Optimal Control Design Method Research Articles

Dynamic optimal control of flow front position in injection molding process: A control parameterization-based method

High dynamic and precise control of process variables within permissible limits is the key to high product quality in the injection molding industry. Among these variables, the injection flow rate of molten polymer is particularly significant. In this paper, an effective optimal open-loop and state feedback controller design method is designed to realize the optimal tracking control of the melt polymer flow front position flow of melt polymer fluid during injection molding. To this end, the dynamic model of the filling process is firstly established, taking into account the nonlinearity of hydraulic control system and the effect of molten polymer flow on the dynamics of the injection ram, and then the dynamic optimal tracking control problem of flow front position of molten polymer in injection molding machine is proposed. Then, an open-loop controller and a multi-level feedback control law are well designed, wherein the control signal and the control feedback kernels are parameterized by control parameterization. The controller design problems are transformed into sequential optimal parameter decision problems. The explicit expressions of the gradient information of the objective function and constraints on the parameters of the decision variables are solved by using the state sensitivity equation analysis method, and the gradient information is combined with the nonlinear programming algorithm to solve the optimization problems efficiently. Finally, the viability and effectiveness of the proposed design method are verified by numerical simulations.

Coordinated Control Design for Ethical Maneuvering of Autonomous Vehicles

This paper proposes a coordinated control design method, with which the autonomous vehicle is able to perform ethical maneuvers. The starting point of the provided method is a thorough analysis on the ethical concepts for autonomous vehicle control design methods. Using the results of the analysis, an own concept is provided based on some principles of Protestant ethics. The concept focuses on improving trust in vehicle control through clear rules and predictable vehicle motion, and it is in line with the state-of-the-art ethical vehicle control methods. Moreover, an optimal Model Predictive Control (MPC) design method is formed, in which the provided ethical concept is incorporated. The outputs of the optimal control are steering angle and velocity profile, with which the ethical maneuvering can be achieved. The contribution of the paper is a coordinated control design method, which is able to involve ethical principles. Moreover, the application of Protestant ethics in this context is also a novel achievement in the paper. The effectiveness of the method through different simulation scenarios is illustrated.

Optimal consensus control for multi-satellite assembly in elliptic orbit with input saturation

This paper presents an optimal control design method for multi-satellite assembly in an elliptic orbit in close proximity operations considering input saturation constraints. Tschauner–Hempel (T–H) equations are utilized to model the relative motion dynamics of the satellites in the Local Vertical Local Horizontal (LVLH) frame of the target satellite, where every satellite in the assembly is modeled as a point mass. The communication topology between the satellites in the assembly is modeled using graph theory, where the graph has several nodes representing the satellites and several edges representing the data exchange direction. It is assumed that every satellite exchanges its states with a few neighbors in the team, where the neighbors of every satellite are prespecified and do not change during the mission. This graph is utilized to construct the global dynamic model of the assembly, in which every node is represented by the dynamic model of a single satellite. The local control law, which is applied to every satellite in the assembly, consists of a state feedback gain and a coupling gain. The state feedback gain is designed using the discrete-time periodic Riccati equation to guarantee the local stability of every satellite separately, while the coupling gain is selected to satisfy the Lyapunov condition to guarantee the global stability of the assembly. The invariant-set method is utilized to prove the stability of the global dynamic system that is subjected to symmetric input saturation. The precision and optimality of the proposed control law are successfully demonstrated by numerical nonlinear simulations in a MATLAB environment for a cubic formation satellite assembly.

Adaptive optimal trajectory tracking control of AUVs based on reinforcement learning

In this paper, an adaptive model-free optimal reinforcement learning (RL) neural network (NN) control scheme based on filter error is proposed for the trajectory tracking control problem of an autonomous underwater vehicle (AUV) with input saturation. Generally, the optimal control is realized by solving the Hamilton–Jacobi–Bellman (HJB) equation. However, due to its inherent nonlinearity and complexity, the HJB equation of AUV dynamics is challenging to solve. To deal with this problem, an RL strategy based on an actor–critic framework is proposed to approximate the solution of the HJB equation, where actor and critic NNs are used to perform control behavior and evaluate control performance, respectively. In addition, for the AUV system with the second-order strict-feedback dynamic model, the optimal controller design method based on filtering errors is proposed for the first time to simplify the controller design and accelerate the response speed of the system. Then, to solve the model-dependent problem, an extended state observer (ESO) is designed to estimate the unknown nonlinear dynamics, and an adaptive law is designed to estimate the unknown model parameters. To deal with the input saturation, an auxiliary variable system is utilized in the control law. The strict Lyapunov analysis guarantees that all signals of the system are semi-global uniformly ultimately bounded (SGUUB). Finally, the superiority of the proposed method is verified by comparative experiments.

