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MIMO-Systems Identification by Minimum Error Bounds

IFAC Proceedings Volumes 1993年第2期26卷 85-88页

作者： T.J.J. van den Boom Control Laboratories Department of Electrical Engineering Delft University of Technology P.O Box 5031 Delft The Netherlands

In this paper a system identification procedure for MIMO-systems is presented, that yields a model with bounded error. Various model error structures (additive, multiplicative or coprime factor)are considered. The input and out put noise are assumed to be bounded in the frequency domain. An upper bound for the model error is derived, using measured data and the knowledge of the noise. Themodel error bound can be minimized in H ∞ -norm sense by tuning the model parameters. The choice of a linear parametrization will lead to a convex optimization problem, and the algorithms will be robustly convergent.

关键词： System identification multivariable systems parameter estimation additive multiplicative or coprime factor model error structures robust control convex programming

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Method for TDOA localisation in over-the-horizon environments

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JOURNAL OF ENGINEERING-JOE 2019年第20期2019卷 6522-6526页

作者： Liu, Jian-Xin Mao, Xing-Peng Harbin Inst Technol Sch Elect & Informat Engn Harbin 150001 Heilongjiang Peoples R China

Here, the authors propose a new over-the-horizon time-difference-of-arrival localisation model based on the ground-wave and simultaneously put forward a modified semi-definite programming algorithm, which is called Ground-wave semi-definite programming (G-SDP). If both the target and the base stations are on the surface of the earth and far away from each other, the propagation path of the signal is a curve along the surface instead of a straight line, thus making the traditional positioning model inefficient. To overcome the problem, they develop a novel localisation model and explore a priori information to achieve improvements on SDP algorithms. An iteration trick is also utilised to obtain better performance when the signal-to-noise ratio is low. The simulation results show the merits of the improved model and G-SDP.

关键词： target tracking convex programming mathematical programming time-of-arrival estimation signal-to-noise ratio SDP algorithms traditional positioning model straight line propagation path base stations G-semidefinite programming modified semidefinite programming algorithm ground-wave over-the-horizon time difference-of-arrival localisation model over-the-horizon environments TDOA localisation

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L2 Observers for a Class of Nonlinear Systems with Unknown Inputs 18

L2 Observers for a Class of Nonlinear Systems with Unknown I...

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18th European Control Conference (ECC)

作者： Corless, Martin Chakrabarty, Ankush Purdue Univ Sch Aeronaut & Astronaut W Lafayette IN 47907 USA Mitsubishi Elect Res Labs Control & Dynam CD Syst Grp Cambridge MA 02139 USA

ISBN: (纸本)9783907144008

We consider the problem of estimating the state and unknown input for a large class of nonlinear systems subject to unknown exogenous inputs. The exogenous inputs themselves are modeled as being generated by a nonlinear system subject to unknown inputs. The nonlinearities considered in this work are characterized by multiplier matrices that include many commonly encountered nonlinearities. We obtain a linear matrix inequality (LMI), that, if feasible, provides the gains for an observer which results in certified L-2 performance of the error dynamics associated with the observer. We also present conditions which guarantee that the L-2 norm of the error can be made arbitrarily small and investigate conditions for feasibility of the proposed LMIs.

关键词： Unknown input observers convex programming nonlinear disturbance model internal model quadratic constraints fault detection and isolation

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An accelerated proximal augmented Lagrangian method and its application in compressive sensing

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JOURNAL OF INEQUALITIES AND APPLICATIONS 2017年第1期2017卷 263页

作者： Sun, Min Liu, Jing Qufu Normal Univ Sch Management Jining 276826 Shandong Peoples R China Zaozhuang Univ Sch Math & Stat Zaozhuang 277160 Shandong Peoples R China Zhejiang Univ Finance & Econ Sch Data Sci Hangzhou 310018 Zhejiang Peoples R China

As a first-order method, the augmented Lagrangian method (ALM) is a benchmark solver for linearly constrained convex programming, and in practice some semi-definite proximal terms are often added to its primal variable's subproblem to make it more implementable. In this paper, we propose an accelerated PALM with indefinite proximal regularization (PALM-IPR) for convex programming with linear constraints, which generalizes the proximal terms from semi-definite to indefinite. Under mild assumptions, we establish the worst-case O(1/t(2)) convergence rate of PALM-IPR in a non-ergodic sense. Finally, numerical results show that our new method is feasible and efficient for solving compressive sensing.

