states and parameters. The estimator is realised using the dual extended Kalman filter (DEKF) technique, which makes use of two Kalman filters running in parallel, thus ‘splitting’ the state and parameter estimation problems. Note that the two problems cannot be entirely separated due to their inherent interdependencies. This technique provides several advantages, such as the possibility to switch off the parameter estimator, once a sufficiently good set of estimates has been obtained. The estimator is based on a four-wheel vehicle model with four degrees of freedom, which accommodates the dominant modes only, and is designed to make use of several interchangeable tyre models. The paper demonstrates the appropriateness of the DEKF. Results to date indicate that this is an effective approach, which is considered to be of potential benefit to the automotive industry.

Robust filtering for a class of stochastic uncertain nonlinear time-delay systems via exponential state estimation

We investigate the robust filter design problem for a class of nonlinear time-delay stochastic systems. The system under study involves stochastics, unknown state time-delay, parameter uncertainties, and unknown nonlinear disturbances, which are all often encountered in practice and the sources of instability. The aim of this problem is to design a linear, delayless, uncertainty-independent state estimator such that for all admissible uncertainties as well as nonlinear disturbances, the dynamics of the estimation error is stochastically exponentially stable in the mean square, independent of the time delay. Sufficient conditions are proposed to guarantee the existence of desired robust exponential filters, which are derived in terms of the solutions to algebraic Riccati inequalities. The developed theory is illustrated by numerical simulation.

Optimization of beam orientation in radiotherapy using planar geometry

This paper proposes a new geometrical formulation of the coplanar beam orientation problem combined with a hybrid multiobjective genetic algorithm. The approach is demonstrated by optimizing the beam orientation in two dimensions, with the objectives being formulated using planar geometry. The traditional formulation of the objectives associated with the organs at risk has been modified to account for the use of complex dose delivery techniques such as beam intensity modulation. The new algorithm attempts to replicate the approach of a treatment planner whilst reducing the amount of computation required. Hybrid genetic search operators have been developed to improve the performance of the genetic algorithm by exploiting problem-specific features. The multiobjective genetic algorithm is formulated around the concept of Pareto optimality which enables the algorithm to search in parallel for different objectives. When the approach is applied without constraining the number of beams, the solution produces an indication of the minimum number of beams required. It is also possible to obtain non-dominated solutions for various numbers of beams, thereby giving the clinicians a choice in terms of the number of beams as well as in the orientation of these beams.

On designing observers for time-delay systems with non-linear disturbances

In this paper, the observer design problem is studied for a class of time-delay non-linear systems. The system under consideration is subject to delayed state and non-linear disturbances. The time-delay is allowed to be time-varying, and the non-linearities are assumed to satisfy global Lipschitz conditions. The problem addressed is the design of state observers such that, for the admissible time-delay as well as non-linear disturbances, the dynamics of the observation error is globally exponentially stable. An effective algebraic matrix inequality approach is developed to solve the non-linear observer design problem. Specifically, some conditions for the existence of the desired observers are derived, and an explicit expression of desired observers is given in terms of some free parameters. A simulation example is included to illustrate the practical applicability of the proposed theory.

Stability analysis and observer design for neutral delay systems

This paper deals with the observer design problem for a class of linear delay systems of the neutral-type. The problem addressed is that of designing a full-order observer that guarantees the exponential stability of the error dynamic system. An effective algebraic matrix equation approach is developed to solve this problem. In particular, both the observer analysis and design problems are investigated. By using the singular value decomposition technique and the generalized inverse theory, sufficient conditions for a neutral-type delay system to be exponentially stable are first established. Then, an explicit expression of the desired observers is derived in terms of some free parameters. Furthermore, an illustrative example is used to demonstrate the validity of the proposed design procedure.

Coordinated control of distribution supply chains in the presence of fuzzy customer demand

This paper considers a single product inventory control in a Distribution Supply Chain (DSC). The DSC operates in the presence of uncertainty in customer demands. The demands are described by imprecise linguistic expressions that are modelled by discrete fuzzy sets. Inventories at each facility within the DSC are replenished by applying periodic review policies with optimal order up-to-quantities. Fuzzy customer demands imply fuzziness in inventory positions at the end of review intervals and in incurred relevant costs per unit time interval. The determination of the minimum of defuzzified total cost of the DSC is a complex problem which is solved by applying decomposition; the original problem is decomposed into a number of simpler independent optimisation subproblems, where each retailer and the warehouse determine their optimum periodic reviews and order up-to-quantities. An iterative coordination mechanism is proposed for changing the review periods and order up-to-quantities for each retailer and the warehouse in such a way that all parties within the DSC are satisfied with respect to total incurred costs per unit time interval. Coordination is performed by introducing fuzzy constraints on review periods and fuzzy tolerances on retailers and warehouse costs in local optimisation subproblems.

