Conservative-variable average states for equilibrium gas multi-dimensional fluxes

Modern split component evaluations of the flux vector Jacobians are thoroughly analyzed for equilibrium-gas average-state determinations. It is shown that all such derivations satisfy a fundamental eigenvalue consistency theorem. A conservative-variable average state is then developed for arbitrary equilibrium-gas equations of state and curvilinear-coordinate fluxes. Original expressions for eigenvalues, sound speed, Mach number, and eigenvectors are then determined for a general average Jacobian, and it is shown that the average eigenvalues, Mach number, and eigenvectors may not coincide with their classical pointwise counterparts. A general equilibrium-gas equation of state is then discussed for conservative-variable computational fluid dynamics (CFD) Euler formulations. The associated derivations lead to unique compatibility relations that constrain the pressure Jacobian derivatives. Thereafter, alternative forms for the pressure variation and average sound speed are developed in terms of two average pressure Jacobian derivatives. Significantly, no additional degree of freedom exists in the determination of these two average partial derivatives of pressure. Therefore, they are simultaneously computed exactly without any auxiliary relation, hence without any geometric solution projection or arbitrary scale factors. Several alternative formulations are then compared and key differences highlighted with emphasis on the determination of the pressure variation and average sound speed. The relevant underlying assumptions are identified, including some subtle approximations that are inherently employed in published average-state procedures. Finally, a representative test case is discussed for which an intrinsically exact average state is determined. This exact state is then compared with the predictions of recent methods, and their inherent approximations are appropriately quantified

Maximum Likelihood Estimation in Data-Driven Modeling and Control

Recently, various algorithms for data-driven simulation and control have been proposed based on the Willems' fundamental lemma. However, when collected data are noisy, these methods lead to ill-conditioned data-driven model structures. In this work, we present a maximum likelihood framework to obtain an optimal data-driven model, the signal matrix model, in the presence of output noise. Data compression and noise level estimation schemes are also proposed to apply the algorithm efficiently to large datasets and unknown noise level scenarios. Two approaches in system identification and receding horizon control are developed based on the derived optimal estimator. The first one identifies a finite impulse response model. This approach improves the least-squares estimator with less restrictive assumptions. The second one applies the signal matrix model as the predictor in predictive control. The control performance is shown to be better than existing data-driven predictive control algorithms, especially under high noise levels. Both approaches demonstrate that the derived estimator provides a promising framework to apply data-driven algorithms to noisy data

Scalable tube model predictive control of uncertain linear systems using ellipsoidal sets

This work proposes a novel robust model predictive control (MPC) algorithm for linear systems affected by dynamic model uncertainty and exogenous disturbances. The uncertainty is modeled using a linear fractional perturbation structure with a time-varying perturbation matrix, enabling the algorithm to be applied to a large model class. The MPC controller constructs a state tube as a sequence of parameterized ellipsoidal sets to bound the state trajectories of the system. The proposed approach results in a semidefinite program to be solved online, whose size scales linearly with the order of the system. The design of the state tube is formulated as an offline optimization problem, which offers flexibility to impose desirable features such as robust invariance on the terminal set. This contrasts with most existing tube MPC strategies using polytopic sets in the state tube, which are difficult to design and whose complexity grows combinatorially with the system order. The algorithm guarantees constraint satisfaction, recursive feasibility, and stability of the closed loop. The advantages of the algorithm are demonstrated using two simulation studies.Comment: Submitted to International Journal of Robust and Nonlinear Contro

Computationally efficient robust MPC using optimized constraint tightening

A robust model predictive control (MPC) method is presented for linear, time-invariant systems affected by bounded additive disturbances. The main contribution is the offline design of a disturbance-affine feedback gain whereby the resulting constraint tightening is minimized. This is achieved by formulating the constraint tightening problem as a convex optimization problem with the feedback term as a variable. The resulting MPC controller has the computational complexity of nominal MPC, and guarantees recursive feasibility, stability and constraint satisfaction. The advantages of the proposed approach compared to existing robust MPC methods are demonstrated using numerical examples.Comment: Submitted to the 61st IEEE Conference on Decision and Control 202

A Dual System-Level Parameterization for Identification from Closed-Loop Data

This work presents a dual system-level parameterization (D-SLP) method for closed-loop system identification. The recent system-level synthesis framework parameterizes all stabilizing controllers via linear constraints on closed-loop response functions, known as system-level parameters. It was demonstrated that several structural, locality, and communication constraints on the controller can be posed as convex constraints on these system-level parameters. In the current work, the identification problem is treated as a {\em dual} of the system-level synthesis problem. The plant model is identified from the dual system-level parameters associated to the plant. In comparison to existing closed-loop identification approaches (such as the dual-Youla parameterization), the D-SLP framework neither requires the knowledge of a nominal plant that is stabilized by the known controller, nor depends upon the choice of factorization of the nominal plant and the stabilizing controller. Numerical simulations demonstrate the efficacy of the proposed D-SLP method in terms of identification errors, compared to existing closed-loop identification techniques

Heavy metal distribution in a sediment phytoremediation system at pilot scale

The continuous stream of polluted sediments, dredged from harbors and water bodies in order to maintain the navigation, is a common practice, but the fate of these sediments is an issue recognized worldwide. This pilot case study evaluated the application of phytoremediation as sustainable management strategy for the decontamination of polluted dredged marine sediments. The synergic action of different plant species (Paspalum vaginatum; P. vaginatum + Spartium junceum and P. vaginatum + Tamarix gallica) and organic matter (compost) in removing both heavy metals (Cd, Ni, Zn, Pb and Cu) and total petroleum hydrocarbons, and in recovering the nutritive and biological sediment properties were evaluated. In addition to the detection of total metal removal efficiency, the chemical distribution of metals in the sediment phases (exchangeable, manganese and iron oxides, organic matter and residual minerals) was also measured in order to make a more realistic estimation of the phytoremediation efficiency for the sediment decontamination. Finally, a complete picture of the metal flux was obtained by investigating the metal mass-balance in the treated sediments. The results of metal content in the sediment phases showed that metal distribution was not uniform and each metal predominated in different fractions; the solubility of metals in the sediment in the decreasing order was: Cd>Zn>Cu>Pb>Ni. The higher proportion of Ni and Pb in the residual phase can be the reason of the lower translocation of these metals in the plant tissues. On the other hand, Cd, Zn and Cu were the metals most easily translocated in plant tissues, both aboveground and roots, confirming their higher availability for the plants. The results of mass balance indicated that, at the end of the experimentation, a high content of metals were still found in the sediment. The greatest contribution in metal removal was attributed to a phytostabilization process at rhizosphere level followed by gravel and sand absorption. The capacity of rhizophere to precipitate heavy metals, could be considered as an alternative option for reducing the metal availability and, consequently, the toxicity in contaminated sediments