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Robust Control for Urban Road Traffic Networks

The aim of the presented research is to elaborate a traffic-responsive optimal signal split algorithm taking uncertainty into account. The traffic control objective is to minimize the weighted link queue lengths within an urban network area. The control problem is formulated in a centralized rolling-horizon fashion in which unknown but bounded demand and queue uncertainty influences the prediction. An efficient constrained minimax optimization is suggested to obtain the green time combination, which minimizes the objective function when worst case uncertainty appears. As an illustrative example, a simulation study is carried out to demonstrate the effectiveness and computational feasibility of the robust predictive approach. By using real-world traffic data and microscopic traffic simulator, the proposed robust signal split algorithm is analyzed and compared with well-tuned fixed-time signal timing and to nominal predictive solutions under different traffic conditions.

Linear Parameter Varying Identification of Freeway Traffic Models

This paper deals with linear parameter varying (LPV) modeling and identification of a generic, second-order freeway traffic flow model. A non-conventional technique is proposed to transform the nonlinear freeway traffic flow model into a parameter-dependent form. The resulting exact LPV model is equivalent to the original nonlinear dynamics. Simplification of the nonlinear model gives rise to the introduction of an approximate LPV description. The application of parameter varying identification approaches are made possible by the transformation. Closed-loop predictor-based subspace identification for LPV systems (PBSID LPV) is applied to estimate the affine parameter matrices of the LPV freeway models developed. If the model structure of the original plant is assumed to be known, this paper shows a solution how to estimate LPV model parameters based on the identified model. Parameter-dependent models are identified and validated using real detector measurement data in order to emphasize the applicability of the kernel PBSID LPV methodology. Comparison with traditional nonlinear parametric identification, generally used in traffic identification, is also provided.

Constrained Freeway Traffic Control via Linear Parameter Varying Paradigms

A novel freeway traffic control design framework is proposed in the chapter. The derivation is based on the parameter-dependent reformulation of the second-order macroscopic freeway model. Hard physical constraints are handled implicitly, by introducing additional scheduling parameter for controller saturation measure. The ramp metering problem is then formulated as an induced \({\mathcal{L}}_{2}\) norm minimization, where the effects of undesired traffic phenomena are attenuated on the network throughput. The solution of the resulting problem involves convex optimization methods subjected to Linear Matrix Inequalities. A numerical example is given to validate the parameter-dependent controller and evaluate its effectiveness under various traffic situations.

Modeling and optimal control of travel times and traffic emission on freeways

Abstract In this paper a modeling method and a control approach is proposed for minimising both travel times and traffic emission on freeways. A simulation-based investigation among emission models is performed to determine the model to be engaged for a model-based control. The chosen model is imposed on a second-order macroscopic traffic model. A constrained LQ control is proposed for optimization. An emission-optimal control and a multicriteria (travel time and emission) optimization are compared to conventional, solely travel-time optimal control. Simulations prove that ramp metering can be used to reduce both emission and travel times on motorways.

Uncertainty modeling and robust control in urban traffic

The paper investigates the problem of uncertainty modeling and constrained robust control of urban traffic. Linear polytopic approach is used by state-space representations to describe the uncertain network system. In order to handle model mismatches, robust and infinite horizon model predictive control (MPC) method is proposed. The control strategy is an efficient method to reduce travel time and improve homogeneous traffic flow under changing model conditions. Centralized numerical solution has been carried out as a solution of Linear Matrix Inequalities (LMI) by using semidefinite programming (SDP). Closed-loop control results were tested in simulation environment taking alternative model uncertainty levels into account.

Robust linear parameter-varying control of blood pressure using vasoactive drugs

Resuscitation of emergency care patients requires fast restoration of blood pressure to a target value to achieve hemodynamic stability and vital organ perfusion. A robust control design methodology is presented in this paper for regulating the blood pressure of hypotensive patients by means of the closed-loop administration of vasoactive drugs. To this end, a dynamic first-order delay model is utilised to describe the vasoactive drug response with varying parameters that represent intra-patient and inter-patient variability. The proposed framework consists of two components: first, an online model parameter estimation is carried out using a multiple-model extended Kalman-filter. Second, the estimated model parameters are used for continuously scheduling a robust linear parameter-varying (LPV) controller. The closed-loop behaviour is characterised by parameter-varying dynamic weights designed to regulate the mean arterial pressure to a target value. Experimental data of blood pressure response of anesthetised pigs to phenylephrine injection are used for validating the LPV blood pressure models. Simulation studies are provided to validate the online model estimation and the LPV blood pressure control using phenylephrine drug injection models representing patients showing sensitive, nominal and insensitive response to the drug.

