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.

Stability of switched Markovian jump systems with time-varying generally bounded transition rates

2021 ◽  
pp. 014233122098753
Author(s):  
Dunke Lu ◽  
Xiaohang Li
Keyword(s):  
Sufficient Conditions ◽  
Markovian Jump Systems ◽  
Time Varying ◽  
Transition Rates ◽  
Mean Square ◽  
Markovian Jump ◽  
Mean Square Stability ◽  
Special Cases ◽  
Jump Systems ◽  
Exponential Mean Square Stability

This paper addresses the exponential mean-square stability for a kind of switched Markovian jump systems, which have time-varying generally bounded transition rates and mode-dependent time delay. Since these transition rates are time-varying and generally bounded, they turn out to be more practical. In fact, those existing transition rates can be treated as special cases of the proposed ones in this paper. By constructing a new Lyapunov-Krasovskii function, sufficient conditions in a tractable form are derived for the exponential mean-square stability of the considered systems. For good measure, a numerical example is given to show the efficiency and potential of the proposed method.

A novel full-order and reduced-order fault detection filters design method for continuous-time singular Markov jump systems with complexity transition rates

2021 ◽  
pp. 014233122199096
Author(s):  
Yunling Shi ◽  
Xiuyan Peng
Keyword(s):  
Fault Detection ◽  
Continuous Time ◽  
Design Method ◽  
Transition Rates ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Reduced Order ◽  
Jump Systems ◽  
Stochastic Admissibility ◽  
Fault Detection Filters

This work is concerned with the problem of full-order and reduced-order fault detection filters (FDFs) design in a convex optimization frame for continuous-time singular Markov jump systems (CTSMJSs) with complexity transition rates (TRs). A novel Lyapunov function construct approach is utilized to cope with the stochastic admissibility problem for CTSMJSs with complexity TRs. In order to obtain effective full-order and reduced-order FDFs, we decoupled the inequality using the presupposed Lyapunov matrix. Owing to the use of Lyapunov stochastic admissibility theory and a novel decoupling method based on convex polyhedron technique, some sufficient conditions are obtained to guarantee that the resulting full-order and reduced-order FDFs are suitable for CTSMJSs with complexity TRs. In particular, the reduced-order FDF has the advantages of small storage space and fast detection speed compared with the full order FDF. Four illustrative examples are given to explain the effectiveness of the proposed full-order and reduced-order FDFs design method.

Robust Distributed Model Predictive Control of Constrained Continuous-Time Nonlinear Systems Using Two-Layer Invariant Sets

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
Xiaotao Liu ◽  
Yang Shi ◽  
Daniela Constantinescu
Keyword(s):  
Nonlinear Systems ◽  
Model Predictive Control ◽  
Predictive Control ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Invariant Sets ◽  
Cost Functions ◽  
Distributed Model ◽  
Design Parameters ◽  
Distributed Model Predictive Control

This paper introduces a robust distributed model predictive control (DMPC) strategy for constrained continuous-time nonlinear systems coupled through their cost functions. In the proposed technique, all the subsystems receive the assumed control trajectories of their neighbors and compute their controls by optimizing local cost functions with coupling terms. Provided that the initial state is feasible and the disturbances are bounded, a two-layer invariant sets-based controller design ensures robustness while appropriate tuning of the design parameters guarantees recursive feasibility. This paper first derives sufficient conditions for the convergence of all the subsystem states to a robust positive invariant set. Then, it exploits the κ ∘ δ controllability set to propose a less conservative robust model predictive control (MPC) strategy that permits the adoption of a shorter prediction horizon and tolerates larger disturbances. A numerical example illustrates that the designed algorithm leads to stronger cooperation among subsystems compared to an existing robust DMPC technique.

scholarly journals Finite-Time Asynchronous Stabilization for Nonlinear Hidden Markov Jump Systems with Parameter Varying in Continuous-Time Case

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Lianjun Xiao ◽  
Xiaofeng Wang ◽  
Lingling Gao
Keyword(s):  
Continuous Time ◽  
Finite Time ◽  
Hidden Markov ◽  
Sufficient Conditions ◽  
Linear Parameter ◽  
Markov Jump ◽  
Linear Parameter Varying ◽  
Markov Jump Systems ◽  
Parameter Varying ◽  
Jump Systems

The finite-time asynchronous stabilization problem has received great attention because of the wide application of actual engineering. In this paper, we consider the problem of finite-time asynchronous stabilization for nonlinear hidden Markov jump systems (HMJSs) with linear parameter varying. Compared with the existing research results on Markov jump systems, this paper considers the HMJSs which contain both the hidden state and the observed state in continuous-time case. Moreover, we consider the parameters of the systems are time varying. The aim of the paper is to design a proper observation-mode-based asynchronous controller such that the closed-loop HMJSs with linear parameter varying be stochastically finite-time bounded with H ∞ performance (SFTB- H ∞ ). Then, we give some sufficient conditions to solve the SFTB- H ∞ asynchronous controller by considering the stochastic Lyapunov–Krasovskii functional (SLKF) methods. Finally, a numerical example is used to show the validity of the main results.

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