A novel hybrid model predictive control design with application to a quadrotor helicopter

In this paper, a novel control design strategy based on a hybrid model predictive control in combination with fuzzy logic control is presented for a quadrotor helicopter system. In the proposed scheme, a 2‐part control structure is used. In the first part, a linear model predictive controller with receding horizon design strategy is combined with a nonlinear model predictive controller, which is applied as the main controller. In the second part, a 2‐level fuzzy logic controller is utilized to assist the first controller when the error exceeds a predefined value. The proposed nonlinear predictive control method utilizes a novel approach in which a prediction of the future outputs is used in the modeling stage. Using this simple technique, the problem can be solved using linear methods and, thereby, due to considerable reduction in the computational cost, it will be applicable for the systems with fast dynamics. Moreover, the fuzzy logic controller is used as a supervisor to adjust a proportional‐integral‐derivative controller to enhance the system performance by decreasing the tracking error. The proposed scheme is applied to a model of quadrotor system such that the difference between the predicted output of the system and the reference value is minimized while there are some constraints on inputs and outputs of the nonlinear quadrotor system. Simulation results demonstrate the efficiency of the proposed control scheme for the quadrotor system model.     

Learning-based parametrized model predictive control for trajectory tracking

This article is concerned with the tracking of nonequilibrium motions with model predictive control (MPC). It proposes to parametrize input and state trajectories of a dynamic system with basis functions to alleviate the computational burden in MPC. As a result of the parametrization, an optimization problem with fewer variables is obtained, and the memory requirements for storing the reference trajectories are reduced. The article also discusses the generation of feasible reference trajectories that account for the system's dynamics, as well as input and state constraints. In order to cope with repeatable disturbances, which may stem from unmodeled dynamics for example, an iterative learning procedure is included. The approach relies on a Kalman filter that identifies the repeatable disturbances based on previous trials. These are then included in the system's model available to the model predictive controller, which compensates them in subsequent trials. The proposed approach is evaluated on a quadcopter, whose task is to balance a pole, while flying a predefined trajectory.     

Observer‐based tracking controller design for quasi‐one‐sided Lipschitz nonlinear systems

In this paper, the observer‐based controller design problem for tracking a constant reference input for quasi‐one‐sided Lipschitz nonlinear systems is considered. For this purpose, at first, a state feedback controller is proposed and sufficient conditions for solvability of the problem are obtained in terms of linear matrix inequality feasibility conditions. Then, an observer for estimating the states of the system is designed. Subsequently, it is shown that the separation principle for the proposed feedback controller holds, and consequently, the designing of the state feedback controller and the observer can be done separately. Simulation results are given to verify the effectiveness of the proposed methodology.     

Cost function optimization for predictive control of a five-phase IM drive

Model predictive control has been used, for some time now, as a method to directly control power converters in electrical systems. The usual practice is tuning the cost function of the controller to obtain a certain compromise solution over the whole operating range of the system. This method is extended here to consider multiple, locally optimal, and tunings. The design objectives (tracking error, switching frequency, etc) are used to define a unique performance index that is locally optimized. In this way, the parameters of the cost function are linked to the current operating point. The tuning at each operating point is obtained numerically solving the optimization of the performance index. Although the idea can be applied to induction machines with any number of phases, in this paper, a five-phase induction motor is considered for presentation. This system is a demanding case due to the extra number of phases compared with the traditional three-phase motor. Simulation and experimental results are presented to assess the proposed predictive controller.     

