Self-Triggered Predictive Control with Time-Dependent Activation Costs of Mixed Logical Dynamical Systems

2014 ◽  
Vol E97.A (2) ◽  
pp. 476-483 ◽  
Author(s):  
Shogo NAKAO ◽  
Toshimitsu USHIO
Keyword(s):  
Dynamical Systems ◽  
Predictive Control ◽  
Time Dependent ◽  
Mixed Logical Dynamical

Ellipsoidal Lyapunov-based hybrid model predictive control for mixed logical dynamical systems with a recursive feasibility guarantee

2018 ◽  
Vol 41 (9) ◽  
pp. 2475-2487
Author(s):  
Alireza Olama ◽  
Mokhtar Shasadeghi ◽  
Amin Ramezani ◽  
Mostafa Khorramizadeh ◽  
Paulo R C Mendes
Keyword(s):  
Dynamical Systems ◽  
Model Predictive Control ◽  
Hybrid Model ◽  
Predictive Control ◽  
Robust Stability ◽  
Optimization Problem ◽  
Closed Loop ◽  
Loop System ◽  
Closed Loop System ◽  
Mixed Logical Dynamical

This paper proposes an ellipsoidal hybrid model predictive control approach to solve the robust stability problem of uncertain hybrid dynamical systems modelled by the mixed logical dynamical framework. In this approach, the traditional terminal equality constraint is replaced by an ellipsoid that results in a maximal positive invariant set for the closed-loop system. Then, a Lyapunov decreasing condition along with the robustness criterion is introduced to the optimization problem to achieve the robust stability of the closed-loop system. As the main advantages, the ellipsoidal terminal set proposed in this paper attains a larger domain of attraction along with the recursive feasibility guarantee. Moreover, the stability and robustness constraints are achieved by a lower prediction horizon, which leads to a smaller dimension optimization problem. In addition, to reduce the computational complexity of the corresponding optimization problem, a suboptimal version of the proposed algorithm is introduced. Finally, numerical and car suspension system examples show the capabilities of the proposed method.

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

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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