Distributed model predictive control with saturated inputs by a saturation‐dependent Lyapunov function

In this paper, distributed model predictive control (MPC) problems are considered for input‐saturated polytopic uncertain systems by a saturation‐dependent Lyapunov function approach. The actuator saturation is processed by the transformation into the linear convex combination form. By the decomposition of the control input, distributed MPC controllers are designed in parallel for each subsystems. The Lyapunov Function we select is saturation dependent, which is less conservative than the general Lyapunov Function approach. An invariant set condition is provided and min–max distributed MPC is proposed based on the invariant set. The robust distributed MPC controllers are determined by solving a linear matrix inequality (LMI) optimization problem. To reduce the conservatism, we present a robust distributed MPC algorithm, which is not only saturation dependent but also parameter dependent. A Jacobi iterative algorithm is developed to coordinate the distributed MPC controllers. A simulation example with multi‐subsystem is carried out to demonstrate the effectiveness of the proposed distributed MPC algorithms. Copyright © 2016 John Wiley & Sons, Ltd.     

Exponential stability and stabilization of positive T-S fuzzy delayed systems

The analysis of positive nonlinear delayed systems is of great importance for many real-world applications. Such systems' stability and stabilization assessment is still an open topic, and there is limited literature on this field. Moreover, further convergence conditions should be considered for many experimental processes, such as exponential stability analysis, which is highly important. Considering the above, we deal in this study with the problem of exponential stability and stabilization of nonlinear fuzzy positive systems with delay. We establish exponential stability criteria using Lyapunov–Krasovskii functional (LKF) and a delay bi-decomposition approach for bounded and time-varying delayed systems. The obtained results are then extended to the exponential stabilization case. The control law is designed using Parallel distributed compensation (PDC). The proposed approach, formulated in terms of linear matrix inequalities (LMIs), allows reducing the conservativeness of the delay-dependent conditions. A comparative study is presented to illustrate the superiority of our method. Moreover, simulation results for the two tanks process show the advantages of the proposed control design.     

Constructive model predictive control for constrained nonlinear systems

This paper develops a new model predictive control (MPC) design for stabilization of continuous‐time nonlinear systems subject to state and input constraints. The key idea is to construct an analytic form of the controller with some undetermined parameters and to calculate the parameters by minimizing online a performance index. By using the method of control Lyapunov functions (CLFs), we construct an appropriate variation on Sontag's formula, with one degree of freedom reflecting ‘decay rate’ of CLFs. Moreover, the constructed univariate control law is used to characterize the terminal region that guarantees the feasibility of the optimal control problem. Provided that the initial feasibility of the optimization problem is satisfied, the stability of the control scheme can be guaranteed. An example is given to illustrate the application of the constructive MPC design. Copyright © 2008 John Wiley & Sons, Ltd.     

Gain-scheduled controller design for linear parameter varying systems subject to pole assignment

This paper addresses a pole-assignment control problem for discrete-time linear parameter varying (LPV) systems. Based on LPV modeling approach, time-varying systems can be mathematically described via combining several linear systems and a specific weighting function. For the LPV systems, gain-scheduled (GS) control scheme is applied to deal with stabilization problem subject to pole-assignment constraint. Moreover, two cases of Lyapunov function are respectively employed to derive some sufficient conditions which belong to linear matrix inequality (LMI) problems. Solving those derived conditions, the corresponding GS scheduled controller can be designed such that the asymptotical stability and pole assignment of LPV systems are guaranteed. Finally, a controller problem of truck-trailer system is used to demonstrate the applicability and effectiveness of the proposed design methods.     

Robust load–frequency regulation: A real-time laboratory experiment

This paper addresses a new method for robust decentralized design of proportional-integral-based load–frequency control (LFC) with communication delays. In the proposed methodology, the LFC problem is reduced to a static output feedback control synthesis for a multiple delays power system, and then the control parameters are easily carried out using robust H_∞ control technique. To demonstrate the efficiency of the proposed control strategy, an experimental study has been performed on the Analog Power System Simulator at the Research Laboratory of the Kyushu Electric Power Co. in Japan. Copyright © 2007 John Wiley & Sons, Ltd.     