关键词： proximal augmented Lagrangian multiplier method convex programming global convergence compressive sensing

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Robust Control Synthesis by convex Optimization: Projective Parameterization and Duality

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IFAC Proceedings Volumes 1993年第2期26卷 5-8页

作者： A. Megretski A. Rantzer University of Newcastle CICS Shortland NSW 2308 Australia University of Minnesota IMA Minneapolis MN 55455-0436 USA

This paper treats a robustness optimization problem for linear time-invariant systems with real parameteric uncertainty. It is shown that arbitrarily accurate upper and lower bounds on the optimal "robustness margin" can be obtained by finite-dimensional convex optimization. The upper bound is based on a new duality result for a generalized interpolation problem.

关键词： Robust control linear systems stability synthesis methods convex programming

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Predispatch Optimization for a Hydrothermal System

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IFAC Proceedings Volumes 1985年第7期18卷 79-84页

作者： G. Espinosa A. Tirapegui Empresa Nacional de Electricidad ENDESA Chile

The predispatch problem in a hydrothermal system consists in scheduling the hourly output of each power plant for the next day, so as to meet the expected demand at minimum cost under constrained generation from reservoirs. Other constraints such as spinning reserve and area balances may also exist, summing up a nonlinear optimization problem, generally with dimensionality difficulties. The paper presents a combination of the Kelley's cutting plane algorithm with a branch and bound technique which is thought to be of interest for medium size systems where transmission losses play an important role. This is the case of the Chilean Inter-connected System where the method is being applied and is presented as a case study in the paper.

关键词： Daily scheduling Power Generation convex programming Linearisation Techniques Optimization

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Passive Fuzzy Controller Design with Variance Constraint for Nonlinear Synchronous Generator Systems

Passive Fuzzy Controller Design with Variance Constraint for...

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IEEE 10th International Conference on Power Electronics and Drive Systems (PEDS)

作者： Chang, Wen-Jer Huang, Bo-Jyun Natl Taiwan Ocean Univ Dept Marine Engn Keelung Taiwan

ISBN: (纸本)9781467317924;9781467317900

A passive fuzzy controller design methodology is developed in this paper to achieve state variance constraint for continuous-time Takagi-Sugeno (T-S) fuzzy models. The proposed fuzzy controller is constructed by the concept of Parallel Distributed Compensation (PDC). Based on the Lyapunov theory, the sufficient conditions are derived to guarantee the stability of the closed-loop system. Besides, the passivity and variance constraints are also considered in the derivations of these sufficient conditions. These sufficient conditions belong to the Linear Matrix Inequality (LMI) forms, which can be solved by the convex optimal programming algorithm. Finally, the feasibility and validity of the proposed method are illustrated with a numerical simulation example.

关键词： Lyapunov methods closed loop systems compensation control system synthesis convex programming fuzzy control linear matrix inequalities machine control nonlinear control systems stability synchronous generators

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A note on the blind deconvolution of multiple sparse signals from unknown subspaces 17

A note on the blind deconvolution of multiple sparse signals...

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Conference on Wavelets and Sparsity XVII

作者： Cosse, Augustin NYU Courant Inst Math Sci New York NY 10003 USA NYU Ctr Data Sci NYC New York NY 10003 USA Ecole Normale Super Dept Math & Applicat Paris France

