The Multi-Parametric Toolbox is a collection of algorithms for modeling, control, analysis, and deployment of constrained optimal controllers developed under Matlab. It features a powerful geometric library that extends the application of the toolbox beyond optimal control to various problems arising in computational geometry. The new version 3.0 is a complete rewrite of the original toolbox with a more flexible structure that offers faster integration of new algorithms. The numerical side of the toolbox has been improved by adding interfaces to state of the art solvers and by incorporation of a new parametric solver that relies on solving linear-complementarity problems. The toolbox provides algorithms for design and implementation of real-time model predictive controllers that have been extensively tested.

/pdf/multi-parametric-toolbox-3-0-hw4ne6qnaz.pdf

Multi-Parametric Toolbox 3.0

The paper presents a review of active set (AS) algorithms that have been deployed for implementation of fast model predictive control (MPC). The main purpose of the survey is to identify the dominant features of the algorithms that contribute to fast execution of online MPC and to study their influence on the speed. The simulation study is conducted on two benchmark examples where the algorithms are analyzed in the number of iterations and in the workload per iteration. The obtained results suggest directions for potential improvement in the speed of existing AS algorithms.

/pdf/dominant-speed-factors-of-active-set-methods-for-fast-mpc-3lm9o9b12w.pdf

Dominant speed factors of active set methods for fast MPC

Maximum likelihood detection for MIMO systems can be formulated as an integer quadratic programming problem. In this paper, we introduce depth-first branch and bound algorithm with variable dichotomy into MIMO detection. More nodes may be pruned with this structure. At each stage of the branch and bound algorithm, active set algorithm is adopted to solve the dual box-constrained quadratic programming subproblem. Numerical results show that the complexity of MIMO detection based on branch and bound algorithm is very low, especially in low SNR and large constellations.

Low Complexity MIMO Detection based on Branch and Bound Algorithm

New sphere decoding and synchronization algorithms for multiple-input-multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems are proposed in this paper. In particular, an iterative list branch-and-bound (BB) algorithm based on the basic BB algorithm is described to obtain a candidate list to compute soft information that is used in the iterative detector. Furthermore, an improved algorithm that uses prior information from the preceding iteration to calculate the lower bound is proposed, and the candidate list is updated every iteration. To obtain a complete modem architecture, we propose an efficient expectation-maximization (EM)-based iterative algorithm for synchronization and channel estimation to interface with the proposed list-sphere-decoding detector, and we investigate the performance of the designed MIMO-OFDM modem on a realistic fading channel. The obtained performance results show that it is possible to practically design a performing MIMO-OFDM modem with high spectral efficiency, i.e., 8 bit/s/Hz with a 4times4 16-QAM MIMO-OFDM system.

New List Sphere Decoding (LSD) and Iterative Synchronization Algorithms for MIMO-OFDM Detection With LDPC FEC

Niu L.A., Hao J.M. (2017): Impacts of fertilizer application rates on phosphorus dynamics in salt-affected soil. Plant Soil Environ., 63: 468–474. As a new rebuilding agricultural soil on the North China plains, the salt-affected soil had a short soil-forming process of about 30 years. This paper describes the effect of different fertilization systems on phosphorus (P) dynamics in saline-alkali uncultivated land, in the reserved natural salt-vegetation back zone, and in different phases of fertilization for 24 years on the North China plains. The treatments included control (or check, CK), N1, N2, P1, P2, N1P1, N1P2, N2P1, N2P2. The contents of total phosphorus (TP) showed a significantly decreasing trend from 1.32–1.38 g P/kg to 0.40–0.96 g P/kg. The contents of rapidly available P (RP) were low in the no-P fertilizer treatments and the RP concentrations increased with P fertilizer applications. Corn was the crop that used the most P, especially in the no-P and P fertilizer-only treatments. The treatment with 270 kg N/ha/year and 59 kg P/ha/year represents the most economical fertilizer rates for these salt-affected soils on the North China plains.

/pdf/impacts-of-fertilizer-application-rates-on-phosphorus-4uctgw7jag.pdf

Impacts of fertilizer application rates on phosphorus dynamics in salt-affected soil

A convex quadratic programming problem with simple bound constraints can be reformulated as an unconstrained minimization problem with a convex quadratic spline (i.e., a differentiable convex piecewise quadratic function) as the objective function. This leads to a new paradigm for solving the original quadratic programming problem, in which various unconstrained minimization algorithms can be used to find a stationary point of the convex quadratic spline. In this paper, we give an implementation of a regularized Newton method (called the QSPLINE method) for finding a stationary point of the convex quadratic spline. The QSPLINE method can also be considered as an implicit active-set method with two novel features: (i) a mixed primal-dual approach for identifying active indices and (ii) a line search strategy for a dynamic balance between the need for minimizing the original objective function and that of forcing the iterates to stay in the feasible region. The implemented version of the QSPLINE method uses a matrix updating technique for computing Newton directions and a correction strategy for robust reduction of the convex quadratic spline when line search in a Newton direction fails. We have tested the code on a variation of the test problems used by Móre and Toraldo [42]. For our generated test problem, the Hessian of the objective function could be an n × n positive semidefinite matrix with rank 2n 3 , and one-third of the Lagrange multipliers corresponding to active constraints at a generated optimal solution could be zero. That is, our test problems are degenerate and have highly singular Hessians. The code finds very accurate numerical solutions for all 2800 randomly generated test problems (with n = 300 and 500), even though all these problems are degenerate and about 60% of these problems have infinitely many solutions.

An Implementation of the QSPLINE Method for Solving Convex Quadratic Programming Problems With Simple Bound Constraints

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An Implementation of the QSPLINE Method for Solving Convex Quadratic Programming Problems With Simple Bound Constraints