Lagrangian solution methods for nonlinear model predictive control

Dyeing process is a serious nonlinear process, and can't be accurately controlled by traditional linear control algorithms. Generalized Predictive Control (GPC) based on linear model has good performance and strong robust, thus can be used to tacking the control probleim with delay and unmodelled errors such as a thermal process for batch dyeing. In order to apply the good linear GPC to the nonlinear batch dyeing process, we introduce a Nonlinear Generalized Predictive Control (NLGPC) based on the Hammerstein model. The simulation results are given and it is concluded that the NLGPC control gives much better performance than the linear GPC.

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“…(4) to obtain x(k) and then use Newton-Raphson recursive method to solve the control input u(k) , whereby U 1(k)=u (k)_[fnx(I(lI (6) …”

Section: Nonlinear Generalized Predictivementioning

confidence: 99%

Nonlinear generalized predictive control in a thermal process for batch dyeing

Zhang

Chen

Zhong

2003

Fifth International Symposium on Instrumentation and Control Technology

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“…It is critical to observe that this hierarchical low-rank structure is not invariant to row and column permutations. GOFMM appropriately permutes K using only entries from K, before constructing the matrices U, V, D, and S. Background and significance: Dense SPD matrices appear in Cholesky and LU factorization [4], in Schur complement matrices [5], in Hessian operators in optimization in simulation [6] and machine learning [7], in kernel methods for statistical learning [8], [9], and in N -body methods and integral equations [10], [2]. In many applications, the entries of the input matrix K are given by K ij = K(x i , x j ), where x i and x j are points in D dimensions and K is a kernel function, for example a Gaussian with bandwidth h: exp(−1/2h −2 x i −x j ).…”

Section: Introductionmentioning

confidence: 99%

“…Left: Compression time and break down into three phases: neighbor search, tree creation, and skeletonization. Right: Matrix-matrix multiplication of kernel matrix with 5M-by-512 matrix for both synchronous kernel (light brown) and asynchronous version (dark brown) (6,…”

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confidence: 99%

Distributed-Memory Hierarchical Compression of Dense SPD Matrices

Reiz

Biros

2018

SC18: International Conference for High Performance Computing, Networking, Storage and Analysis

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We present a distributed memory algorithm for the hierarchical compression of symmetric positive definite (SPD) matrices. Our method is based on GOFMM, an algorithm that appeared in doi:10.1145/3126908.3126921. For many SPD matrices, GOFMM enables compression and approximate matrix-vector multiplication that for many matrices can reach N log N time-as opposed to N 2 required for a dense matrix. But GOFMM supports only shared memory parallelism. In this paper, we use the message passing interface (MPI) and extend the ideas of GOFMM to the distributed memory setting. We also propose and implement an asynchronous algorithm for faster multiplication. We present different usage scenarios on a selection of SPD matrices that are related to graphs, neural-networks, and covariance operators. We present results on the Texas Advanced Computing Center's "Stampede 2" system. We also compare with the STRUMPACK software package, which, to our knowledge, is the only other available software that can compress arbitrary SPD matrices in parallel. In our largest run, we were able to compress a 67M-by-67M matrix in less than three minutes and perform a multiplication with 512 vectors within 5 seconds on 6,144 Intel "Skylake" cores.

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“…Dense SPD matrices appear in scienti c computing, statistical inference, and data analytics. They appear in Cholesky and LU factorization [16], in Schur complement matrices for saddle point problems [6], in Hessian operators in optimization [36], in kernel methods for statistical learning [17,23], and in N-body methods and integral equations [19,20]. In many applications, the entries of the input matrix K are given by K i j = K(x i , x j ) : R d × R d → R, where K is a kernel function.…”

Section: Introductionmentioning

confidence: 99%

Geometry-Oblivious FMM for Compressing Dense SPD Matrices

Yu¹,

Levitt²,

Reiz³

et al. 2017

Preprint

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We present GOFMM (geometry-oblivious FMM), a novel method that creates a hierarchical low-rank approximation, or "compression, " of an arbitrary dense symmetric positive de nite (SPD) matrix. For many applications, GOFMM enables an approximate matrix-vector multiplication in N log N or even N time, where N is the matrix size. Compression requires N log N storage and work. In general, our scheme belongs to the family of hierarchical matrix approximation methods. In particular, it generalizes the fast multipole method (FMM) to a purely algebraic setting by only requiring the ability to sample matrix entries. Neither geometric information (i.e., point coordinates) nor knowledge of how the matrix entries have been generated is required, thus the term "geometry-oblivious. " Also, we introduce a shared-memory parallel scheme for hierarchical matrix computations that reduces synchronization barriers. We present results on the Intel Knights Landing and Haswell architectures, and on the NVIDIA Pascal architecture for a variety of matrices.

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Lagrangian solution methods for nonlinear model predictive control

Cited by 4 publications

References 9 publications

Nonlinear generalized predictive control in a thermal process for batch dyeing

Nonlinear generalized predictive control in a thermal process for batch dyeing

Distributed-Memory Hierarchical Compression of Dense SPD Matrices

Geometry-Oblivious FMM for Compressing Dense SPD Matrices

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