Design and application of nonlinear model‐based tracking control schemes employing DEKF estimation

This paper deals with the design and application of nonlinear model‐based control schemes for stable and nonlinear benchmark industrial processes. The primary control objective is to facilitate set‐point (constant/time‐varying) tracking in the presence of external disturbances, process noise, measurement noise, parametric uncertainty, and model mismatch. We first propose a “noninferential‐type” model‐based control scheme which involves a finite‐dimensional, nonlinear, and deterministic process model to generate the model states. Secondly, an “inferential‐type” model‐based control scheme has been introduced particularly to take into account the stochastic uncertainties such as process noise and measurement noise. The second scheme exploits the dual extended Kalman filter for estimating the immeasurable states and the process parameters through which disturbance is injected. Unlike fixed‐parameter controllers, the proposed schemes update the controller gains at each step depending on the real‐time process gains. In order to demonstrate the usefulness of the proposed closed‐loop tracking control schemes, two exhaustive case studies have been carried out on the CSTR and Van de Vusse reactor processes, which are considered to be benchmark industrial processes due to highly nonlinear and unpredictable behaviour and due to nonminimum phase property. Finally, the performance of the proposed schemes are compared with an EKF‐based adaptive PI control framework and the simulation results reveal that the transient performance of the proposed schemes are better than that of the aforementioned PI technique especially in perturbed condition (ie, in presence of model mismatch and measurement noise).     

An MPC‐based position controller for a tilt‐rotor tricopter VTOL UAV

This study presents a novel framework, namely, the fusion of a conventional controller and a linear model predictive controller, for the position control of a tilt‐rotor tricopter. While the conventional controller in the outer loop is responsible for the position control, the inner‐loop model predictive control–based controller handles the angular dynamics and vertical body velocity. Furthermore, a novel control allocation algorithm for the proposed controller is introduced. In addition, this study also covers mathematical modeling and trim analysis of the tilt‐rotor tricopter dynamics. An evaluation of the designed control system is accomplished with a nonlinear 6‐degree‐of‐freedom simulation model of the tilt‐rotor tricopter in which realistic actuator limitations are considered. The efficiency of the proposed control algorithm is elaborated for a trajectory tracking problem where basic surveillance operation is considered. The simulation results show that the proposed model predictive controller is able to provide a satisfactory trajectory tracking performance under the realistic actuator limits.     

Qualitative analysis of tumor growth model under antiangiogenic therapy – choosing the effective operating point and design parameters for controller design

Every therapy that fights against cancer aims to reduce the tumor volume as far as possible. However, the price of low tumor volume has to be paid twice: as financial cost and also as side effect cost. In this article, we present qualitative correlation between the steady‐state tumor volume and inhibitor serum concentration based on the tumor growth model. Assuming standard state feedback, we present qualitative correlation between the steady‐state tumor volume and the parameters of the controller. In case of using an observer, we specify the steady‐state tumor volume and the expression for determining the steady‐state error of the state observer. We apply a limit for the state feedback to guarantee the stability of the closed‐loop system and the positivity of the control signal. The controller parameters depend on the applied operation point where the nonlinear system was linearized. We have investigated the effect of the operation point via simulations, and we present a quantitative theory for choosing the effective operating point. Copyright © 2015 John Wiley & Sons, Ltd.     

A BMI approach to guaranteed cost control of discrete‐time uncertain system with both state and input delays

In this study, the guaranteed cost control of discrete time uncertain system with both state and input delays is considered. Sufficient conditions for the existence of a memoryless state feedback guaranteed cost control law are given in the bilinear matrix inequality form, which needs much less auxiliary matrix variables and storage space. Furthermore, the design of guaranteed cost controller is reformulated as an optimization problem with a linear objective function, bilinear, and linear matrix inequalities constraints. A nonlinear semi‐definite optimization solver—PENLAB is used as a solution technique. A numerical example is given to demonstrate the effectiveness of the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.     

