scholarly journals Parameterized Regulator Synthesis for Bimodal Linear Systems Based on Bilinear Matrix Inequalities

2008 ◽  
Vol 2008 ◽  
pp. 1-22 ◽  
Author(s):  
Zhizheng Wu ◽  
Foued Ben Amara
Keyword(s):  
Linear Systems ◽  
Design Method ◽  
Second Step ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Switched Linear System ◽  
Central Controller ◽  
Bilinear Matrix Inequalities ◽  
Synthesis Approach ◽  
Selection Of

A regulator design method is presented for switched bimodal linear systems, where it is desired to reject known disturbance signals and/or track known reference inputs. The switching in the bimodal system is defined by a switching surface. The regulator design approach consists of three steps. The first step is based on constructing a switched observer-based state feedback central controller for the switched linear system. The second step involves augmenting the switched central controller with additional dynamics to construct a parameterized set of switched controllers. In the third step, two sufficient regulation conditions are derived for the resulting switched closed loop system. The regulation conditions present guidelines for the selection of the additional dynamics used to parameterize the switched controllers to yield the desired regulator. A regulator synthesis approach is proposed based on solving properly formulated bilinear matrix inequalities. Finally, a numerical example is presented to illustrate the performance of the proposed regulator.

Parameterized Regulator Design Method for Switched Linear Systems

2006 ◽  
Author(s):  
Zhizheng Wu ◽  
Foued Ben Amara
Keyword(s):  
Linear Systems ◽  
Closed Loop ◽  
Design Method ◽  
Loop System ◽  
Closed Loop System ◽  
Switched Linear System ◽  
Switched Linear Systems ◽  
Central Controller ◽  
Synthesis Approach ◽  
System Switching

In this paper, a parameterized regulator design method based on bilinear matrix inequalities (BMIs) is presented for switched linear systems, where it is desired to reject known disturbance signals and/or track known reference inputs. Switching among plant models as well among disturbance and reference signals is defined according to a switching surface. The regulator design approach consists of three steps. The first step consists of constructing a switched observer-based state-feedback central controller for the switched linear system. Switching in the controller is performed according to the same switching rule as in the plant. The second step involves augmenting the switched central-controller to construct a parameterized set of switched controllers. Conditions for internal stability of the resulting switched closed loop system are presented. In the third step, regulation conditions are derived for the switched closed loop system. Based on the regulation conditions, a regulator synthesis approach is proposed based on solving properly formulated BMIs. Finally, a numerical example is presented to illustrate the performance of the proposed regulator.

Reliable Η∞ Control for Discrete-Time Switched Linear Systems with Intermittent Measurements

2011 ◽  
Vol 181-182 ◽  
pp. 145-150
Author(s):  
Dong Sheng Du
Keyword(s):  
Linear Systems ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Stochastic Variable ◽  
Switched Linear Systems ◽  
Stochastically Stable ◽  
Intermittent Measurements

In this paper, a scheme of reliable control for switched linear systems with intermittent measurements is developed. The stochastic variable is assumed to be a Bernoulli distributed white sequence appearing in measured output. Sufficient conditions for the existence of the switched observer and the switched controller are derived in terms of linear matrix inequalities (LMIs), which can maintain the closed-loop system is stochastically stable with a prescribed performance level.

Stabilizing Q-Parameterized Regulator Design for Discrete-Time Switched Bimodal Systems

2011 ◽  
Vol 48-49 ◽  
pp. 1097-1100
Author(s):  
Zhi Zheng Wu
Keyword(s):  
Linear Systems ◽  
Linear Matrix Inequalities ◽  
Discrete Time ◽  
Design Method ◽  
Synthesis Method ◽  
Switched System ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Numerical Example ◽  
Stabilizing Controllers

This paper considers a regulation problem for discrete-time switched bimodal linear systems. First, a set of observer-based -parameterized stabilizing controllers for the switched system is constructed. Then, a regulator synthesis method is proposed based on solving a set of linear matrix inequalities which is derived from a regulation condition for the switched system. Finally, a numerical example is presented to illustrate the effectiveness of the proposed design method.

scholarly journals Design of delay observer-based controllers for uncertain time-lag systems

1999 ◽  
Vol 5 (2) ◽  
pp. 121-137 ◽  
Author(s):  
Magdi S. Mahmoud ◽  
Mohamed Zribi
Keyword(s):  
Uncertain Systems ◽  
Closed Loop ◽  
Time Lag ◽  
Linear Matrix ◽  
Time Lags ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Delayed Measurements ◽  
Uncertain Time ◽  
Theoretical Developments

In this paper, the problem of designing observers and observer-based controllers for a class of uncertain systems with input and state time lags is considered. We construct delay-type observers in which both the instantaneous as well as the delayed measurements are utilized. Using feedback control based on the reconstructed state, the behavior of the closed-loop system is investigated. It is established that the uncertain time-lag system with delay observer-based control is asymptotically stable. Expressions for the gain matrices are given based on two linear-matrix inequalities. A numerical example is given to illustrate the theoretical developments.

scholarly journals Finite-Time Stabilization for Stochastic Inertial Neural Networks with Time-Delay via Nonlinear Delay Controller

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Deyi Li ◽  
Yuanyuan Wang ◽  
Guici Chen ◽  
Shasha Zhu
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Finite Time ◽  
Design Method ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Nonlinear Feedback ◽  
Inertial Neural Networks ◽  
Finite Time Stabilization

This paper pays close attention to the problem of finite-time stabilization related to stochastic inertial neural networks with or without time-delay. By establishing proper Lyapunov-Krasovskii functional and making use of matrix inequalities, some sufficient conditions on finite-time stabilization are obtained and the stochastic settling-time function is also estimated. Furthermore, in order to achieve the finite-time stabilization, both delayed and nondelayed nonlinear feedback controllers are designed, respectively, in terms of solutions to a set of linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate the correction of the theoretical results and the effectiveness of the proposed control design method.

A Control-Theoretic Approach to Neural Pharmacology: Optimizing Drug Selection and Dosing

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
Gautam Kumar ◽  
Seul Ah Kim ◽  
ShiNung Ching
Keyword(s):  
Design Method ◽  
Target Space ◽  
Theoretic Approach ◽  
Time Varying ◽  
Drug Selection ◽  
Modeling Paradigm ◽  
Dosing Strategies ◽  
Dose Dependent ◽  
Optimal Construction ◽  
Selection Of

The induction of particular brain dynamics via neural pharmacology involves the selection of particular agonists from among a class of candidate drugs and the dosing of the selected drugs according to a temporal schedule. Such a problem is made nontrivial due to the array of synergistic drugs available to practitioners whose use, in some cases, may risk the creation of dose-dependent effects that significantly deviate from the desired outcome. Here, we develop an expanded pharmacodynamic (PD) modeling paradigm and show how it can facilitate optimal construction of pharmacologic regimens, i.e., drug selection and dose schedules. The key feature of the design method is the explicit dynamical-system based modeling of how a drug binds to its molecular targets. In this framework, a particular combination of drugs creates a time-varying trajectory in a multidimensional molecular/receptor target space, subsets of which correspond to different behavioral phenotypes. By embedding this model in optimal control theory, we show how qualitatively different dosing strategies can be synthesized depending on the particular objective function considered.

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