Model Predictive Control for Hybrid Dynamical Systems: Sufficient Conditions for Asymptotic Stability with Persistent Flows or Jumps

In this paper, sufficient conditions for almost sure stability and asymptotic stability of certain classes of linear stochastic distributed-parameter dynamical systems are derived. These systems are described by a set of linear partial differential or differential-integral equations with stochastic parameters. Various examples are given to illustrate the application of the main results.

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Formation Reconfiguration Using Model Predictive Control Techniques for Multi-agent Dynamical Systems

Developments in Model-Based Optimization and Control - Lecture Notes in Control and Information Sciences ◽

10.1007/978-3-319-26687-9_9 ◽

2015 ◽

pp. 183-205

Author(s):

Minh Tri Nguyen ◽

Cristina Stoica Maniu ◽

Sorin Olaru ◽

Alexandra Grancharova

Keyword(s):

Dynamical Systems ◽

Model Predictive Control ◽

Predictive Control ◽

Control Techniques ◽

Formation Reconfiguration ◽

Multi Agent

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Optimally designed Lyapunov–Krasovskii terminal costs for robust stable–feasible model predictive control of uncertain time-delay nonlinear dynamical systems

Proceedings of the Institution of Mechanical Engineers Part I Journal of Systems and Control Engineering ◽

10.1177/0959651820952193 ◽

2020 ◽

pp. 095965182095219

Author(s):

S Yaqubi ◽

MR Homaeinezhad

Keyword(s):

Time Delay ◽

Dynamical Systems ◽

Model Predictive Control ◽

Predictive Control ◽

Robust Stability ◽

Control Algorithm ◽

Nonlinear Dynamical Systems ◽

Prediction Horizon ◽

Delay Effects ◽

Uncertain Time

This article details a new Model Predictive Control algorithm ensuring robust stability and control feasibility for uncertain nonlinear multi-input multi-output dynamical systems considering uncertain time-delay effects. The proposed control algorithm is based on construction of a Lyapunov–Krasovskii functional as terminal cost. Incorporation of this terminal cost into the Model Predictive Control optimization problem and calculation of the associated admissible set result in robust feasibility and robust stability of closed-loop system in presence of uncertain time-delay effects and bounded disturbance signals. The Lyapunov–Krasovskii functional term is constructed with respect to predicted sliding functions over the prediction horizon and considers the effects of dynamical variations over the prediction horizon in generation of control inputs. As dynamical variations are investigated in a sample-to-sample basis, feasible sliding regions are updated at each sample as well. Finally, based on expression of sliding functions as a combination of dynamical variations and input-based terms, required control inputs are calculated in the admissible bound by the optimization algorithm. Construction of control scheme on this basis permits straightforward calculation of robust stability and feasibility conditions for a general class of uncertain nonlinear system in finite prediction horizon whereas in the previous works, often-restrictive conditions were considered for the investigated dynamical systems. Numerical illustrations indicate precision and efficiency of control algorithm and improved stability and convergence rate for multivariable nonlinear dynamical systems considering uncertain time-delay effects. Finally, hardware-in-the-loop implementation indicates applicability of the proposed scheme in real-time control applications particularly in case appropriate compromises between optimality and calculation speed are considered.

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Nonfragile Robust Model Predictive Control for Uncertain Constrained Systems with Time-Delay Compensation

Mathematical Problems in Engineering ◽

10.1155/2016/1945964 ◽

2016 ◽

Vol 2016 ◽

pp. 1-14 ◽

Cited By ~ 1

Author(s):

Wei Jiang ◽

Hong-li Wang ◽

Jing-hui Lu ◽

Wei-wei Qin ◽

Guang-bin Cai

Keyword(s):

Time Delay ◽

Model Predictive Control ◽

Predictive Control ◽

Optimization Problems ◽

Sufficient Conditions ◽

Constrained Systems ◽

Delay Compensation ◽

Robust Model Predictive Control ◽

Robust Model ◽

Time Delay Compensation

This study investigates the problem of asymptotic stabilization for a class of discrete-time linear uncertain time-delayed systems with input constraints. Parametric uncertainty is assumed to be structured, and delay is assumed to be known. In Lyapunov stability theory framework, two synthesis schemes of designing nonfragile robust model predictive control (RMPC) with time-delay compensation are put forward, where the additive and the multiplicative gain perturbations are, respectively, considered. First, by designing appropriate Lyapunov-Krasovskii (L-K) functions, the robust performance index is defined as optimization problems that minimize upper bounds of infinite horizon cost function. Then, to guarantee closed-loop stability, the sufficient conditions for the existence of desired nonfragile RMPC are obtained in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to illustrate the effectiveness of the proposed approaches.

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