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This paper aims to investigate an identification strategy for the nonlinear state-space model (SSM) in the presence of an unknown output time-delay. The equations to estimate the unknown model parameters and output time-delay are derived simultaneously in the proposed strategy.

The unknown integer-valued time-delay is processed as a latent variable which is uniformly distributed in a priori known range. The estimations of the unknown time-delay and model parameters are both realized using the Expectation-Maximization (EM) algorithm, which has a good performance in dealing with latent variable issues. Moreover, the particle filter (PF) with an unknown time-delay is introduced to calculated the Q-function of the EM algorithm.

Although amounts of effective approaches for nonlinear SSM identification have been developed in the literature, the problem of time-delay is not considered in most of them. The time-delay is commonly existed in industrial scenario and it could cause extra difficulties for industrial process modeling. The problem of unknown output time-delay is considered in this paper, and the validity of the proposed approach is demonstrated through the numerical example and a two-link manipulator system.

The novel approach to identify the nonlinear SSM in the presence of an unknown output time-delay with EM algorithm is put forward in this work.

The model for digitally controlled three-phase pulse width modulation (PWM) boost rectifiers is a sampled data model, which is different from the continuous time domain models presented in previous studies. The controller, which is tuned according to the model in continuous time domain and discretized by approximation methods, may exhibit some unpredictable performances and even result in unstable systems under some extreme situations. Consequently, a small-signal discrete-time model of digitally controlled three-phase PWM boost rectifier is required. The purpose of this paper is to provide a simple but accurate small-signal discrete-time model of digital controlled three-phase PWM boost rectifier, which explains the effect of the sampling period, modulator and time delays on system dynamic and improves the control performance.

Based on the Laplace domain analysis and the waveforms of up-down-count modulator, the small signal model of digital pulse width modulation (DPWM) in the Laplace domain is presented. With a combination of state-space average and a discrete-time modeling technique, a simplified large signal discrete time model is developed. With rotation transformation and feed-forward decoupling, the large-signal model is decoupled into a single input single output system with rotation transformation. Then, an integrated small signal model in the Laplace domain is constructed that included the time delay and modulation effect. Implementing the modified z-transform, a small-signal discrete-time model is derived from the integrated small signal model.

In a digital control system, besides the circuit parameters, the location of pole of open-loop transfer function is also related to system sampling time, affecting the system stability, and the time delay determines the location of the zero of open-loop transfer function, affecting the system dynamic. In addition to the circuit parameters discussed in previous literature, the right half plane (RHP) zero is also determined by the sampling period and the time delay. Furthermore, the corner frequency of the RHP zero is mainly determined by the sampling period.

The model developed in this paper, accounting for the effect of the sampling period, modulator and time delays on the system dynamic, give a sufficient insight into the behavior of the digitally controlled three-phase PWM rectifier. It can also explain the effect of sampling period and control delay time on system dynamic, accurately predict the system stability boundary and determine the oscillation frequency of the current loop in critical stable. The experimental results verify that the model is a simple and accurate control-oriented small-signal discrete-time model for the digitally controlled three-phase PWM boost rectifier.

The purpose of this paper is to deal with a new generalized model of thermoelasticity theory with memory-dependent derivatives (MDD).

The two-dimensional equations of generalized thermoelasticity with MDD are solved using a state-space approach. The numerical inversion method is employed for the inversion of Laplace and Fourier transforms.

The solutions are presented graphically for different values of time delay and kernel function.

The governing coupled equations of the new generalized thermoelasticity with time delay and kernel function, which can be chosen freely according to the necessity of applications, are applied to a two-dimensional problem of an isotropic plate.

A distinctive feature of tilt-rotor UAVs is that they can be fully actuated, whereas in fixed-angle rotor UAVs (e.g. common-type quadrotors, octorotors, etc.), the associated dynamic model is characterized by underactuation. Because of the existence of more control inputs, in tilt-rotor UAVs, there is more flexibility in the solution of the associated nonlinear control problem. On the other side, the dynamic model of the tilt-rotor UAVs remains nonlinear and multivariable and this imposes difficulty in the drone's controller design. This paper aims to achieve simultaneously precise tracking of trajectories and minimization of energy dissipation by the UAV's rotors. To this end elaborated control methods have to be developed.

