Regularized economic model predictive control with barrier functions

In this article, we consider the use of barrier functions as a regularizing cost in economic model predictive control (EMPC). We focus on a specific variant, EMPC with generalized terminal constraints (G-EMPC), as it is suitable for tackling large-scale problems commonly arising in multiagent settings, which motivates our work. The benefits of using barrier functions are providing smoothing of the constrained problem, allowing the use of second-order methods and warm-starting, which reduces the iteration count significantly. Apart from these numerical benefits, recentered barrier functions can be used as a regularizing cost in the EMPC problem for enhancing closed-loop convergence properties. We show that in the case of G-EMPC, which allows the terminal state to be any equilibrium point, regularizing the problem provides (i) convergence of the predicted terminal state to a neighborhood of a globally optimal equilibrium point, (ii) asymptotic average performance guarantees for the closed-loop system, and (iii) empirical evidence of accelerated numerical solution of the optimal control problem. Specifically we use a proximal-like regularization, which penalizes the deviation from the previously predicted trajectories. We analyze system theoretic properties of the proposed scheme and provide simulation examples illustrating the numerical and system theoretical benefits of using barriers.     

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.     

Design of a supervisory predictive controller and its application to thermal power plants

The optimization at supervisory level of thermal power plant controls is investigated. The design of a predictive supervisory controller that optimizes an objective function in order to determine the set‐points for a given regulatory level is described. The objective function includes both an economic criterion and a regulatory criterion. The proposed supervisory controller is applied to the gas turbine of a thermal power plant and it is compared with the control strategy for constant optimum set‐points. Copyright © 2005 John Wiley & Sons, Ltd.     

Minimizing control energy in a class of bounded‐control linear‐quadratic regulator problems

Minimal‐control‐energy strategies are substantiated and illustrated for linear‐quadratic problems with penalized endpoints and no state‐trajectory cost, when bounds in control values are imposed. The optimal solution for a given process with restricted controls, starting at a known initial state, is shown to coincide with the saturated solution to the unrestricted problem that has the same coefficients but starts at a generally different initial state. This result reduces the searching span for the solution: from the infinite‐dimensional set of admissible control trajectories to the finite‐dimensional Euclidean space of initial conditions. An efficient real‐time scheme is proposed here to approximate (eventually to find) the optimal control strategy, based on the detection of the appropriate initial state while avoiding as much as possible the generation and evaluation of state and control trajectories. Numerical (including model predictive control) simulations are provided, compared, and checked against the analytical solution to ‘the cheapest stop of a train’ problem in its pure‐upper‐bounded brake, flexible‐endpoint setting. Copyright © 2013 John Wiley & Sons, Ltd.     

Model predictive control of blood sugar in patients with type‐1 diabetes

In this article, two adaptive model predictive controllers (AMPC) are applied to regulate the blood glucose in type 1 diabetic patients. The first controller is constructed based on a linear model, while the second one is designed by using a nonlinear Hammerstein model. The adaptive version of these control schemes is considered to make them more robust against model mismatches and external disturbances. The least squares method with forgetting factor is used to update the model parameters. For simulation study, two well‐known mathematical models namely, Puckett and Hovorka which describe the dynamical behavior of patient's body have been selected. The performances and robustness of the proposed controllers are tested for regulating the blood glucose of diabetic patients in presences of model mismatches and measurement noises. Simulation results indicate that the non‐linear model predictive controller (NMPC) outperforms the linear one. To improve the performance of the NMPC in rejecting the meal disturbances, two different feedforward control strategies have been considered. Simulation results indicate that the combined adaptive NMPC with feedforward controller has a better performance over the other considered control schemes. Copyright © 2015 John Wiley & Sons, Ltd.     

On fusion of PCA and a physical model‐based predictive control strategy for efficient load‐cycling operation of a thermal power plant

Controlling a thermal power plant optimally during load‐cycling operation is a very challenging control problem. The control complexity is enhanced further by the possibility of simultaneous occurrence of sensor malfunctions and a plethora of system disturbances. This paper proposes and evaluates the effectiveness of a sensor validation and reconstruction approach using principal component analysis (PCA) in conjunction with a physical plant model. For optimal control under severe operating conditions in the presence of possible sensor malfunctions, a predictive control strategy is devised by appropriate fusion of the PCA‐based sensor validation and reconstruction approach and a constrained model predictive control (MPC) technique. As a case study, the control strategy is applied for thermal power plant control in the presence of a single sensor malfunction. In particular, it is applied to investigate the effectiveness and relative advantage of applying rate constraints on main steam temperature and heat‐exchanger tube‐wall temperature, so that faster load cycling operation is achieved without causing excessive thermal stresses in heat‐exchanger tubes. In order to account for unstable and non‐minimum phase boiler–turbine dynamics, the MPC technique applied is an infinite horizon non‐linear physical model‐based state‐space MPC strategy, which guarantees asymptotic stability and feasibility in the presence of output and state constraints. Copyright © 2007 John Wiley & Sons, Ltd.     