High-Frequency Modelling of Constant On-Time Current Mode Buck Converter and Controller Design by Combining Genetic Algorithm

Constant on-time current mode (COTCM) Buck converters are widely used in power management integrated circuit (ICs) for microprocessors. Small-signal models are necessary tools to design high-quality controllers. Existing models neglect output voltage ripples (OVRs) and spectrum extension caused by switching, which makes significant errors under high control bandwidth. This article adopts Fourier series to describe OVRs precisely. Then, influences of OVRs on COTCM are analyzed. Finally, spectrum coupling from current loop and voltage loop is incorporated to obtain a high-frequency model, and four universal analytical expressions in frequency domain are obtained with the aid of matrix calculation. Based on the proposed model and genetic algorithm, an optimal controller design method is developed. Simulation and experiment validate the accuracy of proposed model and the effectiveness of proposed design method.

Optimal Sliding Mode Preview Repetitive Control for Three-Phase Z-Source Inverters

Aiming at high output voltage and obvious current fluctuation of the off grids inverters with unbalanced and nonlinear loads, a compound control strategy of sliding mode controller and optimal preview controller based on Z-source inverter (ZSI) is proposed. ZSI can boost the pressure and improve the system energy conversion rate through by combining the state with the linear quadratic design method of optimal control. The preview controller is introduced in the feedforward compensation link. With the help of difference operator, an extended state error system covering the target value signal and lag link feedback is designed. The optimal preview repetitive control (PRC) is transformed into a linear quadratic regulation matter of the discrete systems. Furthermore, a preview repetitive controller is obtained by using the Lyapunov method, linear matrix inequality, and the design method of optimal controller, which can realize sliding mode control, state feedback, repetitive control, and preview compensation. Finally, a 10 kV A prototype is built to verify the effectiveness of the proposed strategy.

Learning-Based Adaptive Optimal Control for Connected Vehicles in Mixed Traffic: Robustness to Driver Reaction Time.

Through vehicle-to-vehicle (V2V) communication, both human-driven and autonomous vehicles can actively exchange data, such as velocities and bumper-to-bumper distances. Employing the shared data, control laws with improved performance can be designed for connected and autonomous vehicles (CAVs). In this article, taking into account human-vehicle interaction and heterogeneous driver behavior, an adaptive optimal control design method is proposed for a platoon mixed with multiple preceding human-driven vehicles and one CAV at the tail. It is shown that by using reinforcement learning and adaptive dynamic programming techniques, a near-optimal controller can be learned from real-time data for the CAV with V2V communications, but without the precise knowledge of the accurate car-following parameters of any driver in the platoon. The proposed method allows the CAV controller to adapt to different platoon dynamics caused by the unknown and heterogeneous driver-dependent parameters. To improve the safety performance during the learning process, our off-policy learning algorithm can leverage both the historical data and the data collected in real time, which leads to considerably reduced learning time duration. The effectiveness and efficiency of our proposed method is demonstrated by rigorous proofs and microscopic traffic simulations.

Finite-time optimal tracking control using augmented error system method

This paper proposes a design method of finite-time optimal tracking controller for quadratic performance index. A novel nonlinear finite-time optimal controller is designed to solve the finite-time optimal tracking control problem for linear system. By applying augmented error system method and finite-time optimal state feedback control, sufficient conditions involving V-function are obtained, and eventually, a nonlinear controller based on the V-function is derived. In addition, the construction of a specific V-function satisfying those conditions is discussed in detail. The nonlinear controller which we introduced makes closed-loop system finite-time stable, so that the tracking error of original system converges in finite time. The simulation example illustrates the efficiency of our results.

