HNN-based generalized predictive control for turbofan engine direct performance optimization

1 A Survey on Computational Optimal Control.- Issues in the Direct Transcription of Optimal Control Problems to Sparse Nonlinear Programs.- Optimization in Control of Robots.- Large-scale SQP Methods and their Application in Trajectory Optimization.- Solving Optimal Control and Pursuit-Evasion Game Problems of High Complexity.- 2 Theoretical Aspects of Optimal Control and Nonlinear Programming.- Continuation Methods In Boundary Value Problems.- Second Order Optimality Conditions for Singular Extremals.- Synthesis of Adaptive Optimal Controls for Linear Dynamic Systems.- Control Applications of Reduced SQP Methods.- Time Optimal Control of Mechanical Systems.- 3 Algorithms for Optimal Control Calculations.- Second Order Algorithm for Time Optimal Control of a Linear System.- An SQP-type Solution Method for Constrained Discrete-Time Optimal Control Problems.- Numerical Methods for Solving Differential Games, Prospective Applications to Technical Problems.- Construction of the Optimal Feedback Controller for Constrained Optimal Control Problems with Unknown Disturbances.- Repetitive Optimization for Predictive Control of Dynamic Systems under Uncertainty.- Optimal Control of Multistage Systems Described by High-Index Differential-Algebraic Equations.- A New Class of a High Order Interior Point Method for the Solution of Convex Semiinfinite Optimization Problems.- A Structured Interior Point SQP Method for Nonlinear Optimal Control Problems.- 4 Software for Optimal Control Calculations.- Automated Approach for Optimizing Dynamic Systems.- ANDECS: A Computation Environment for Control Applications of Optimization.- Application of Automatic Differentiation to Optimal Control Problems.- OCCAL: A mixed symbolic-numeric Optimal Control CALculator.- 5 Applications of Optimal Control.- A Robotic Satellite with Simplified Design.- Nonlinear Control under Constraints of a Biological System.- An Object-Oriented Approach to Optimally Describe and Specify a SCADA System Applied to a Power Network.- Near-Optimal Flight Trajectories Generated by Neural Networks.- Performance of a Feedback Method with Respect to Changes in the Air-Density during the Ascent of a Two-Stage-To-Orbit Vehicle.- Linear Optimal Control for Reentry Flight.- Steady-State Modelling of Turbine Engine with Controllers.- Shortest Paths for Satellite Mounted Robot Manipulators.- Optimal Control of the Industrial Robot Manutec r3.

In this paper, we present an optimal control approach using Linear Matrix Inequalities (LMIs) for trajectory tracking control of a three-wheeled omnidirectional mobile robot in the presence of external disturbances on the robot's actuators and noise in the robot's sensor measurements. First, a state-space representation of the omnidirectional robot dynamics is derived using a point-mass dynamic model. Then, we propose an LMI-based full-state feedback H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller for the tracking problem. The robot's tracking performance with the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller is compared to its performance with a classical full-state feedback tracking controller in simulations with circular and bowtie-shaped reference trajectories. In order to evaluate our proposed controller in practice, we also implement the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal and classical controllers for these reference trajectories on a three-wheeled omnidirectional robot. The H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller guarantees stabilization of the robot motion and attenuates the effects of frictional disturbances and measurement noise on the robot's tracking performance. Using the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller, the robot is able to track the reference trajectories with up to a 47.8% and 45.8% decrease in the maximum pose and twist errors, respectively, over a full cycle of the trajectory compared to the classical controller. The simulation and experimental results show that our LMI-based H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller is robust to undesired effects of disturbances and noise on the dynamic behavior of the robot during trajectory tracking and can outperform the classical controller in attenuating their effects.

In this study, the problem of finding an optimal controller for nonlinear systems with one input and a reference tracking signal is approached. With the problem's formulation, any desired signal can be tracked instantly with a closed-loop controller without the need for integral terms. Presentation lies at the heart of optimal control. This study, however, does not consider the integral term, allowing tracking and stability to occur naturally. It has a broad scope with a wide range of applications, namely when dealing with affine nonlinear systems, which provide geometric control unification with asymptotic stability in some cases. A common scenario that comes from optimal control involves the minimization of integral cost functionals. Issues like asymptotic stability or even tracking to the desired reference signal have always been the main limitations. In this study, the main theorem allows the solution of optimal control problems with no-integral terms, in other words tracking problems with input/state constraints, providing closed-loop controllers. A DC motor with a pendulum in upright position is an example of an application for which singular optimal control is tested in this study. The results confirm both asymptotic stability and optimal tracking with an accuracy of 95%. The main contributions of this study include an optimal closed-loop controller with no mixed initial/final conditions, input/state constraints, asymptotic stability guarantee, a strong connection with geometric tools and finally the possibility to generalize to systems with multiple inputs. As a conclusion, general nonlinear control systems can be included in the optimal control methodology presented in this study including input/state constraints. Due to the lack of integral terms, the problem can be solved in closed form by using an optimal closed-loop controller.