Distributed model predictive control for energy management in a network of microgrids using the dual decomposition method

This paper deals with the application of model predictive control (MPC) to optimize power flows in a network of interconnected microgrids (MGs). More specifically, a distributed MPC (DMPC) approach is used to compute for each MG how much active power should be exchanged with other MGs and with the outer power grid. Due to the presence of coupled variables, the DMPC approach must be used in a suitable way to guarantee the feasibility of the consensus procedure among the MGs. For this purpose, we adopt a tailored dual decomposition method that allows us to reach a feasible solution while guaranteeing the privacy of single MGs (ie, without having to share private information like the amount of generated energy or locally consumed energy). Simulation results demonstrate the features of the proposed cooperative control strategy and the obtained benefits with respect to other classical centralized control methods.     

Model predictive control of a dual fuel engine integrated with waste heat recovery used for electric power in buildings

Waste heat recovery (WHR) system uses the thermal energy from the exhaust gases of an internal combustion engine (ICE) to assist in the electricity generated by the ICE generator in buildings. This paper presents a model predictive control (MPC) framework to minimize the fuel consumption of an ICE by integrating it with a WHR system. To this end, a control oriented model of a WHR system is developed and then integrated to a control oriented model of a turbocharged dual fuel diesel-natural gas ICE. The ICE model is derived based on experimental data collected from a 6.7 L Cummins ISB engine modified for dual fuel operation. The designed MPC framework optimizes the ICE combustion, turbocharger, and organic Rankine cycle (ORC) system in the WHR to minimize fuel consumption of the ICE. The designed control framework also allows to meet time-varying exhaust gas temperature requirements of the ICE to meet exhaust emission constraints. The results show that the optimal operation of the WHR and the ICE reduces the fuel consumption of the ICE by 6.7%.     

The asymptotic ii-test for singular periodic control problems with an application to the management of a class of ecosystems

A basic problem in optimal control theory is to identify circumstances under which a (non-constant or proper) periodic control exists which is better than the optimal constant one. Considerable attention has therefore been devoted in the literature to the development of criteria to test for properness, i.e. to test whether the optimal constant operation of a given system can definitely be improved by (proper) cycling in the sense that the average return associated with the latter is greater than the obviously constant one associated with the former. One of the most powerful results in this direction is the so-called II -test. In this paper, a special form of the II -test, valid for singular optimal periodic control problems, is presented (asymptotic II -test), and an application to the periodic control of a class of multispecies ecosystems is discussed.     

Hybrid predictive control of a DC–DC boost converter in both continuous and discontinuous current modes of operation

Developing efficient and appropriate modeling and control techniques for DC–DC converters is of major importance in power electronics area and has attracted much attention from automatic control theory. Since DC–DC converters have a complex hybrid nature, recently several techniques based on hybrid modeling and control have been introduced. These techniques have shown better results as compared with conventional averaging‐based schemes with limited modeling and control abilities. But the current works in this field have not considered all possible dynamics of the converters in both continuous and discontinuous current modes (CCM, DCM) of operations. These dynamics are results of controlled and uncontrolled switching phenomena in DC–DC converters. This paper proposes a new switching scheme for modeling and controlling a DC–DC boost converter. The converter is represented as a hybrid automaton by considering the all three possible modes. The hybrid automaton is translated into the mixed logical dynamical (MLD) mathematical framework. The switching among these modes is generated by hybrid predictive control method which is calculated by Mixed Integer Quadratic Programming (MIQP). Using the exact model of the converter, the proposed switching algorithm can globally control the converter in all operation regimes, including CCM and DCM operations, considering all constraints in the physical plant, such as maximum inductor current and capacitor voltage limits. The switching algorithm is applied to a real converter circuit, modeled with various parasitic components. Simulation results are provided to show the advantages of the proposed control scheme. Copyright © 2010 John Wiley & Sons, Ltd.     

Optimal control of two‐dimensional parabolic partial differential equations with application to steel billets cooling in continuous casting secondary cooling zone

Our work is devoted to an optimal control problem for two‐dimensional parabolic partial differential equations(PDEs) and its application in engineering sciences. An adjoint problem approach is used for analysis of the Fréchet gradient of the cost functional, and we prove the gradient is Lipschitz continuous. An improved conjugate gradient method is proposed to solve this problem. Based on Lipschitz continuity of the gradient, the convergence analysis of the conjugate gradient algorithm we proposed is studied. Results of some computational experiments obtained by the conjugate gradient algorithm are illustrated. The results show that the improved conjugate gradient algorithm is effective. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimal parameter selection problem with application to the synchronization of delivery cycles in a supply chain with Wiener process

In this paper, we use optimal parameter selection technique to develop two models involving single‐vendor–multiple‐buyer supply chain, which are called the dynamic independent optimization (DIO) model and the dynamic synchronized cycles (DSC) model, respectively. These models are, respectively, similar to the traditional static independent policy model and the traditional static synchronized cycle model, except that the deterministic demands of the buyers in the above two static models are now being replaced by the stochastic demands satisfying a Wiener process, which have more real‐life applications. Similar to the above static synchronized cycles model, the synchronization of the supply chain in our DSC model is also achieved by scheduling the delivery days of the buyers and coordinating them with the vendor's production cycle. Finding the optimal expected system costs of the DIO model and the DSC model involves solving optimal parameter selection problems governed by ordinary differential equations, whose final times are continuous decision variables and discrete decision variables, respectively. Computational methods have been developed for solving these problems. Numerical results show that the coordinated policy is better than the independent optimization policy, in terms of minimizing the expected system cost of the entire supply chain. Sensitivity analysis is performed to test the effect of changing the cost coefficients and the value on the performances of these models, where is the ratio of the total mean demand rate of all the buyers over the vendor's production rate.