Asymptotic Stability of POD based Model Predictive Control for a semilinear parabolic PDE

In this article a stabilizing feedback control is computed for a semilinear parabolic partial differential equation utilizing a nonlinear model predictive (NMPC) method. In each level of the NMPC algorithm the finite time horizon open loop problem is solved by a reduced-order strategy based on proper orthogonal decomposition (POD). A stability analysis is derived for the combined POD-NMPC algorithm so that the lengths of the finite time horizons are chosen in order to ensure the asymptotic stability of the computed feedback controls. The proposed method is successfully tested by numerical examples

Variable sampling-time nonlinear model predictive control of satellites using magneto-torquers

Satellite control using magneto-torquers represents a control challenge combined with strong nonlinearity, variable dynamics and partial controllability. An automatic differentiation-based nonlinear model predictive control (NMPC) algorithm is developed in this work to tackle these issues. Based on the previously developed formulation of NMPC, a novel variable sampling-time scheme is proposed to provide a better trade-off between transient control performance and closed-loop stability. More specifically, a small sampling time is adopted to improve the response speed when the satellite is far away from the desired position, and a large sampling time is employed for the closed-loop stability when the satellite is around its equilibrium position. This scheme also significantly reduces the online computational burden associated with fixed sampling-time NMPC where a large prediction horizon has to be adopted in order to the ensure closed-loop stability. The proposed approach is demonstrated through nonlinear simulation of a specific satellite case with satisfactory results obtained

Multi-agent model predictive control for transport phenomena processes

Throughout the last decades, control systems theory has thrived, promoting new areas of development, especially for chemical and biological process engineering. Production processes are becoming more and more complex and researchers, academics and industry professionals dedicate more time in order to keep up-to-date with the increasing complexity and nonlinearity. Developing control architectures and incorporating novel control techniques as a way to overcome optimization problems is the main focus for all people involved. Nonlinear Model Predictive Control (NMPC) has been one of the main responses from academia for the exponential growth of process complexity and fast growing scale. Prediction algorithms are the response to manage closed-loop stability and optimize results. Adaptation mechanisms are nowadays seen as a natural extension of prediction methodologies in order to tackle uncertainty in distributed parameter systems (DPS), governed by partial differential equations (PDE). Parameters observers and Lyapunov adaptation laws are also tools for the systems in study. Stability and stabilization conditions, being implicitly or explicitly incorporated in the NMPC formulation, by means of pointwise min-norm techniques, are also being used and combined as a way to improve control performance, robustness and reduce computational effort or maintain it low, without degrading control action. With the above assumptions, centralized (or single agent) or decentralized and distributed Model Predictive Control (MPC) architectures (also called multi-agent) have been applied to a series of nonlinear distributed parameters systems with transport phenomena, such as bioreactors, water delivery canals and heat exchangers to show the importance and success of these control techniques

Feedback linearizing model predictive excitation controller design for multimachine power systems

In this paper, a nonlinear excitation controller is designed for multimachine power systems in order to enhance the transient stability under different operating conditions. The two-axis models of synchronous generators in multimachine power systems along with the dynamics of IEEE Type & #x2013;II excitation systems, are considered to design the proposed controller. The partial feedback linearization scheme is used to simplify the multimachine power system as it allows to decouple a multimachine power system based on the excitation control inputs of synchronous generators. A receding horizon-based continuous-time model predictive control scheme is used for partially linearized power systems to obtain linear control inputs. Finally, the nonlinear control laws, which also include receding horizon-based control inputs, are implemented on an IEEE 10-machine, 39-bus New England power system. The superiority of the proposed scheme is evaluated by providing comparisons with a similar existing nonlinear excitation controller where the control input for the feedback linearized model is obtained using the linear quadratic regulator (LQR) approach. The simulation results demonstrate that the proposed scheme performs better as compared to the LQR-based partial feedback linearizing excitation controller in terms of enhancing the stability margin

Gaussian process based model predictive control : a thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Engineering, School of Engineering and Advanced Technology, Massey University, New Zealand

The performance of using Model Predictive Control (MPC) techniques is highly dependent on a model that is able to accurately represent the dynamical system. The datadriven modelling techniques are usually used as an alternative approach to obtain such a model when first principle techniques are not applicable. However, it is not easy to assess the quality of learnt models when using the traditional data-driven models, such as Artificial Neural Network (ANN) and Fuzzy Model (FM). This issue is addressed in this thesis by using probabilistic Gaussian Process (GP) models. One key issue of using the GP models is accurately learning the hyperparameters. The Conjugate Gradient (CG) algorithms are conventionally used in the problem of maximizing the Log-Likelihood (LL) function to obtain these hyperparameters. In this thesis, we proposed a hybrid Particle Swarm Optimization (PSO) algorithm to cope with the problem of learning hyperparameters. In addition, we also explored using the Mean Squared Error (MSE) of outputs as the fitness function in the optimization problem. This will provide us a quality indication of intermediate solutions. The GP based MPC approaches for unknown systems have been studied in the past decade. However, most of them are not generally formulated. In addition, the optimization solutions in existing GP based MPC algorithms are not clearly given or are computationally demanding. In this thesis, we first study the use of GP based MPC approaches in the unconstrained problems. Compared to the existing works, the proposed approach is generally formulated and the corresponding optimization problem is eff- ciently solved by using the analytical gradients of GP models w.r.t. outputs and control inputs. The GPMPC1 and GPMPC2 algorithms are subsequently proposed to handle the general constrained problems. In addition, through using the proposed basic and extended GP based local dynamical models, the constrained MPC problem is effectively solved in the GPMPC1 and GPMPC2 algorithms. The proposed algorithms are verified in the trajectory tracking problem of the quadrotor. The issue of closed-loop stability in the proposed GPMPC algorithm is addressed by means of the terminal cost and constraint technique in this thesis. The stability guaranteed GPMPC algorithm is subsequently proposed for the constrained problem. By using the extended GP based local dynamical model, the corresponding MPC problem is effectively solved

On output feedback nonlinear model predictive control using high gain observers for a class of systems

In recent years, nonlinear model predictive control schemes have been derived that guarantee stability of the closed loop under the assumption of full state information. However, only limited advances have been made with respect to output feedback in connection to nonlinear predictive control. Most of the existing approaches for output feedback nonlinear model predictive control do only guarantee local stability. Here we consider the combination of stabilizing instantaneous NMPC schemes with high gain observers. For a special MIMO system class we show that the closed loop is asymptotically stable, and that the output feedback NMPC scheme recovers the performance of the state feedback in the sense that the region of attraction and the trajectories of the state feedback scheme are recovered for a high gain observer with large enough gain and thus leading to semi-global/non-local results