STUDY OF INFLUENCE OF QUADROCOPTER DESIGN AND SETTINGS ON QUALITY OF ITS WORK DURING MONITORING OF GROUND OBJECTS

The subject of the article is methods of reducing quadcopter magnetometer crosstalk by changing the design and settings of the copter to improve the quality of its work during the monitoring of ground objects. The relevance of the development is determined by the need to increase the physical safety of quadcopters when monitoring ground facilities in various industries because the magnetometer is the most noise-sensitive sensor, and its failure leads to the fall and loss of the drone. The purpose of the article is to determine the optimal design and settings of the quadcopter in terms of its physical safety and quality of work during monitoring of ground facilities in various industries. The research task is to check whether it is possible to protect the magnetometer placed inside the drone body from the power cables crosstalk by grounding, shielding and changing the initial settings of the copter, namely by changing the value of the startup power factor of the motors. Research methods are as follows: theory of automatic control, methods of optimal control and hardware design methods. Conclusions. The role of the drone magnetometer in the monitoring of ground objects has been studied. The study has shown that copters at monitoring ground objects must be equipped with a magnetometer and GPS. The magnetometer is the most sensitive to interference of all sensors. If it does not work properly, the entire drone navigation system stops working. We have carried out experimental studies of the influence of quadcopter design and settings on the quality of its magnetometer work, and hence on work of the copter as a whole. In this paper it is proposed to place a magnetometer inside the body of the drone that will increase its physical safety and simplify the design of the drone, but at the same time it will increase the coupling from the power cables of motors, so it is necessary to choose effective methods of protection. It has been tested whether it is possible to protect the magnetometer from interference from power cables when placing it inside the drone body by grounding, shielding and changing the initial settings of the copter, namely by changing the value of the startup power factor of the motors. The results of the experiments showed that to protect against the interference for magnetometer placed inside the drone body, it is necessary to combine shielding of the magnetometer and decreasing of the startup power factor of the motors.

Design of nonlinear optimal tracking control law based on finite-time stability for quadratic performance index

In this paper, a design method of optimal tracking control based on finite-time stability for quadratic performance index is proposed. Finite-time stability of tracking control involves dynamical systems whose actual output can track desired output in finite time while satisfying Lyapunov stability. A nonlinear control law which guaranteed finite-time stability is designed depending on the core idea of dynamic programming. By using Hamilton–Jacobi–Bellman (HJB) equation and finite-time stability theory, sufficient conditions involving V-function are provided, and design steps for nonlinear finite-time tracking control law are derived by constructing augmented systems. In addition, the V-function is constructed to obtain corresponding law for given systems, which verified that the design method is feasible. Simulation examples validate the efficiency of the results.

Bounded and inverse optimal formation stabilization of second-order agents

This paper formulates and solves a new problem of both bounded and inverse optimal formation stabilization control for a group of second-order dynamic mobile agents with collision avoidance and limited sensing range. The control design is based on new Lyapunov functions, new non-zero convergence and dominating lemmas, new pairwise collision avoidance functions, and forwarding and inverse optimal control design methods. The proposed formation stabilization control design guarantees no collision between any agents, “almost global” asymptotic stability of desired equilibrium points and instability of undesired equilibrium points, an infinite gain margin, bounded controls by a pre-specified constant, and minimization of a cost function that penalizes both stabilization errors and the control inputs without having to solve a Hamilton–Jacobi–Bellman or Hamilton–Jacobi–Isaacs equation.

Neural Network-Based Model-Free Learning Approach for Approximate Optimal Control of Nonlinear Systems

This paper studies the infinite time horizon optimal control problem for continuous-time nonlinear systems. A completely model-free approximate optimal control design method is proposed, which only makes use of the real-time measured data from trajectories instead of a dynamical model of the system. This approach is based on the actor-critic structure, where the weights of the critic neural network and the actor neural network are updated sequentially by the method of weighted residuals. It should be noted that an external input is introduced to replace the input-to-state dynamics to improve the control policy. Moreover, strict proof of convergence to the optimal solution along with the stability of the closed-loop system is given. Finally, a numerical example is given to show the efficiency of the method.