ISBN: (数字)9781510612464

ISBN: (纸本)9781510612464;9781510612457

This note studies the recovery of multiple sparse signals, x(n) is an element of R-L, n = 1, . . .N, from the knowledge of their convolution with an unknown point spread function h is an element of R-L. When the point spread function is known to be nonzero, vertical bar h[k]vertical bar > 0, this blind deconvolution problem can be relaxed into a linear, ill-posed inverse problem in the vector concatenating the unknown inputs x(n) together with the inverse of the filter, d is an element of R-L where d[k] = 1/h [k]. When prior information is given on the input subspaces, the resulting overdetermined linear system can be solved efficiently via least squares ( see Ling et al. 2016(1)). When no information is given on those subspaces, and the inputs are only known to be sparse, it still remains possible to recover these inputs along with the filter by considering an additional l(1) penalty. This note certifies exact recovery of both the unknown PSF and unknown sparse inputs, from the knowledge of their convolutions, as soon as the number of inputs N and the dimension of each input, L, satisfy L greater than or similar to N and N greater than or similar to T-max(2), up to log factors. Here T-max = max(n){T} and T-n, n = 1, . . . , N denote the supports of the inputs x(n). Our proof system combines the recent results on blind deconvolution via least squares to certify invertibility of the linear map encoding the convolutions, with the construction of a dual certificate following the structure first suggested in Candes et al. 2007.(2) Unlike in these papers, however, it is not possible to rely on the norm parallel to(A*(T)A(T))(-1)parallel to to certify recovery. We instead use a combination of the Schur Complement and Neumann series to compute an expression for the inverse (A*(T)A(T))(-1). Given this expression, it is possible to show that the poorly scaled blocks in (A*(T)A(T))(-1) are multiplied by the better scaled ones or vanish in the construction of the certificate.

关键词： Blind deconvolution l(1)-minimization Compressed sensing convex programming Schur complement

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Distributed equalisation strategy for multi-battery energy storage systems

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JOURNAL OF ENGINEERING-JOE 2019年第16期2019卷 1986-1990页

作者： Fan, Feilong Tai, Nengling Huang, Wentao Zheng, Xiaodong Fan, Chunju Shanghai Jiao Tong Univ Sch Elect Informat & Elect Engn Shanghai Peoples R China

Multi-battery energy storage systems (MBESSs) are widely adopted to overcome the uncertainty problem of renewable energy sources. However, state-of-charge (SOC) imbalance issue of MBESSs brings great challenges to the optimal dispatching strategy and the lifetime management strategy for the MBESS. This study proposes a distributed equalisation strategy for the MBESSs to solve the stated problem. An equitable operation optimisation model is proposed in the distributed equalisation strategy. The equitable optimisation model can be simplified as a convex quadratic optimisation problem. An equitable approximation method is utilised to solve the convex quadratic optimisation problem according to the Karush-Kuhn-Tucker optimality conditions. Based on the equitable approximation method, the SOC balance process is distributed into different iteration steps. The iteration of the SOC balance process is implemented by the communication system connecting the distributed management systems (DMSs). The distributed SOC balance step is implemented by the DMSs of the batteries. The proposed strategy is validated by a hardware-in-the-loop simulation system based on the RT-LAB. Test results show that the proposed strategy ensure the SOC balance and improve the robustness of the MBESS.

关键词： battery management systems power generation dispatch convex programming quadratic programming renewable energy sources secondary cells iterative methods approximation theory convex quadratic optimisation problem equitable approximation method SOC balance process distributed management systems distributed SOC balance step distributed equalisation strategy multibattery energy storage systems uncertainty problem renewable energy sources state-of-charge imbalance issue optimal dispatching strategy lifetime management strategy equitable operation optimisation model Karush-Kuhn-Tucker optimality conditions MBESS iteration steps hardware-in-the-loop simulation system RT-LAB DMS

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Step-Affine Functions, Halfspaces, and Separation of convex Sets with Applications to convex Optimization Problems

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PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS 2021年第SUPPL 1期313卷 S83-S99页

作者： Gorokhovik, V. V. Natl Acad Sci Belarus Inst Math Minsk 220072 BELARUS

We introduce the class of step-affine functions defined on a real vector space and establish the duality between step-affine functions and halfspaces, i.e., convex sets whose complements are convex as well. Using this duality, we prove that two convex sets are disjoint if and only if they are separated by some step-affine function. This criterion is actually the analytic version of the Kakutani-Tukey criterion of the separation of disjoint convex sets by halfspaces. As applications of these results, we derive a minimality criterion for solutions of convex vector optimization problems considered in real vector spaces without topology and an optimality criterion for admissible points in classical convex programming problems not satisfying the Slater regularity condition.

关键词： step-affine functions halfspaces separation of convex sets convex vector optimization problems convex programming

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