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IFAC Proceedings Volumes 1991年第8期24卷 77-82页

作者： M.A. Rotea School of Aeronautics and Astronautics Purdue University West Lafayette IN 47907 USA

In this paper we consider the problem of finding a feedback controller such that the controlled or regulated signals have a guaranteed maximum peak value in response to arbitrary (but bounded) energy exogenous inputs. More specifically, we give a complete solution to the problem of finding a stabilizing controller such that the closed loop gain from L 2 [0,∞) to L ∞ [0,∞) is below any specified level. We consider both state-feedback and output feedback problems. In the state-feedback case it is shown that if this synthesis problem is solvable, then a solution can be chosen to be a constant state-feedback gain. Necessary and sufficient conditions for the existence of solutions as well as a formula for a state-feedback gain that solves this control problem are obtained in terms of a finite dimensional convex feasibility program. The output feedback case is reduced to a state-feed back problem by using a novel separation property.

关键词： Multivariate control theory linear optimal control state-space methods convex programming

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Configuration improvement for micropressure sensor with vibration interference

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Micro & Nano Letters 2014年第10期9卷 680-685页

作者： Zhongliang Yu Yulong Zhao Lili Li Bian Tian Rongjun Cheng Cun Li State Key Laboratory for Manufacturing Systems Engineering Xi'an Jiaotong University Xi'an Shaanxi 710049 People's Republic of China

Presented is the configuration design for piezoresistive absolute micropressure sensors. A figure of merit called the performance factor (PF) is defined as a quantitative index to describe the comprehensive performances of a sensor including sensitivity, resonant frequency and acceleration interference. Two configurations are proposed through introducing islands and sensitive beams into the typical flat diaphragm. The stress distributions of sensitive elements are analysed by a finite element method. Multivariate fittings based on ANSYS simulation results are performed to establish the equations on surface stresses and deflections of the two sensors. Optimisation by MATLAB is carried out to determine the dimensions of the configurations. convex corner undercutting is analysed to estimate the final dimensions of the islands. Each PF of the two configurations with the determined dimensions has been calculated and compared. Silicon bulk micromachining is utilised to fabricate the prototypes of the sensors. The outputs of the sensors under both static and dynamic conditions are tested. Experimental results reveal that the configuration with quad islands presents the highest PF of 210.947 Hz 1/4 . The favourable overall performances make the sensor more suitable for altimetry.

关键词： microsensors pressure sensors vibration measurement interference piezoresistive devices diaphragms stress measurement finite element analysis convex programming micromachining silicon elemental semiconductors vibration interference piezoresistive absolute micropressure sensor performance factor PF quantitative index acceleration interference resonant frequency flat diaphragm stress distribution finite element method multivariate fitting ANSYS simulation surface stress equation optimisation MATLAB convex corner undercutting analysis silicon bulk micromachining altimetry Si

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A MIN-MAX PREDICTIVE CONTROL ALGORITHM FOR UNCERTAIN NORM-BOUNDED LINEAR SYSTEMS

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IFAC Proceedings Volumes 2002年第1期35卷 279-284页

作者： Alessandro Casavola Domenico Famularo Giuseppe Franzè DEIS - Università degli studi della Calabria Rende(CS) 87036 ITALY ISI - Consiglio Nazionale delle Ricerche Rende (CS) 87036 ITALY

A novel robust predictive control algorithm for input-saturated uncertain linear discrete-time systems with structured norm-bounded uncertainties is presented. The solution is based on the minimization, at each time instant, of a LMI convex optimization problem obtained by a recursive use of the S-procedure. The general case of N free moves is presented. Stability and feasibility are proved and comparisons with robust multi-model (polytopic) MPC algorithms are also presented via an example.