Inverse optimal controller based on extended Kalman filter for discrete‐time nonlinear systems

In this study, we present an inverse optimal control approach based on extended Kalman filter (EKF) algorithm to solve the optimal control problem of discrete‐time affine nonlinear systems. The main aim of inverse optimal control is to circumvent the tedious task of solving the Hamilton‐Jacobi‐Bellman equation that results from the classical solution of a nonlinear optimal control problem. Here, the inverse optimal controller is based on defining an appropriate quadratic control Lyapunov function (CLF) where the parameters of this candidate CLF were estimated by adopting the EKF equations. The root mean square error of the system states is used as the observed error in the case of classical EKF algorithm application, whereas, here, the EKF tries to eliminate the same root mean square error defined over the parameters by generating a CLF matrix with appropriate elements. The performance and the applicability of the proposed scheme is illustrated through both simulations performed on a nonlinear system model and a real‐time laboratory experiment. Simulation study demonstrate the effectiveness of the proposed method in comparison with 2 other inverse control approaches. Finally, the proposed controller is implemented on a professional control board to stabilize a DC‐DC boost converter and minimize a meaningful cost function. The experimental results show the applicability and effectiveness of the proposed EKF‐based inverse optimal control even in real‐time control systems with a very short time constant.     

Fully autonomous preload-sensitive control of implantable rotary blood pumps

A pulsatility-based control algorithm with a self-adapting pulsatility reference value is proposed for an implantable rotary blood pump and is to be tested in computer simulations. The only input signal is the pressure difference across the pump, which is deduced from measurements of the pump's magnetic bearing. A pulsatility index (PI) is calculated as the mean absolute deviation from the mean pressure difference. As a second characteristic, the gradient of the PI with respect to the pump speed is derived. This pulsatility gradient (GPI) is used as the controlled variable to adjust the operating point of the pump when physiological variables such as the systemic arterial pressure, left ventricular contractility, or heart rate change. Depending on the selected mode of operation, the controller is either a linear controller or an extremum-seeking controller. A supervisory mechanism monitors the state of the system and projects the system into the region of convergence when necessary. The controller of the GPI continuously adjusts the reference value for PI. An underlying robust linear controller regulates the PI to the reference value in order to take into account changes in pulmonary venous return. As a means of reacting to sudden changes in the venous return, a suction detection mechanism was included. The control system is robustly stable within a wide range of physiological variables. All the clinician needs to do is to select between the two operating modes. No other adjustments are required. The algorithm showed promising results which encourage further testing in vitro and in vivo.     

Neural net control of nonlinear plants through state feedback

A heuristic design method for state feedback fixed (non‐adaptive) neural net controller in nonlinear plants is presented. The design method evolves as a natural extension of the optimal control strategies employed in linear systems. A multi‐layered feed‐forward neural network is used as the feedback controller. The controller is trained to directly minimize a suitable cost function comprised of the plant output, states and the input. The optimization is carried out using a gradient scheme that employs the recently developed concept of block partial derivatives. The applicability of the proposed design method is demonstrated through simulated examples. Simulation studies include a variety of optimal control problems in nonlinear plants such as: minimum energy and minimum fuel problems, state tracking, output servo with integrator, and unconstrained and constrained regulation. Copyright © 2000 John Wiley & Sons, Ltd.     

A constrained sub‐optimal controller for glucose regulation in type 1 diabetes mellitus

Patients with type 1 diabetes mellitus require exogenous insulin infusion to avoid chronic complications related to elevated glucose levels. With diabetes reaching epidemic proportions, recent times have witnessed an increased attention in the field of optimal glucose management by closed‐loop insulin delivery system. A proper glucose management scheme, in addition of maintaining the glucose level within the normal range of 80–120 mg/dL, should avoid excessive insulin delivery leading to hypoglycemia. By considering the glucose regulation as a linear quadratic problem, a constrained novel sub‐optimal controller is proposed in the present work, for the maintenance of normal glucose level in type 1 diabetic subjects. The observer free state feedback controller is based on the feedback of only physiological variables (plasma glucose and plasma insulin). Constraining the feedback elements corresponding to the non‐physiological variables avoids the use of an observer while maintaining the advantages of state feedback control. The implementation of the proposed scheme requires simple measurement protocol with no online computation. The closed‐loop performance of the controller is evaluated on a physiologically relevant model for a meal disturbance and continuous glucose infusion. Copyright © 2013 John Wiley & Sons, Ltd.     

