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.

Control of magnetic levitation system using recurrent neural network-based adaptive optimal backstepping strategy

2020 ◽  
Vol 42 (13) ◽  
pp. 2382-2395
Author(s):  
Armita Fatemimoghadam ◽  
Hamid Toshani ◽  
Mohammad Manthouri
Keyword(s):  
Neural Network ◽  
Recurrent Neural Network ◽  
Optimization Problem ◽  
Closed Loop ◽  
Magnetic Levitation ◽  
Backstepping Control ◽  
Loop System ◽  
Closed Loop System ◽  
Levitation System ◽  
Magnetic Levitation System

In this paper, a novel approach is proposed for adjusting the position of a magnetic levitation system using projection recurrent neural network-based adaptive backstepping control (PRNN-ABC). The principles of designing magnetic levitation systems have widespread applications in the industry, including in the production of magnetic bearings and in maglev trains. Levitating a ball in space is carried out via the surrounding attracting or repelling magnetic forces. In such systems, the permissible range of the actuator is significant, especially in practical applications. In the proposed scheme, the procedure of designing the backstepping control laws based on the nonlinear state-space model is carried out first. Then, a constrained optimization problem is formed by defining a performance index and taking into account the control limits. To formulate the recurrent neural network (RNN), the optimization problem is first converted into a constrained quadratic programming (QP). Then, the dynamic model of the RNN is derived based on the Karush-Kuhn-Tucker (KKT) optimization conditions and the variational inequality theory. The convergence analysis of the neural network and the stability analysis of the closed-loop system are performed using the Lyapunov stability theory. The performance of the closed-loop system is assessed with respect to tracking error and control feasibility.

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.

Speed Model Predictive Control Based on the Track Error Rate

2013 ◽  
Vol 336-338 ◽  
pp. 839-842
Author(s):  
Jin Huang ◽  
Cheng Zhi Yang ◽  
Ji Feng Wang
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Closed Loop ◽  
Tracking Error ◽  
Matlab Simulation ◽  
Closed Loop System ◽  
Index Function ◽  
Dynamical Characteristics ◽  
Simulation Results ◽  
Controlled Object

In order to make the controlled object have better dynamical characteristics, through introducing the differential item of error into optimal performance index function of tracking error, an improved algorithm of model predictive control is discussed in this paper. The theoretical analysis and Matlab simulation results show that it has better controlled quality and stronger robustness for closed-loop system.

scholarly journals Model-Predictive Control and Closed-Loop Stability Considerations for Nonlinear Plants Described by Local ARX-Type Models

2013 ◽  
Author(s):  
Michael E. Cholette ◽  
Dragan Djurdjanovic
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Optimization Problem ◽  
Closed Loop ◽  
Type Model ◽  
Control Input ◽  
Dual Purpose ◽  
Nonlinear Plants ◽  
And Control ◽  
Local Input

In this paper, a model-predictive control (MPC) method is detailed for the control of nonlinear systems with stability considerations. It will be assumed that the plant is described by a local input/output ARX-type model, with the control potentially included in the premise variables, which enables the control of systems that are nonlinear in both the state and control input. Additionally, for the case of set point regulation, a suboptimal controller is derived which has the dual purpose of ensuring stability and enabling finite-iteration termination of the iterative procedure used to solve the nonlinear optimization problem that is used to determine the control signal.

A Dual-Mode Model Predictive Control Algorithm Trajectory Tracking in Discrete-Time Nonlinear Dynamic Systems

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Asad A. Ul Haq ◽  
Michael E. Cholette ◽  
Dragan Djurdjanovic
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Discrete Time ◽  
Dynamic Systems ◽  
Trajectory Tracking ◽  
Closed Loop ◽  
Linear Control ◽  
Nonlinear Dynamic Systems ◽  
Closed Loop System ◽  
Dual Mode

In this paper, a dual-mode model predictive/linear control method is presented, which extends the concept of dual-mode model predictive control (MPC) to trajectory tracking control of nonlinear dynamic systems described by discrete-time state-space models. The dual-mode controller comprises of a time-varying linear control law, implemented when the states lie within a sufficiently small neighborhood of the reference trajectory, and a model predictive control strategy driving the system toward that neighborhood. The boundary of this neighborhood is characterized so as to ensure stability of the closed-loop system and terminate the optimization procedure in a finite number of iterations, without jeopardizing the stability of the closed-loop system. The developed controller is applied to the central air handling unit (AHU) of a two-zone variable air volume (VAV) heating, ventilation, and air conditioning (HVAC) system.

scholarly journals Intelligent Swing-Up and Robust Stabilization via Tube-based Nonlinear Model Predictive Control for A Rotational Inverted-Pendulum System

2020 ◽  
Vol 45 (1) ◽  
pp. 49-64
Author(s):  
Alvaro Prado ◽  
Marco Herrera ◽  
Oswaldo Menéndez
Keyword(s):  
Predictive Control ◽  
Nonlinear Model ◽  
Closed Loop ◽  
Inverted Pendulum ◽  
Angular Position ◽  
Loop System ◽  
Invariant Sets ◽  
Closed Loop System ◽  
Pendulum System ◽  
Inverted Pendulum System

The purpose of this paper is to introduce a new robust nonlinear model-based predictive control scheme applied to a rotational inverted-pendulum system. The rotational pendulum is composed by a mechanical arm attached to a free-motion pendulum (orthogonal to the arm), namely Furuta Pendulum. In principle, a Fuzzy controller enables the robotic arm bar to lift the rotational pendulum through oscillatory swing-up motion up to automatically achieve the upper equilibrium position in a prescribed stabilizing operation range. After the pendulum reaches the operating range, an intelligent control bypass system allows the transition between the swing-up motion controller and a robust predictive controller to maintain the angular position of the pendulum around the upward critical position. To achieve robust performance, a centralized control framework combines a triplet of control actions. The first one compensates for disturbances using the regulation trajectory ?feedforward control. The second control action corrects errors produced by modelling mismatch. The third controller assures robustness on the closed-loop system whilst compensating for deviations of the state trajectories from the nominal ones (i.e, disturbance-free). The control strategy provides robust feasibility despite constraints on the arm bar and pendulum's actuators are met. Such constraints are calculated on-line based on robust positively invariant sets characterised by polytopic sets (tubes). The proposed controller is tested in a series of simulations, and experimentally validated on a high-fidelity simulation environment including a rotational inverted-pendulum built for educational purposes. The results show that robust control performance is strengthened against disturbances of the closed-loop system benchmarked to inherently-robust linear and nonlinear predictive controllers.

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