In this paper, we study the optimal control problem for Takagi–Sugeno (T-S) fuzzy systems with disturbances. Due to the presence of disturbances in the T-S fuzzy systems, a fuzzy optimal state feedback control approach is presented by employing a two-player zero-sum game. Since the analytical optimal control solutions and the worst-case disturbance policies of T-S fuzzy systems can be boiled down to solving the algebraic Riccati equations (AREs), which are difficult to be obtained directly, a model-free policy iteration (PI) learning algorithm is proposed to obtain their approximation solutions. It is proved that the developed fuzzy optimal state feedback controller can ensure the fuzzy systems to be asymptotically stable and satisfy the disturbance attenuation condition simultaneously. Also, the designed PI learning algorithm can converge to their optimal solutions. Finally, we apply the developed fuzzy optimal state feedback control method to the truck-trailer system and the simulation results demonstrated the effectiveness of the developed scheme.

Optimal yaw moment control law for improved vehicle handling

Optimal control of interconnected systems with time-correlated noises: Application to vehicle platoon

Mutation Hopfield neural network and its applications

To find effective control of the duplex process of induction melting in conditions of uncertainties, a method was suggested that made it possible to obtain optimal controls for both stages: melting and thermal treatment. It is shown how the search for an optimal melting control strategy can be performed using the theory of statistical games. At the same time, it is selected which of the melting regimes will be the best with the existing provision of the shop with charge materials. The costs of melting are the total costs, consisting of: – costs for the selected technological mode of melting (including costs for materials), – costs from the potential rejection of castings due to the non-conformity of the chemical composition of the alloy to the specified – due to the incorrectly chosen melting mode, – costs from the downtime due to the fact that the necessary amount of metal from the furnace is not delivered to the conveyor. The choice of an optimal control strategy in accordance with the proposed procedure can remove uncertainty in the evaluation of input process variables if they are taken as indicators of the charge quality. To find the optimal control at the stage of the heat treatment, a multialternative description of the final state is proposed on the basis of solving the problem of ridge analysis. This makes it possible to remove the uncertainty in the estimation of the final state, which allows a lot of optimal solutions in the sense of achieving a given quality. It is shown that such approach makes it possible not only to synthesize the optimal controller of the temperature regime on the basis of an analysis of the system of differential equations describing the control object, but also the application of the Pontryagin maximum principle to search for optimal control of the thermal treatment. The proposed method allows to determine the optimal control in the sense of stabilization for a given process parameter of the duplex process of induction melting. The resulting solutions form the necessary logical conditions for the logic control unit for the control system of the duplex induction melting process.

In this paper, the nonlinear optimal control problem is investigated for spacecraft formation flying with collision avoidance. Based on a nonlinear model of formation flying, two optimal tracking control laws are proposed to ensure the formation pattern converges to the predetermined configuration. The first optimal control law which combines Lyapunov optimizing control with a trajectory-following optimization technique is developed to solve the finite-time nonlinear optimal control problem. For the second controller, an extended [Formula: see text]-[Formula: see text] method is applied to design a closed-form feedback control scheme for nonlinear control problem of spacecraft formation flying with non-standard cost functions. By taking into account the flying safety, a repulsive control scheme is incorporated in the optimal controller to ensure collision avoidance and minimize the performance index. Finally, a numerical example is performed to demonstrate the effectiveness of the proposed approaches.

This paper is concerned with the optimal output synchronization control problem for a class of heterogeneous complex dynamical networks (CDNs) with partially unknown system dynamics. By defining a new quadratic performance index including the information of state couplings, an optimal controller consisting of a feedback control and a compensated feedforward control is then designed. A necessary and sufficient condition for the optimal control minimizing the quadratic performance index is established. Especially, an algebraic Riccati equation (ARE) associated with a discount factor is obtained, and a novel online iteration algorithm by iteratively solving the ARE is proposed to compute the optimal controller gain for the case that the CDNs are with partially unknown system dynamics. Moreover, it is proved that the output synchronization errors converge to zero asymptotically by applying the optimal control laws. Finally, two simulation examples are provided to verify the effectiveness of the proposed control method.