An anti-suction control for an intra-aorta pump using blood assistant index: a numerical simulation

With the extensive use of the left ventricular assist device (LVAD) as a treatment of heart failure, suction detection has become a key issue that directly affects the treatment. To detect the phenomenon of suction, a blood assistant index (BAI) is defined, which reflects the unloading level of the pump. The BAI is a ratio of the external work of LVAD and the input power of cardiovascular system. Using the theory of model‐free adaptive control algorithm, an anti‐suction controller, which chooses the heart rate and BAI as control variables, is designed. As a key feature, the proposed control algorithm adjusts the pump speed according to not only the blood demand of circulatory system but also the function of the native heart. Subsequently, the performance and robustness of the controller are evaluated using a numerical simulation of the assisted circulation and an in vitro experiment. The simulation and experimental results demonstrate that the BAI detects the suction occur accurately, and the controller can maintain the heart rate and BAI tracking the reference values with a response time of less than 6 s.     

Engine idle speed control using nonlinear multiparametric model predictive control

In this article, a real-time nonlinear model predictive idle speed controller based on multiparametric programming is designed for an SI engine. Idle speed is a crucial recurring condition in urban vehicles demanding proper control to avoid stall. As will be seen, the nonlinear model predictive control (NMPC) system designed, besides complying with the predefined constraints, demonstrates a far better performance than the prevalent industrial controllers and even conventional linear MPC controllers. More importantly, a new special structure combining offline nonlinear MPC and classical controller is employed to provide both robustness and fast response. Not only is the computational burden of the controller within that of the ordinary ECU controllers, it is also able to readily damp a disturbance of 20 N·m in less than 2.5 seconds and easily deal with parameter uncertainties. The control system also regulates engine gas pedal release, and converges to the set point with a settling time of less than 3 seconds and minimum fluctuations.     

Adaptive continuous‐time model predictive controller for implantable insulin delivery system in Type I diabetic patient

This paper presents a physiological model of glucose–insulin (GI) interaction and design of a Continuous‐time Model Predictive Controller (CMPC) to regulate the blood glucose (BG) level in Type I diabetes mellitus (TIDM) patients. For the designing of the CMPC, a nonlinear physiological model of TIDM patient is linearized as a ninth‐order state‐space model with an implanted insulin delivery device. A novel control approach based on Continuous‐time Model Predictive technique is proposed for the BG regulation with rejection of periodic or random meal and exercise disturbances in the process. To justify its efficacy a comparative analysis with Linear Quadratic Gaussian (LQG) control, and recently published control techniques like Proportional‐Integral‐Derivative (PID), Linear Quadratic Regulator with Loop Transfer Recovery (LQR/LTR) and H‐infinity has been established. The efficiency of the controller with respect to accuracy and robustness has been verified via simulation. The proposed controller performances are assessed in terms of ability to track a normoglycaemic set point of 81 mg/dl (4.5 mmol/l) in the presence of Gaussian and stochastic noise. Copyright © 2016 John Wiley & Sons, Ltd.     

A robust control system scheme based on model predictive controller (MPC) for continuous‐time systems

In this paper, an LMI framework based on model predictive strategy is addressed to design a robust dynamical control law in a typical control system. In the proposed method, instead of traditional static controller, a dynamic control law is used. With a suitable matrix transformation, the controller parameters selection are translated into an optimization problem with some LMI constraints. The plant input and output constraints are also handled with another LMIs. The controller is represented in state space form, and its parameters are computed in real‐time operation. For achieving this goal, by solving an optimization problem, a dynamic controller is designed, which meets the required plant performances. These results are used in 2 numerical examples to demonstrate the effectiveness of the proposed approach.     