A solution of the nonlinear control problem of tilt-rotor UAVs is attempted using a novel nonlinear optimal control method. This method is characterized by computational simplicity, clear implementation stages and proven global stability properties. At the first stage, approximate linearization is performed on the dynamic model of the tilt-rotor UAV with the use of first-order Taylor series expansion and through the computation of the system's Jacobian matrices. This linearization process is carried out at each sampling instance, around a temporary operating point which is defined by the present value of the tilt-rotor UAV's state vector and by the last sampled value of the control inputs vector. At the second stage, an H-infinity stabilizing controller is designed for the approximately linearized model of the tilt-rotor UAV. To find the feedback gains of the controller, an algebraic Riccati equation is repetitively solved, at each time-step of the control method. Lyapunov stability analysis is used to prove the global stability properties of the control scheme. Moreover, the H-infinity Kalman filter is used as a robust observer so as to enable state estimation-based control. The paper's nonlinear optimal control approach achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs. Finally, the nonlinear optimal control approach for UAVs with tilting rotors is compared against flatness-based control in successive loops, with the latter method to be also exhibiting satisfactory performance.

So far, nonlinear model predictive control (NMPC) methods have been of questionable performance in treating the nonlinear optimal control problem for tilt-rotor UAVs because NMPC's convergence to optimum depends often on the empirical selection of parameters while also lacking a global stability proof. In the present paper, a novel nonlinear optimal control method is proposed for solving the nonlinear optimal control problem of tilt rotor UAVs. Firstly, by following the assumption of small tilting angles, the state-space model of the UAV is formulated and conditions of differential flatness are given about it. Next, to implement the nonlinear optimal control method, the dynamic model of the tilt-rotor UAV undergoes approximate linearization at each sampling instance around a temporary operating point which is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector. The linearization process is based on first-order Taylor series expansion and on the computation of the associated Jacobian matrices. The modelling error, which is due to the truncation of higher-order terms from the Taylor series, is considered to be a perturbation that is asymptotically compensated by the robustness of the control scheme. For the linearized model of the UAV, an H-infinity stabilizing feedback controller is designed. To select the feedback gains of the H-infinity controller, an algebraic Riccati equation has to be repetitively solved at each time-step of the control method. The stability properties of the control scheme are analysed with the Lyapunov method.

There are no research limitations in the nonlinear optimal control method for tilt-rotor UAVs. The proposed nonlinear optimal control method achieves fast and accurate tracking of setpoints by all state variables of the tilt-rotor UAV under moderate variations of the control inputs. Compared to past approaches for treating the nonlinear optimal (H-infinity) control problem, the paper's approach is applicable also to dynamical systems which have a non-constant control inputs gain matrix. Furthermore, it uses a new Riccati equation to compute the controller's gains and follows a novel Lyapunov analysis to prove global stability for the control loop.

There are no practical implications in the application of the nonlinear optimal control method for tilt-rotor UAVs. On the contrary, the nonlinear optimal control method is applicable to a wider class of dynamical systems than approaches based on the solution of state-dependent Riccati equations (SDRE). The SDRE approaches can be applied only to dynamical systems which can be transformed to the linear parameter varying (LPV) form. Besides, the nonlinear optimal control method performs better than nonlinear optimal control schemes which use approximation of the solution of the Hamilton–Jacobi–Bellman equation by Galerkin series expansions. The stability properties of the Galerkin series expansion-based optimal control approaches are still unproven.