Finite‐time convergence results in robust model predictive control

Robust asymptotic stability (asymptotic attractivity and ?‐δ stability) of equilibrium regions under robust model predictive control (MPC) strategies was extensively studied in the last decades making use of Lyapunov theory in most cases. However, in spite of its potential application benefits, the problem of finite‐time convergence under fixed prediction horizon has not received, with some few exceptions, much attention in the literature. Considering the importance in several applications of having finite‐time convergence results in the context of fixed horizon MPC controllers and the lack of studies on this matter, this work presents a new set‐based robust MPC (RMPC) for which, in addition to traditional stability guarantees, finite‐time convergence to a target set is proved, and moreover, an upper bound on the time necessary to reach that set is provided. It is remarkable that the results apply to general nonlinear systems and only require some weak assumptions on the model, cost function, and target set.     

Robust guaranteed cost control of discrete‐time networked control systems

This paper is concerned with the robust guaranteed cost control problem for networked control systems (NCSs). The plant considered is an uncertain linear discrete‐time system, where the communication limitations include packet‐loss and signal transmission delay. Our purpose is to design a robust state‐feedback guaranteed cost controller such that the resulting closed‐loop system is robustly stable, and a specified quadratic cost function is upper bound for all admissible uncertainties under such communication limitations. A model of NCSs is established which contains two additive delay components, one being a known constant, and the other unknown constant. By introducing a novel Lyapunov‐Krasoviskii function with the idea of delay partitioning, new sufficient conditions for the existence of guaranteed cost controllers are proposed. Numerical examples are provided to demonstrate the usefulness of the developed theory. Copyright © 2010 John Wiley & Sons, Ltd.     

Adaptive dynamic surface control using neural networks for hypersonic flight vehicle with input nonlinearities

This study proposes an effective adaptive dynamic surface control (DSC) method based on the radial basis function neural networks and the auxiliary system for hypersonic flight vehicle (HFV) systems in the presence of system uncertainties, external disturbances, and state variable and control input constraints. Firstly, to enhance the robustness of the system, the neural network is combined with the robust term to deal with the uncertainties and external disturbances of the system. Secondly, to prevent the deterioration of the dynamic performance of the system due to the over-adaptation of the neural networks and the robust terms caused by the state and control input constraints, the auxiliary system is added at each step in the DSC design to adjust the dynamic process of the reference signal and virtual control. Furthermore, the variable structure control is used to solve the problem of dead zone in the control input. Using the Lyapunov analysis method, all signals of the closed-loop system are semi-globally uniformly ultimate bounded. The simulation results illustrate the effectiveness of the proposed control scheme for the HFVs.     

Hybridized gravitational search algorithm tuned sliding mode controller design for load frequency control system with doubly fed induction generator wind turbine

In this paper, the load frequency regulation problem of 2‐area interconnected power system is resolved using the sliding mode control (SMC) methodology. Interconnected 2‐area power systems with and without doubly fed induction generator wind turbines are considered for implementing the proposed optimal control methodology. Here, a heuristic gravitational search algorithm (GSA) and its variants such as opposition learning–based GSA (OGSA), disruption‐based GSA (DGSA), and disruption based oppositional GSA (DOGSA) are employed to optimize the switching vector and feedback gains of SMC. In order to overcome the inherent chattering problem in SMC, the control signals are considered in the objective function. The robustness of optimized SMC is analyzed by the inclusion of nonlinearities such as generation rate constraint (GRC), governor deadband, and time delay during the signal processing between the control areas, which are present in the real‐time power system. The insensitiveness of the optimal controller is shown by variation in system parameters like loading condition, speed governor constant, turbine constant, and tie‐line power coefficient. Further, the optimal SMC has been studied with significant load variations and wind power penetration levels in the control areas. The potential of proposed SMC design with chattering reduction feature is shown and validated by comparing the results obtained with the other reported methods in the literature.     

