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Robust structural control with system constraints

STRUCTURAL CONTROL & HEALTH MONITORING 2012年第3期19卷 472-490页

作者： Materazzi, Annibale Luigi Ubertini, Filippo Univ Perugia Dept Civil & Environm Engn I-06125 Perugia Italy

Physical limits of real control systems, such as force saturations and state variable constraints, if attained during the motion, may cause actuator damages, loss of control effectiveness or even a dynamic instability. In order to overcome these drawbacks and improve the overall reliability of the control policy without turning to uneconomic designs, it might be convenient to account for physical limitations directly in the control law. This philosophy is embraced in this paper, where a general approach is presented based on the tool of the state-dependent Riccati equation, in the general framework of nonlinear regulation. The proposed formulation is meant to be feasible to handle limitations on both state variables and control forces. This general control strategy is then specialized to the case of a seismically excited multi-storey frame structure equipped with an active mass damper subjected to actuator saturation and stroke limitation. In-depth numerical simulations are also performed in order to investigate the effectiveness of the proposed approach, for different levels of constraint severities, and its robustness against unknown random variations of structural parameters, also in the case of incomplete number of sensors, measurements affected by noise and the presence of process disturbances. Copyright (c) 2011 John Wiley & Sons, Ltd.

关键词： structural control state variable constraints saturation limits linear quadratic regulator state-dependent Riccati equation

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Hierarchical Design of Sigmoidal Generalized Moments of Manipulator under Uncertainty

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AUTOMATION AND REMOTE CONTROL 2018年第3期79卷 554-570页

作者： Krasnova, S. A. Antipov, A. S. Russian Acad Sci Trapeznikov Inst Control Sci Moscow Russia Natl Res Univ Bauman Moscow State Tech Univ Moscow Russia

For the orientation control system of the manipulator's end effector with electrical actuators, we develop a decomposition pr ocedure of feedback law design to track given trajectories in the end effector's coordinate system. Owing to the S-shaped smooth sigma-functions used as the local feedback laws and corrections of the state observer, the tracking system is invariant with a given accuracy with respect to existing uncertainties under constraints imposed on the variables of the mechanical subsystem. The suggested approach does not involve the solution of the inverse kinematics and dynamics problems and also relaxes the requirements to the volume of a priori information about the plant and external perturbations.

关键词： manipulator tracking invariance state variable constraints sigma-function state observer

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MAXIMUM PRINCIPLE FOR TIME-LAG CONTROL PROBLEMS WITH BOUNDED state

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1977年第4期22卷 563-606页

作者： BUNCE, GR WINONA STATE UNIV DEPT MATH SCIWINONAMN 55987

A maximum principle is obtained for control problems involving a constant time lag τ in both the control and state variables. The problem considered is that of minimizing ... 详细信息

A maximum principle is obtained for control problems involving a constant time lag τ in both the control and state variables. The problem considered is that of minimizing $$I(x) = \int_{t^0 }^{t^1 } {L (t,x(t), x(t - \tau ), u(t), u(t - \tau )) dt} $$ subject to the constraints 1 $$\begin{gathered} \dot x(t) = f(t,x(t),x(t - \tau ),u(t),u(t - \tau )), \hfill \\ x(t) = \phi (t), u(t) = \eta (t), t^0 - \tau \leqslant t \leqslant t^0 , \hfill \\ \end{gathered} $$ 1 $$\psi _\alpha (t,x(t),x(t - \tau )) \leqslant 0,\alpha = 1, \ldots ,m,$$ 1 $$x^i (t^1 ) = X^i ,i = 1, \ldots ,n$$ . The results are obtained using the method of Hestenes.

关键词： bounded state problems maximum principle optimal control problems retarded control problems state variable constraints Time-delay systems

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A Numerical Study of Augmented Penalty Function Algorithms for Terminally Constrained Optimal Control Problems

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1974年第4期14卷 393-403页

作者： O'Doherty, R. J. Pierson, B. L. Martin Marietta Corp Denver CO USA Iowa State Univ Dept Aerosp Engn Ames IA USA Iowa State Univ Engn Res Inst Ames IA USA

Three augmented penalty function algorithms are tested and compared with an ordinary penalty function algorithm for two demonstration optimal control problems. Although the augmented penalty function is quite helpful in solving control problems with terminal state constraints, the convergence can be improved significantly by providing systematic increases in the penalty constant.

关键词： Augmented penalty function penalty function methods method of multipliers numerical methods state variable constraints

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EMBEDDING THEOREM FOR INTEGRAL-EQUATIONS

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1975年第5-6期16卷 539-548页

作者： BAKKE, VL UNIV ARKANSAS DEPT MATHFAYETTEVILLEAR 72701

In this paper, an embedding theorem is established for a system of nonlinear integral equations of the Volterra type. The main result is basic in the development of a maximum principle for an optimal control problem i... 详细信息

关键词： control theory Embedding theorems integral equations state variable constraints

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A Nonlinear Programming Approach to Space Shuttle Trajectory Optimization

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1974年第1期13卷 94-118页

作者： Brusch, R. G. Convair Aerosp Div Gen Dynam San Diego CA USA

Space shuttle trajectory design requires the optimization of highly-constrained, branched, atmospheric trajectories. This paper presents a general mathematical model for trajectory optimization incorporating multiple simulation sections, state variable discontinuities, subarc elimination, branching, and six types of equality and inequality constraints. A solution is sought using a nonlinear programming approach based on SUMT, the sequential unconstrained minimization technique. Results of the numerical solution of a highly constrained space shuttle reentry problem are presented.

关键词： Nonlinear programming penalty-function methods trajectories state variable constraints flight mechanics

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Zone Control with Model Predictive Control for Much Constrained states Process

Zone Control with Model Predictive Control for Much Constrai...

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31st Chinese Control Conference

作者： Luo Xionglin Zhou Xiaolong Wang Shubin Xu Feng China Univ Petr Res Inst Automat Beijing 102249 Peoples R China

ISBN: (纸本)9789881563811

In industrial process, especially in chemical process control, controlled process has the characteristic of many intermediate state variables. The problem of how to handle the amplitude constraints of input, output and some important state variables, which commonly exists in process control, is the nodus of current researches. Model Predictive Control (MPC) can bring the constraints of input, output variables into the optimization problem, which is solved on-line to obtain the control law. With this advantage MPC is superior to other control methods to control constrained system. However, the disposal of amplitude constraint of important state variables in current MPC algorithms, usually consider it as one part of constraints of output variables, increases the number of controlled variables. A new zone predictive control algorithm is presented in this paper to deal with the constraint of important state variables This new algorithm transforms constraint of important state variables to matrix inequality form of input increment on-line, and brings it into the optimization problem for obtaining the control law. In the end, simulation results of control problem about side-stream quality of crude tower show the effectiveness and feasibleness of the proposed algorithm.

关键词： Model Predictive Control state variable constraints Zone Control state variable Correction

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