The proposed nonlinear optimal control method is suitable for using in various types of robots, including robotic manipulators and autonomous vehicles. By treating nonlinear control problems for complicated robotic systems, the proposed nonlinear optimal control method can have a positive impact towards economic development. So far the method has been used successfully in (1) industrial robotics: robotic manipulators and networked robotic systems. One can note applications to fully actuated robotic manipulators, redundant manipulators, underactuated manipulators, cranes and load handling systems, time-delayed robotic systems, closed kinematic chain manipulators, flexible-link manipulators and micromanipulators and (2) transportation systems: autonomous vehicles and mobile robots. Besides, one can note applications to two-wheel and unicycle-type vehicles, four-wheel drive vehicles, four-wheel steering vehicles, articulated vehicles, truck and trailer systems, unmanned aerial vehicles, unmanned surface vessels, autonomous underwater vessels and underactuated vessels.

The proposed nonlinear optimal control method is a novel and genuine result and is used for the first time in the dynamic model of tilt-rotor UAVs. The nonlinear optimal control approach exhibits advantages against other control schemes one could have considered for the tilt-rotor UAV dynamics. For instance, (1) compared to the global linearization-based control schemes (such as Lie algebra-based control or flatness-based control), it does not require complicated changes of state variables (diffeomorphisms) and transformation of the system's state-space description. Consequently, it also avoids inverse transformations which may come against singularity problems, (2) compared to NMPC, the proposed nonlinear optimal control method is of proven global stability and the convergence of its iterative search for an optimum does not depend on initialization and controller's parametrization, (3) compared to sliding-mode control and backstepping control the application of the nonlinear optimal control method is not constrained into dynamical systems of a specific state-space form. It is known that unless the controlled system is found in the input–output linearized form, the definition of the associated sliding surfaces is an empirical procedure. Besides, unless the controlled system is found in the backstepping integral (triangular) form, the application of backstepping control is not possible, (4) compared to PID control, the nonlinear optimal control method is of proven global stability and its performance is not dependent on heuristics-based selection of parameters of the controller and (5) compared to multiple-model-based optimal control, the nonlinear optimal control method requires the computation of only one linearization point and the solution of only one Riccati equation.

The purpose of this paper is to investigate a control engineering-based system model that allows for any value of production delay for a three-tier supply chain with information delays between tiers or systems with epos.

A discrete z transform model of automatic pipeline, variable inventory and order based production control system three-tier supply chain is obtained using a state-space model using a reachable control formulation. This model provides a discrete time state-space model conversion using an exponential production delay with no loss of generality.

This work allows a three-tier supply chain model to be computed via a spreadsheet using any production delay and can be modified to include different sales smoothing procedures. The model is fully controllable and observable. Stability of these models is obtained from the system eigenvalues and agrees with our previously published stability boundaries.

The system is described by a linear control model of the production process and does not include production limits or other resource limitations, including history of sales demand and response.

This present model is an extension of the model devised by White and Censlive, in that it allows accurate modelling of multi-tier inventory production systems by permitting flexible selection of delay parameter values for real systems.

The purpose of this paper is to examine the impact of applying two classical controller strategies, including two proportional (P) controllers with two feedback loops and one proportional–integral–derivative (PID) controller with one feedback loop, on the order and inventory performance within a production-inventory control system.

The simulation experiments of the dynamics behaviour of the production-inventory control system are conducted using a model based on control theory techniques. The Laplace transformation of an Order–Up–To (OUT) model is obtained using a state-space approach, and then the state-space representation is used to design and simulate a controlled model. The simulations of each model with two control configurations are tested by subjecting the system to a random retail sales pattern. The performance of inventory level is quantified by using the Integral of Absolute Error (IAE), whereas the bullwhip effect is measured by using the Variance ratio (Var).

The simulation results show that one PID controller with one feedback loop outperforms two P controllers with two feedback loops at reducing the bullwhip effect and regulating the inventory level.

The production-inventory control system is broken down into three components, namely: the forecasting mechanism, controller strategy and production-inventory process. A state-space approach is adopted to design and simulate the different controller strategy.

The purpose of this manuscript, a state feedback gain depends on the optimal design of fractional order PID controller to time-delay system is established. In established optimal design known as advanced cuttlefish optimizer and random decision forest that is combined performance of random decision forest algorithm (RDFA) and advanced cuttlefish optimizer (ACFO).