关键词： Uncertain linear systems Predictive control Constraint satisfaction problems convex programming Minimax techniques

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Fast Model Predictive Control of Input-Affine Systems: Application to the Hindmarsh-Rose Neuron Model

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IFAC-PapersOnLine 2024年第28期58卷 354-359页

作者： Alexandra Grancharova Junhong Xie Sorin Olaru Department of Industrial Automation University of Chemical Technology and Metallurgy Bul. Kl. Ohridski 8 Sofia 1756 Bulgaria Laboratory of Signals and Systems CentraleSupélec-CNRS-Université Paris-Sud Université Paris-Saclay Gif-sur-Yvette Cedex France

The paper presents a low complexity nonlinear MPC design for the class of constrained input-affine systems. Essentially, it builds on the idea of adding a contractive constraint in the NMPC problem formulation, which would ensure the closed-loop system stability when using a small prediction horizon. In particular, the one-step ahead NMPC problem with contractive constraint is considered and an approach to obtain an efficient online solution of the associated convex quadratically constrained quadratic programming problem is developed. The proposed technique is shown to be effective for embedded convex NMPC of input-affine systems, since it will reduce the computational complexity of the online NMPC and simplify the software and hardware implementation. The methodological developments are illustrated with simulations on the Hindmarsh-Rose neuron model.

关键词： Predictive control Nonlinear systems Constraints convex programming Computational complexity

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SYSTEMATIC NONLINEAR CONTROLLER DESIGN FOR A POWER FACTOR CORRECTOR

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IFAC Proceedings Volumes 2002年第1期35卷 305-310页

作者： Seigo SASAKI Department of Electrical and Electronic Engineering National Defense Academy 1-10-20 Hashirimizu Yokosuka 239-8686 JAPAN

A nonlinear controller for a power factor corrector is systematically constructed via Lyapunov-based controller design approach for the bilinear state averaged model. First, a nonlinear gain of the controller is derived to shape the source current and the output voltage be desired form respectively via nonlinear H ∞ control system design approach. Second, a source current reference generator is constructed, which consists of a feedforward loop given by steady state analysis and a feedback loop with output voltage error amplifier. This paper, finally, shows efficiencies of the approach through computer simulations.

关键词： power supplies switching rectifiers bilinear systems H-infinity control Lyapunov function convex programming

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Identification of Linear Time-Invariant Systems via Constrained Step-Based Realization

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IFAC Proceedings Volumes 2012年第16期45卷 1155-1160页

作者： Daniel N. Miller Raymond A. de Callafon Dept. of Mechanical and Aerospace Engineering University of California San Diego La Jolla CA 92093-0411 USA

A constrained step-based realization algorithm is developed to produce linear, time-invariant, state-space system estimates. To match a priori knowledge of the system behavior, the eigenvalues of the estimate are required to be stable, real, and positive; the step response is required to have no undershoot or overshoot; and the steady-state gain is required to match a known value. The standard step-based realization method is augmented to become a convex optimization problem subject to a linear-matrix inequality that constrains eigenvalue location, and a subsequent convex optimization problem is developed to constrain time-domain behavior. Simulation results motivate the need for such constraints and are used for comparison with familiar alternative methods. Although the procedure is applied only to step-response data, it may be generalized to constrain eigenvalues to convex regions of the complex plain and is applicable to all subspace identification methods.

关键词： System identification Subspace methods Step function responses convex programming

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NONLINEAR ROBUST MODEL PREDICTIVE CONTROL FOR LIFTING BODY RE-ENTRY FLIGHT ATTITUDE CONTROL

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IFAC Proceedings Volumes 2007年第7期40卷 323-328页

作者： E.R. van Oort Q.P. Chu J.A. Mulder Delft University of Technology Delft

The dynamics of re-entry vehicles are time varying and notoriously nonlinear due to the large flight envelope and nonlinear aerodynamic flow phenomena. Accuracy of guidance and control of the re-entry vehicle along a predefined trajectory is crucial because of operational and safety considerations. This paper presents the design of a nonlinear attitude controller based on a Robust Model Predictive Controller (RMPC) combined with Feedback Linearization of the vehicle dynamics. Since the re-entry vehicle model contains uncertainties, FBL will not fully linearize the system. This, combined with its constraint handling capabilities, is the motivation for the application of RMPC. The uncertainty is modeled as perturbations of the aerodynamic parameters within a given percentage of their nominal value. The designed controller was tested using the GESARED simulation toolbox and shows excellent performance. The state and input constraints are satisfied, and the robustness of the controller to variations in the aerodynamic parameters has increased significantly compared to a nominal, non-robust controller.