Nonlinear model predictive control based on constraint transformation

The paper presents a constraint transformation approach for nonlinear model predictive control (MPC) subject to a class of state and control constraints. The approach uses a two‐stage transformation technique to incorporate the constraints into a new unconstrained MPC formulation with new variables. As part of the stability analysis, the relationship of the new unconstrained MPC scheme to an interior penalty formulation in the original variables is discussed. The approach is combined with an unconstrained gradient method that allows for computing the single MPC iterations in a real‐time manner. The applicability of the approach, for example, to fast mechatronic systems, is demonstrated by numerical as well as experimental results. Copyright © 2015 John Wiley & Sons, Ltd.     

Optimal control of human‐like musculoskeletal arm: Prediction of trajectory and muscle forces

Optimal trajectory and muscle forces of a human‐like musculoskeletal arm are predicted for planar point‐to‐point movements using optimal control theory. The central nervous system (CNS) is modeled as an optimal controller that performs a reaching motion to final states via minimization of an objective function. For the CNS strategy, a cubic function of muscles stresses is considered as an appropriate objective function that minimizes muscles fatigue. A two‐DOF nonlinear musculoskeletal planar arm model with four states and six muscle actuators is used for the evaluation of the proposed optimal strategy. The nonlinear variational formulation of the corresponding optimal control problem is developed and solved using the method of variation of extremals. The initial and (desired) final states (position and velocity) are used as input kinematic information, while the problem constraints include the motion range of each joint, maximum allowable muscle tension, and stability requirements. The resulting optimal trajectories are compared with experimental data as well as those corresponding to recent researches on model predictions of human arm movements. It is demonstrated that the proposed optimal control strategy using minimum fatigue criterion is more realistic in prediction of motion trajectories in comparison with previous work that has utilized minimum joints' torque criterion. Accordingly, minimization of muscles fatigue is an effective biomechanical criterion for the CNS in prediction of point‐to‐point human arm motions. Copyright © 2016 John Wiley & Sons, Ltd.     

A reinforcement learning‐based scheme for direct adaptive optimal control of linear stochastic systems

Reinforcement learning where decision‐making agents learn optimal policies through environmental interactions is an attractive paradigm for model‐free, adaptive controller design. However, results for systems with continuous state and action variables are rare. In this paper, we present convergence results for optimal linear quadratic control of discrete‐time linear stochastic systems. This work can be viewed as a generalization of a previous work on deterministic linear systems. Key differences between the algorithms for deterministic and stochastic systems are highlighted through examples. The usefulness of the algorithm is demonstrated through a nonlinear chemostat bioreactor case study. Copyright © 2009 John Wiley & Sons, Ltd.     

New methods for the estimation of Takagi–Sugeno model based extended Kalman filter and its applications to optimal control for nonlinear systems

This paper describes new approaches to improve the local and global approximation (matching) and modeling capability of Takagi–Sugeno (T‐S) fuzzy model. The main aim is obtaining high function approximation accuracy and fast convergence. The main problem encountered is that T‐S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the application of the T‐S method because this type of membership function has been widely used during the last 2 decades in the stability, controller design of fuzzy systems and is popular in industrial control applications. The approach developed here can be considered as a generalized version of T‐S identification method with optimized performance in approximating nonlinear functions. We propose a noniterative method through weighting of parameters approach and an iterative algorithm by applying the extended Kalman filter, based on the same idea of parameters’ weighting. We show that the Kalman filter is an effective tool in the identification of T‐S fuzzy model. A fuzzy controller based linear quadratic regulator is proposed in order to show the effectiveness of the estimation method developed here in control applications. An illustrative example of an inverted pendulum is chosen to evaluate the robustness and remarkable performance of the proposed method locally and globally in comparison with the original T‐S model. Simulation results indicate the potential, simplicity, and generality of the algorithm. An illustrative example is chosen to evaluate the robustness. In this paper, we prove that these algorithms converge very fast, thereby making them very practical to use. Copyright © 2011 John Wiley & Sons, Ltd.