A multiple model approach to respiratory motion prediction for real-time IGRT

Respiration induces significant movement of tumours in the vicinity of thoracic and abdominal structures. Real-time image-guided radiotherapy (IGRT) aims to adapt radiation delivery to tumour motion during irradiation. One of the main problems for achieving this objective is the presence of time lag between the acquisition of tumour position and the radiation delivery. Such time lag causes significant beam positioning errors and affects the dose coverage. A method to solve this problem is to employ an algorithm that is able to predict future tumour positions from available tumour position measurements. This paper presents a multiple model approach to respiratory-induced tumour motion prediction using the interacting multiple model (IMM) filter. A combination of two models, constant velocity (CV) and constant acceleration (CA), is used to capture respiratory-induced tumour motion. A Kalman filter is designed for each of the local models and the IMM filter is applied to combine the predictions of these Kalman filters for obtaining the predicted tumour position. The IMM filter, likewise the Kalman filter, is a recursive algorithm that is suitable for real-time applications. In addition, this paper proposes a confidence interval (CI) criterion to evaluate the performance of tumour motion prediction algorithms for IGRT. The proposed CI criterion provides a relevant measure for the prediction performance in terms of clinical applications and can be used to specify the margin to accommodate prediction errors. The prediction performance of the IMM filter has been evaluated using 110 traces of 4-minute free-breathing motion collected from 24 lung-cancer patients. The simulation study was carried out for prediction time 0.1-0.6 s with sampling rates 3, 5 and 10 Hz. It was found that the prediction of the IMM filter was consistently better than the prediction of the Kalman filter with the CV or CA model. There was no significant difference of prediction errors for the sampling rates 5 and 10 Hz. For these sampling rates, the errors of the IMM filter for 0.4 s prediction time were less than 2.1 mm in terms of the 95% CI criterion or 1.1 mm in terms of the standard deviation (SD) or root mean squared errors (RMSE) criterion. For the prediction time of 0.6 s the errors were less than 3.6 mm in terms of the 95% CI criterion or 1.8 mm in terms of the SD/RMSE criterion. The prediction error analysis showed that the average percentage of the target lies outside the 95% CI margin was 5.2% and outside the SD/RMSE margin was 24.3%. This indicates the effectiveness of the 95% CI criterion as a margining strategy to accommodate prediction errors.

Cloud computing concept for Intelligent Transportation Systems

In this paper a cloud computing based urban traffic control system is proposed. Its goals are to increase road throughput and optimise the traffic control for increased safety of the participants, reduced fuel consumption and carbon emissions. The urban vehicle control scenario assumes that the speed of each vehicle in the controlled area is set by an off-board control unit that supervises each traffic intersection. The software component responsible for that is called an Intersection Control Service (ICS). From the systems point of view, the vehicles are treated as cloud services and are discovered and invoked using a cloud computing methodology. Geographical multicast addressing is used to target all vehicles in the specified areas. ICSs are part of a city/region wide cloud system that coordinates flow of traffic between intersections. The systems optimisation objective is carried out on several planning planes simultaneously, the lowest being local to a single intersection and the highest being an entire city or region level. The ICS gathers traffic data from various sensors around the intersection, and from the vehicles themselves, creating a dynamic situation map which can be used to assess the road situation and perform short term predictions for vehicle control purposes.

Regenerative braking strategies, vehicle safety and stability control systems: critical use-case proposals

The sustainable development of vehicle propulsion systems that have mainly focused on reduction of fuel consumption (i.e. CO2 emission) has led, not only to the development of systems connected with combustion processes but also to legislation and testing procedures. In recent years, the low carbon policy has made hybrid vehicles and fully electric vehicles (H/EVs) popular. The main virtue of these propulsion systems is their ability to restore some of the expended energy from kinetic movement, e.g. the braking process. Consequently new research and testing methods for H/EVs are currently being developed. This especially concerns the critical ‘use-cases’ for functionality tests within dynamic events for both virtual simulations, as well as real-time road tests. The use-case for conventional vehicles for numerical simulations and road tests are well established. However, the wide variety of tests and their great number (close to a thousand) creates a need for selection, in the first place, and the creation of critical use-cases suitable for testing H/EVs in both virtual and real-world environments. It is known that a marginal improvement in the regenerative braking ratio can significantly improve the vehicle range and, therefore, the economic cost of its operation. In modern vehicles, vehicle dynamics control systems play the principal role in safety, comfort and economic operation. Unfortunately, however, the existing standard road test scenarios are insufficient for H/EVs. Sector knowledge suggests that there are currently no agreed tests scenarios to fully investigate the effects of brake blending between conventional and regenerative braking as well as the regenerative braking interaction with active driving safety systems (ADSS). The paper presents seven manoeuvres, which are considered to be suitable and highly informative for the development and examination of H/EVs with regenerative braking capability. The critical manoeuvres presented are considered to be appropriate for examination of the regenerative braking mode according to ADSS. The manoeuvres are also important for investigation of regenerative braking system properties/functionalities that are specified by the legal requirements concerning H/EVs braking systems. The last part of this paper shows simulation results for one of the proposed manoeuvres that explicitly shows the usefulness of the manoeuvre.