scholarly journals A Simplified Predictive Control of Constrained Markov Jump System with Mixed Uncertainties

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yanyan Yin ◽  
Yanqing Liu ◽  
Hamid R. Karimi
Keyword(s):  
Predictive Control ◽  
Transition Probability ◽  
Dynamic Performance ◽  
Markov Jump ◽  
Markov Jump System ◽  
Predictive Controller ◽  
Model Predictive Control Algorithm ◽  
Simplified Algorithm ◽  
Jump Systems ◽  
Mixed Uncertainties

A simplified model predictive control algorithm is designed for discrete-time Markov jump systems with mixed uncertainties. The mixed uncertainties include model polytope uncertainty and partly unknown transition probability. The simplified algorithm involves finite steps. Firstly, in the previous steps, a simplified mode-dependent predictive controller is presented to drive the state to the neighbor area around the origin. Then the trajectory of states is driven as expected to the origin by the final-step mode-independent predictive controller. The computational burden is dramatically cut down and thus it costs less time but has the acceptable dynamic performance. Furthermore, the polyhedron invariant set is utilized to enlarge the initial feasible area. The numerical example is provided to illustrate the efficiency of the developed results.

FEEDBACK PREDICTIVE CONTROL OF NONHOMOGENEOUS MARKOV JUMP SYSTEMS WITH NONSYMMETRIC CONSTRAINTS

2014 ◽  
Vol 56 (2) ◽  
pp. 138-149
Author(s):  
YANQING LIU ◽  
FEI LIU
Keyword(s):  
Predictive Control ◽  
Controller Design ◽  
Invariant Set ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Markov Jump System ◽  
Predictive Controller ◽  
Feasibility Region ◽  
Nonhomogeneous Markov Jump System ◽  
Jump Systems

AbstractWe consider feedback predictive control of a discrete nonhomogeneous Markov jump system with nonsymmetric constraints. The probability transition of the Markov chain is modelled as a time-varying polytope. An ellipsoid set is utilized to construct an invariant set in the predictive controller design. However, when the constraints are nonsymmetric, this method leads to results which are over conserved due to the geometric characteristics of the ellipsoid set. Thus, a polyhedral invariant set is applied to enlarge the initial feasible area. The results obtained are for a more general class of dynamical systems, and the feasibility region is significantly enlarged. A numerical example is presented to illustrate the advantage of the proposed method.

State-Space Dynamic Performance Preview-Predictive Controller

2006 ◽  
Vol 129 (2) ◽  
pp. 144-153 ◽  
Author(s):  
Andrzej W. Ordys ◽  
Masayoshi Tomizuka ◽  
Michael J. Grimble
Keyword(s):  
State Space ◽  
Predictive Control ◽  
Performance Index ◽  
Dynamic Performance ◽  
Optimization Procedure ◽  
Control Algorithms ◽  
Optimization Approach ◽  
Linear Quadratic ◽  
Preview Control ◽  
Predictive Controller

The paper discusses state-space generalized predictive control and the preview control algorithms. The optimization procedure used in the derivation of predictive control algorithms is considered. The performance index associated with the generalized predictive controller (GPC) is examined and compared with the linear quadratic (LQ) optimal control formulation used in preview control. A new performance index and consequently a new algorithm is proposed dynamic performance predictive controller (DPPC) that combines the features of both GPC and preview controller. This algorithm minimizes the performance index through a dynamic optimization. A simple example illustrates the features of the three algorithms and prompts a discussion on what is actually minimized in predictive control. The DPPC algorithm, derived in this paper, provides for a minimum of the predictive performance index. The differences and similarities between the preview control and the predictive control have been discussed and optimization approach of predictive control has been explained.

scholarly journals Model Predictive Control for Continuous-Time Singular Jump Systems with Incomplete Transition Rates

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Xinxin Gu ◽  
Jiwei Wen ◽  
Li Peng
Keyword(s):  
Model Predictive Control ◽  
Cost Function ◽  
Predictive Control ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Sampling Period ◽  
Transition Rates ◽  
Mean Square ◽  
Markov Jump ◽  
Jump Systems

This paper is concerned with model predictive control (MPC) problem for continuous-time Markov Jump Systems (MJSs) with incomplete transition rates and singular character. Sufficient conditions for the existence of a model predictive controller, which could optimize a quadratic cost function and guarantee that the system is piecewise regular, impulse-free, and mean square stable, are given in two cases at each sampling time. Since the MPC strategy is aggregated into continuous-time singular MJSs, a discrete-time controller is employed to deal with a continuous-time plant and the cost function not only refers to the singularity but also considers the sampling period. Moreover, the feasibility of the MPC scheme and the mean square admissibility of the closed-loop system are deeply discussed by using the invariant ellipsoid. Finally, a numerical example is given to illustrate the main results.

scholarly journals Stability Analysis for a Class of Discrete-Time Nonhomogeneous Markov Jump Systems with Multiplicative Noises

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Shaowei Zhou ◽  
Xiaoping Liu ◽  
Bing Chen ◽  
Hongxia Liu
Keyword(s):  
Discrete Time ◽  
Transition Probability ◽  
Convex Polytope ◽  
Linear Matrix ◽  
Infinite Matrix ◽  
Matrix Inequalities ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Multiplicative Noises ◽  
Jump Systems

This paper is concerned with a class of discrete-time nonhomogeneous Markov jump systems with multiplicative noises and time-varying transition probability matrices which are valued on a convex polytope. The stochastic stability and finite-time stability are considered. Some stability criteria including infinite matrix inequalities are obtained by parameter-dependent Lyapunov function. Furthermore, infinite matrix inequalities are converted into finite linear matrix inequalities (LMIs) via a set of slack matrices. Finally, two numerical examples are given to demonstrate the validity of the proposed theoretical methods.

Observer-Based H∞ Control on Nonhomogeneous Discrete-Time Markov Jump Systems

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Yanyan Yin ◽  
Peng Shi ◽  
Fei Liu ◽  
Kok Lay Teo
Keyword(s):  
Discrete Time ◽  
Controller Design ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Closed Loop System ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Stochastically Stable ◽  
Jump Transition ◽  
Jump Systems

This paper concerns the problem of observer-based H∞ controller design for a class of discrete-time Markov jump systems with nonhomogeneous jump parameters. A nonhomogeneous jump transition probability matrix is described by a polytope set, in which values of vertices are given. By Lyapunov function approach, under the designed observer-based controller, a sufficient condition is presented to ensure the resulting closed-loop system is stochastically stable and a prescribed H∞ performance is achieved. Finally, a simulation example is given to show the effectiveness of the developed techniques.

scholarly journals Level Control of Quadruple Tank Process using Laguerre Functions based Model Predictive Control Algorithm

2020 ◽  
Vol 5 (2) ◽  
pp. 130-137
Author(s):  
Kamel Menighed ◽  
Issam CHEKAKTA
Keyword(s):  
Predictive Control ◽  
Laguerre Functions ◽  
Level Control ◽  
Constrained System ◽  
Discrete State ◽  
Space Modeling ◽  
Predictive Controller ◽  
Model Predictive Control Algorithm ◽  
Computation Load ◽  
Control Trajectory

This paper aims to present a model predictive controller based on discrete state-space modeling, where the future control trajectory is approximated by a set of discrete-time Laguerre functions instead of shift forward operators. The benefit of using these orthonormal Laguerre functions is that they have fewer parameters to adjust in the optimization problem and the computation load is significantly lower than the standard predictive control. The effectiveness of this controller is illustrated through the quadruple tank process, which is a highly interacted, multivariable and constrained system.

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