Neural network‐based finite horizon optimal adaptive consensus control of mobile robot formations

In this paper, a novel NN‐based optimal adaptive consensus‐based formation control scheme over finite horizon is presented for networked mobile robots or agents in the presence of uncertain robot/agent dynamics. The uncertain robot formation dynamics are approximated online by using an NN‐based identifier and a suitable weight tuning law. In addition, a novel time‐varying value function is derived by using the augmented error vector, which consists of the regulation and consensus‐based formation errors of each robot. By using the value function approximation and the identified dynamics, the near optimal control input over finite horizon is derived. This finite horizon optimal control leads to a time‐varying value function, which becomes the solution of the Hamilton–Jacobi–Bellman equation, and control input is approximated by a second NN with time‐varying activation function. A novel weight update law for the NN value function is developed to tune the value function, satisfy the terminal constraint, and relax an initial admissible controller requirement. The Lyapunov stability method is utilized to demonstrate the consensus of the overall formation. Finally, simulation results are given to verify theoretical claims. Copyright © 2015 John Wiley & Sons, Ltd.     

Numerical simulation of a non-linear feedback controller for a wind tunnel model involving a time delay

This paper describes a non-linear, S-minimum time, feedback controller for a wind tunnel model and a numerical simulation of its performance. The model is a linear third-order system with delay and a state-variable constraint; it represents the dynamics of a Mach number control loop in a cryogenic wind tunnel. The design method involves a singular perturbation technique, an impulse control and a compensation of delay. Peformance of linear and non-linear S-minimum time control is compared in various operating conditions. The closed-loop dynamics of the non-linear system is examined by numerical simulations which exhibit the boundary-layer phenomena in the control and the effects of various changes in parameters.     

The improved H∞ controller design for nonlinear networked control systems with random communication delays

This paper is concerned with the observer‐based H_∞ controller design problem for nonlinear networked control systems with random communication delays. Firstly, the dynamic observer‐based control scheme is modelled, where the control input of the observer is different from the control input of the plant. Then, a less conservative delay‐dependent H_∞ stabilization criterion is derived by using an improved Lyapunov function. And the proof of stabilization criterion is completed in terms of four cases when the time delays in two communication channels are constant or time‐varying, respectively. The derived stabilization criterion is formulated in the form of a non‐convex matrix inequality, which can be solved by an optimal cone complementary linearization iteration algorithm to obtain the minimum disturbance attenuation level. Finally, several numerical examples and an illustrative example are provided to clarify the effectiveness and merits of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Improving the grid frequency by optimal design of model predictive control with energy storage devices

This paper proposes the optimal design of model predictive control (MPC) with energy storage devices by the bat‐inspired algorithm (BIA) as a new artificial intelligence technique. Bat‐inspired algorithm‐based coordinated design of MPCs with superconducting magnetic energy storage (SMES) and capacitive energy storage (CES) is proposed for load frequency control. Three‐area hydrothermal interconnected power system installed with MPC and SMES is considered to carry out this study. The proposed design procedure can account for generation rate constraints and governor dead bands. Transport time delays imposed by governors, thermodynamic processes, and communication telemetry can be captured as well. In recent papers, the parameters of MPC with SMES and CES units are typically set by trial and error or by the designer's expertise. This problem is solved here by applying BIA to tune the parameters of MPC with SMES and CES units simultaneously to minimize the deviations of frequency and tie line powers against load perturbations. Simulation results are carried out to emphasize the superiority of the proposed coordinated design as compared with conventional proportional‐integral controller and with BIA‐based MPC without SMES and CES units.     