A feedforward neural network has been shown to possess the ability of approximating an optimal controller over a subspace of initial conditions. In addition to a feedforward neural network the fuzzy logic/neural network hybrid ANFIS (adaptive network based fuzzy inference system) structure has been shown to be a universal approximator. This paper discusses briefly the use of ANFIS to approximate an optimal feedback controller for the nontrivial problem of guiding a high-speed vehicle (glider) to a ground target and compares results to a three layer feedforward neural network controller. The controllers are trained using optimal open loop state and control data generated by VF02AD. Simulation results show that both controller types guide the vehicle to within 1000 ft of the target with practically no degradation in the optimal impact velocity over a range of initial conditions. The advantages and disadvantages of both controllers are discussed together with some practical limitations of the ANFIS optimal feedback controller.

In this paper, insulin injection process in which the level of glucose is monitored and corrected using optimal robust controller. The Bergman minimal model with unknown parameters was adopted to simulate a diabetes mellitus patient. An exogenous disturbance is considered as a meal effect on the patient. Optimal control approach to robust control design is suggested for glucose problem. The goal is to design a state feedback to stabilize the glucose system under uncertainty and disturbance. Linearized model of glucose system is considered with nonlinearity is lumped as a matched and mismatched uncertainties. Comparison in performance is made between the robust optimal controllers with classical optimal controller. The simulated results showed that the robust optimal controller outperforms the classical optimal controller for the considered cases. Also, the disturbance rejection capability of both controllers has been examined, and the results showed that the robust optimal controller has better rejection characteristics than its counterpart.

Bellman’s discrete dynamic programming is one of the most general approaches to solve optimal control problems. For discrete-time dynamical systems, it is, at least theoretically, capable to determine globally optimal control laws. In most practical cases, both state and control variables are subject to constraints. Due to the necessity for gridding of the range of both state and control variables in numerical implementations of dynamic programming, the computational effort grows exponentially with increasing system dimensions. This fact is well known as the curse of dimensionality. Furthermore, gridding of intervals representing uncertain system parameters is inevitable, if dynamic programming is used for the design of optimal controllers for systems with uncertainties. In this contribution, an interval arithmetic procedure for the design of optimal and robust controllers is presented. This procedure relies on the basic concepts of dynamic programming. Sophisticated techniques for the exclusion of non-optimal control strategies significantly reduce the computational burden. Since interval techniques can be applied to both continuous-time and discrete-time dynamical systems, the interval arithmetic optimization approach presented in this chapter is applicable to both cases. In addition, the inclusion of effects of uncertain parameters in the underlying optimality criteria is demonstrated. For that purpose, interval arithmetic routines for analysis and design of optimal and robust controllers have been developed. Details about computationally efficient implementations of interval arithmetic optimization procedures and numerical results for a mechanical positioning system with statedependent switchings between different dynamical models for viscous and Coulomb friction are summarized.

This paper introduces a renewable-energy-based microgrid that includes Photovoltaic (PV) energy and wind energy generation units. Also, an energy storage system is present. The proposed microgrid is loaded with a constant load impedance. To improve the performance of the proposed microgrid, an optimal control algorithm utilizing Cuckoo Search Algorithm (CSA) is adapted. It has many merits such as fast convergence, simple tunning, and high efficiency. Commonly, the PV and wind energies are suitable for supplying loads under normal conditions. However, the energy storage system recovers the excess load demand. The load frequency and voltage are regulated using the CSA optimal controller. The microgrid responses with the introduced optimal controller are measured under step changes in load demand, wind power, and the PV irradiation level. Matlab simulations are carried out to test the proposed system performance. The simulation results showed that the proposed microgrid fed the load with Alternating Current (AC) power of constant amplitude and frequency for all disturbances. Moreover, the required load demand has been perfectly compensated. Moreover, the performance of the storage system is excellent with the unstable wind speed and variable solar irradiation. Also, the results with the optimal CSA controller are compared to those with the Particle Swarm Optimization (PSO) algorithm at the same conditions. It is also found that the optimal CSA controller provides better responses.

This paper investigates the robust optimal formation control for the position subsystem of quadrotor unmanned aerial vehicles (UAVs) subject to external disturbances and collision constraints. To prevent collision with both members of the formation and external obstacles, a collision avoidance potential function is constructed using relative position and velocity information. The basic bounded control input can ensure the stable flight and collision avoidance of a quadrotor UAV system. Based on the approximate dynamic programming (ADP) framework and two‐player zero‐sum differential game theory, the optimal controller is designed to further enhance the control performance of the system. The optimal value function is approximated by a single layer neural network, which avoids solving complex nonlinear Hamilton‐JacobiIsaac (HJI) equation. The stability of the closed loop system is proved. The effectiveness of the robust optimal formation controller based on learning is validated through MATLAB simulation in two distinct scenarios.