The proposed ACFO uses the concept of crossover and mutation operator depend on position upgrading to enhance its search behavior, calculational speed as well as convergence profile at basic cuttlefish optimizer.

Fractional order proportional-integrator-derivative (FOPID) controller, apart from as tuning parameters (kp, ki and kd) it consists of two extra tuning parameters λ and µ. In established technology, the increase of FOPID controller is adjusted to reach needed responses that demonstrated using RDFA theory as well as RDF weight matrices is probable to the help of the ACFO method. The uniqueness of the established method is to decrease the failure of the FOPID controller at greater order time delay method with the help of controller maximize restrictions. The objective of the established method is selected to consider parameters set point as well as achieved parameters of time-delay system.

In the established technique used to evade large order delays as well as reliability restrictions such as small excesses, time resolution, as well as fixed condition defect. These methods is implemented at MATLAB/Simulink platform as well as outcomes compared to various existing methods such as Ziegler-Nichols fit, curve fit, Wang method, regression and invasive weed optimization and linear-quadratic regression method.

The purpose of this paper is to derive the output predictor for a stationary normal process with rational spectral density and linear stochastic discrete-time state-space model, respectively, as the output predictor is very important in model predictive control. The derivations are only dependent on matrix operations. Based on the output predictor, one quadratic programming problem is constructed to achieve the goal of subspace predictive control. Then an improved ellipsoid optimization algorithm is proposed to solve the optimal control input and the complexity analysis of this improved ellipsoid optimization algorithm is also given to complete the previous work. Finally, by the example of the helicopter, the efficiency of the proposed control strategy can be easily realized.

First, a stationary normal process with rational spectral density and one stochastic discrete-time state-space model is described. Second, the output predictors for these two forms are derived, respectively, and the derivation processes are dependent on the Diophantine equation and some basic matrix operations. Third, after inserting these two output predictors into the cost function of predictive control, the control input can be solved by using the improved ellipsoid optimization algorithm and the complexity analysis corresponding to this improved ellipsoid optimization algorithm is also provided.

Subspace predictive control can not only enable automatically tune the parameters in predictive control but also avoids many steps in classical linear Gaussian control. It means that subspace predictive control is independent of any prior knowledge of the controller. An improved ellipsoid optimization algorithm is used to solve the optimal control input and the complexity analysis of this algorithm is also given.

To the best knowledge of the authors, this is the first attempt at deriving the output predictors for stationary normal processes with rational spectral density and one stochastic discrete-time state-space model. Then, the derivation processes are dependent on the Diophantine equation and some basic matrix operations. The complexity analysis corresponding to this improved ellipsoid optimization algorithm is analyzed.

The purpose of this study is to propose a new dynamic model of a production-inventory control system. The objective of the new model is to maximise the flexibility of the system so that it can be used by decision makers to design inventory systems that adopt various strategies that provide a balance between reducing the bullwhip effect and improving the responsiveness of inventory performance.

The proposed production-inventory control system is modelled and analysed via control theory and simulations. The production-inventory feedback control system is modelled through continuous time differential equations. The simulation experiments design is conducted by using the state-space model of the system. The Automatic Pipeline Inventory and Order-Based Production Control System (APIOBPCS) model is used as a benchmark production-inventory control system.

The results showed that the Two Automatic Pipelines, Inventory and Order-Based Production Control System (2APIOBPCS) model outperforms APIOBPCS in terms of reducing the bullwhip effect. However, the 2APIOBPCS model has a negative impact on Customer Service Level. Therefore, with careful parameter setting, it is possible to design control decisions to be suitably responsive while generating smooth order patterns and obtain the best trade-off of the two objectives.

This research is limited to the dynamics of single-echelon production-inventory control systems with zero desired inventory level.

This present model is an extension and improvement to Towill’s (1982) and John et al.’s (1994) work, since it presents a new dynamic model of a production-inventory control system which utilises an additional flow of information to improve the efficiency of order rate decisions.