Three bounded proofs for nonlinear multi‐input multi‐output approximate dynamic programming based on the Lyapunov stability theory

The approximate dynamic programming needs 2 prerequisites to be an effective optimal control method. Firstly, it must be assured to be stable and convergent before application. Secondly, the control system should mainly be a nonlinear multi‐input multi‐output form. Thus, this paper introduces a nonlinear multi‐input multi‐output approximate dynamic programming and proves that it is stable in Lyapunov sense, therefore it is convergent. Besides, the Lyapunov function design is also analyzed. These proofs are based on the Lyapunov stability theory in the form of the utility function of quadratic, square‐weighted sum, and absolute value. Thereafter, 3 typical control examples of nonlinear multi‐input multi‐output approximate dynamic programming are offered to show their applications and verify the proofs. The proof overcomes the complex derivation, and the results contain 3 practical and systematic bounded proofs. It is for the first time that the proof focuses on nonlinear multi‐input multi‐output approximate dynamic programming from the view of utility function. What is more, the results can also serve as an effective analysis and guide for the utility function design and the stability criterion of nonlinear multi‐input multi‐output approximate dynamic programming as well.     

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.     

A novel neural network discrete-time optimal control design for nonlinear time-delay systems using adaptive critic designs

In this article, a novel neural network (NN) optimal control approach using adaptive critic designs is developed for nonlinear discrete-time (DT) systems with time delays. First, to eliminate the delay term of control input, a time-delay matrix function is developed by designing a M network. Furthermore, the cost function is approximated by the critic NN, and the control signal can be obtained directly by using the information of critic NN according to the equilibrium condition. In addition, to shorten the learning time and reduce the computational burden in the control process, a novel control strategy with less adjustable parameters for the time-delay DT nonlinear systems is proposed in this article, in which the norm of the weight estimations of critic NN is updated to generate a novel long-term performance function. The proposed control algorithm using adaptive critic designs has the advantage of reducing adaptive learning parameters and lessening calculative burden. The Lyapunov stability analysis shows that the time-delay DT controlled systems can be uniformly ultimately bounded stable. Finally, three simulations are presented to demonstrate the control performance of the developed method.     

Optimal control of one‐dimensional cellular uptake in tissue engineering

A control problem motivated by tissue engineering is formulated and solved, in which control of the uptake of growth factors (signaling molecules) is necessary to spatially and temporally regulate cellular processes for the desired growth or regeneration of a tissue. Four approaches are compared for determining one‐dimensional optimal boundary control trajectories for a distributed parameter model with reaction, diffusion, and convection: (i) basis function expansion, (ii) method of moments, (iii) internal model control, and (iv) model predictive control (MPC). The proposed method of moments approach is computationally efficient while enforcing a nonnegativity constraint on the control input. Although more computationally expensive than methods (i)–(iii), the MPC formulation significantly reduced the computational cost compared with simultaneous optimization of the entire control trajectory. A comparison of the pros and cons of each of the four approaches suggests that an algorithm that combines multiple approaches is most promising for solving the optimal control problem for multiple spatial dimensions. Copyright © 2012 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.     

Optimal control of electrical vehicle incorporated hybrid power system with second order fractional-active disturbance rejection controller

This article proposes a novel control methodology employing a fractional-active-disturbance-rejection-controller for the combined operation of load frequency control and automatic voltage regulator of a hybrid power system. A two area hybrid power system with diverse energy sources like solar-thermal, conventional-thermal and wind sources equipped with appropriate system nonlinearities is investigated. In order to ascertain the role of modern-day electric-vehicle (EV), the hybrid power system is incorporated with EVs in both the areas. To establish an effective frequency, voltage and tie line power control of the hybrid power system, a second order fractional-active-disturbance-rejection-controller with fractional-extended state observer is modeled as secondary controller. Magnetotactic-bacteria-optimization (MBO) technique is applied to obtain optimal values of the controller gains and the hybrid system parameters. The robustness of the controller gains is tested under different system parameter changes from their nominal values. In addition, the effect of incorporating a power system stabilizer on the hybrid power system is evaluated. Further, the impact of integrating renewable sources and EVs in the hybrid power system is explored. Moreover, the stability of the hybrid power system is monitored with the inclusion of FACTS device. The developed controller operates encouragingly with reference to system stability, rapidity and accuracy in comparison to testified control strategies available in the literature. The robustness test under load-perturbation, solar-insolation, wind input variations also proves the efficiency of MBO optimized second order fractional-active-disturbance-rejection-controller gains.