关键词： Nonlinear Control Robust Control Model Predictive Control Aerospace Control Feedback Linearization convex programming

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Algorithm of Optimal Time Moving of a Linear System to the convex Compact

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IFAC Proceedings Volumes 1998年第13期31卷 199-203页

作者： G.V. Shevchenko S.L.Sobolev Institute of Mathematics Siberian Branch of Russian Academy of Science 690090 Novosibirsk av. of acad. Koptyug4

In this paper an iterative algorithm for solving the problem of optimal time moving of a linear system from the initial state to the given convex compact. has been proposed. Global convergence of the algorithm is proved.

关键词： Optimal control multivarible systems computational method differential equations convex programming convergence

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The Method of Quasi-Solutions Based on Barrier Functions in the Analysis of Improper convex Programs

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PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS 2022年第SUPPL 1期319卷 S242-S256页

作者： Skarin, V. D. Russian Acad Sci Krasovskii Inst Math & Mech Ural Branch Ekaterinburg 620108 Russia

The paper is devoted to the construction of possible approximations for improper convex programs based on the application of a classical approach to the regularization of ill-posed extremal problems, namely V. K. Ivanov's method of quasi-solutions. While usually the constraints of the original problem in the method of quasi-solutions are aggregated with the help of exterior penalty functions, here we use for this purpose a generalized inverse barrier function, which is a modification of interior penalty. Due to the specifics of the problem, we introduce a number of new control parameters into the minimized barrier function. Along with the penalty coefficients and the regularization parameter, we consider parameters that ensure the correctness of the application of the barrier method, first of all, the existence of interior points in the domain of the method. We also discuss the existence of solutions to the resulting correction problems and analyze the influence of the parameters of the barrier function on the convergence of the proposed modification of the method of quasi-solutions for improper problems.

关键词： convex programming improper problem optimal correction method of quasi-solutions barrier function methods

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Properties of the Quadratic Transformation of Dual Variables

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ALGORITHMS 2023年第3期16卷 148-148页

作者： Krutikov, Vladimir Tovbis, Elena Bykov, Anatoly Stanimirovic, Predrag Chernova, Ekaterina Kazakovtsev, Lev Siberian Fed Univ Lab Hybrid Methods Modeling & Optimizat Complex Sy 79 Prosp Svobodny Krasnoyarsk 660041 Russia Kemerovo State Univ Dept Appl Math 6 Krasnaya St Kemerovo 650043 Russia Reshetnev Siberian State Univ Sci & Technol Institite Informat & Telecommun 31 Krasnoyarskii Rabochii Prospekt Krasnoyarsk 660037 Russia Inst Computat Technol SB RAS 21 Rukavishnikov St Kemerovo 650025 Russia Univ Nis Fac Sci & Math Nish 18000 Serbia

We investigate a solution of a convex programming problem with a strongly convex objective function based on the dual approach. A dual optimization problem has constraints on the positivity of variables. We study the methods and properties of transformations of dual variables that enable us to obtain an unconstrained optimization problem. We investigate the previously known method of transforming the components of dual variables in the form of their modulus (modulus method). We show that in the case of using the modulus method, the degree of the degeneracy of the function increases as it approaches the optimal point. Taking into account the ambiguity of the gradient in the boundary regions of the sign change of the new dual function variables and the increase in the degree of the function degeneracy, we need to use relaxation subgradient methods (RSM) that are difficult to implement and that can solve non-smooth non-convex optimization problems with a high degree of elongation of level surfaces. We propose to use the transformation of the components of dual variables in the form of their square (quadratic method). We prove that the transformed dual function has a Lipschitz gradient with a quadratic method of transformation. This enables us to use efficient gradient methods to find the extremum. The above properties are confirmed by a computational experiment. With a quadratic transformation compared to a modulus transformation, it is possible to obtain a solution of the problem by relaxation subgradient methods and smooth function minimization methods (conjugate gradient method and quasi-Newtonian method) with higher accuracy and lower computational costs. The noted transformations of dual variables were used in the program module for calculating the maximum permissible emissions of enterprises (MPE) of the software package for environmental monitoring of atmospheric air (ERA-AIR).

关键词： convex programming strongly convex functions nonlinear programming dual problem subgradient subgradient methods optimization algorithms

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