Mean-square optimal control of Linear Parameter Varying systems with noisy scheduling parameter measurements

The problem of designing parameter-dependent output feedback controllers by using inaccurate knowledge of the scheduling parameter is addressed in the paper. Discrete time Linear Parameter Varying (LPV) systems are considered with external scheduling variables corrupted by measurement noise. The paper investigates the optimal control of such LPV class in the quadratic mean-square sense. The solution of the controller design problem is obtained as a standard optimization problem subject to Linear Matrix Inequality (LMI) constraints. A comparative simulation example is given to illustrate the proposed methodology and underline the importance of embedding stochastic information in the LPV control design procedure.

Adaptive Parameter Estimation of Blood Pressure Dynamics Subject to Vasoactive Drug Infusion

Dynamic modeling of arterial blood pressure change subject to vasoactive drug infusion can be a valuable tool for computerized decision support of drug administration as well as for automated closed-loop drug delivery to treat hypotension in emergency trauma care. A time-varying time-delayed first-order dynamic model is considered to describe blood pressure response due to continuous injection of the vasorestrictive drug phenylephrine (PHP). The patient-to-patient as well as intrapatient variability of the dynamic response is taken into account by online identification of the varying model parameters. A multiple-model extended Kalman filter (MMEKF) structure is developed for the real-time estimation of mean arterial pressure and the dynamic blood pressure response model to PHP infusion to assist treatment. Convergence analysis is carried out, along with comparison with offline identification methods. Static drug-response curves for dosage recommendation are obtained from the estimation of the model sensitivity parameter. Finally, a detection algorithm is proposed to identify abrupt model variations caused by sudden physiological changes, such as hemorrhage. The proposed MMEKF parameter estimation method and the hemorrhage detection algorithm are tested and validated using data from animal experiments on anesthetized healthy and hemorrhagic swine that are subject to PHP infusion.

Freeway ramp metering: An LPV set theoretical analysis

The paper contributes to the analysis of freeway traffic flow dynamics by set theoretic methods. First, the macroscopic, non-linear and second-order model of freeway traffic flow dynamics is transformed to an equivalent and quasi Linear Parameter Varying (LPV) representation by steady-state centering and state variable factorization. Second, a polytopic LPV model form is obtained from the quasi model reformulation. The latter polytopic LPV form is then used as a basis for the computation and analysis of disturbance invariant sets. This framework is able to characterize constrained sets of states which can be reached by pure ramp metering control input signals. Furthermore, these sets become invariant to other measured and unmeasured disturbance inputs. The application of disturbance invariant set theory provides an analytical tool for constrained freeway ramp metering describing the set of states being invariant under the system dynamics, measured disturbance and other physical constraints regardless to the value unmeasured disturbance signal. The proposed idea is fully based on the analysis of the (transformed) non-linear macroscopic system and aims at filling the gap between the traffic modeling and quantitative freeway ramp metering.

On acceleration of traffic flow

The paper contributes to the derivation and analysis of accelerations in freeway traffic flow models. First, a solution based on fluid dynamics and on pure mathematical manipulations is given to express accelerations. The continuous-time acceleration is then approximated by a discrete-time equivalent. By applying continues time microscopic and macroscopic traffic flow velocity definitions, spatial and material derivatives are used to describe the continuous-time and exact changes in the velocity vector field. A forward-difference Euler method is proposed to discretized the acceleration both in time and space. For applicability purposes the use of average quantities is proposed. The finite-difference approximation by space-mean speed is shown to be consistent, and its solution is convergent to the original continuous-time form. As an alternative, the acceleration obtained from a second-order macroscopic freeway model by means of physical interpretation [1] is analyzed and found to be an appropriate discrete approximations. Comparative remarks as well as future research questions conclude the paper.