Online barrier-actor-critic learning for H∞ control with full-state constraints and input saturation

This paper develops a novel adaptive optimal control design method with full-state constraints and input saturation in the presence of external disturbance. First, to consider the full-state constraints, a barrier function is developed for system transformation. Moreover, it is shown that, with the barrier-function-based system transformation, the stabilization of the transformed system is equivalent to the original constrained control problem. Second, the disturbance attenuation problem is formulated within the zero-sum differential games framework. To determine the optimal control and the worst-case disturbance, a novel barrier-actor-critic algorithm is presented for adaptive optimal learning while guaranteeing the full-state constraints and input saturation. It is proven that the closed-loop signals remain bounded during the online learning phase. Finally, simulation studies are conducted to demonstrate the effectiveness of the presented barrier-actor-critic learning algorithm.

Data-Driven Robust Control of Discrete-Time Uncertain Linear Systems via Off-Policy Reinforcement Learning.

This paper presents a model-free solution to the robust stabilization problem of discrete-time linear dynamical systems with bounded and mismatched uncertainty. An optimal controller design method is derived to solve the robust control problem, which results in solving an algebraic Riccati equation (ARE). It is shown that the optimal controller obtained by solving the ARE can robustly stabilize the uncertain system. To develop a model-free solution to the translated ARE, off-policy reinforcement learning (RL) is employed to solve the problem in hand without the requirement of system dynamics. In addition, the comparisons between on- and off-policy RL methods are presented regarding the robustness to probing noise and the dependence on system dynamics. Finally, a simulation example is carried out to validate the efficacy of the presented off-policy RL approach.

Control allocation-based fault tolerant control

This paper describes a novel scheme for fault tolerant control using a robust optimal control design method. This scheme can also be employed as actuator redundancy management for over-actuated linear systems. In contrast to many existing methods in the literature, this scheme can be applied to systems whose control input matrix cannot be factorised into two matrices whose ranks are equal and less than the minimum of the number of columns and rows of the input matrix. The so-called virtual control, in this scheme, is calculated using a robust ℋ2-based feedback design approach constructed to be robust against uncertainties emanating from visibility of the control allocator to the controller and imperfection in the estimated effectiveness gain. Then, using a new control allocation scheme along with a novel Tikhonov-based re-distributor mechanism, the obtained virtual control signal is re-distributed among remaining (redundant or non-faulty) set of actuators. As the proposed scheme is modular-based, it can be employed as a real-time fault tolerant control scheme with no need to reconfigure the controller in the case of actuator faults or failures. The effectiveness of the proposed scheme is demonstrated by a numerical example.

Optimal Controller Design for Virtual Sensing With Independent Noise Source Measurement

In certain applications, when the placement of sensors at the target location is not feasible, a common practice is to obtain the target information indirectly via sensors at other locations. This technique is known as virtual sensing (or soft sensing), and involves various signal processing techniques. Virtual sensing is applied to such systems to estimate the error signal for feedback control. However, issues regarding both stability and performance degradation become significant because the estimation is not precise. In this brief, we propose a virtual sensing control (VSC) method using a feedforward controller to compensate the mismatch between an error sensor and virtual sensor under the feedback control. The results show that when an independent noise source measurement is available, a feedforward controller is more appropriate than estimation as it maintains the stability of the feedback system while achieving a good performance enhancement. For such a VSC system, the design of both feedforward and feedback controllers is coupled. In this brief, we derive an optimal controller design method to maximize the noise reduction capability. We show the advantages of the proposed VSC method by applying it to the implementation of an active noise control system.

Development of optimal controller design method to compensate for vibrations caused by unbalanced force in rotor system based on Nyquist diagram

In this paper, an optimal controller design method is proposed to compensate for vibrations caused by unbalanced force in the rotor system. The vibrations caused by unbalanced force are the major root cause of excessive whirling vibration in the rotor system, and it is important to compensate for the vibration to maintain its stable operation. The proposed design method can optimize a performance of the controller based on the vector locus of open loop characteristics on the Nyquist diagram. To verifiy the effectiveness, the proposed design method was employed for three typical active vibration control methods. The experimental results show that the proposed method can design the optimal parameters to compensate for the whirling vibrations of the rotor system.

Adaptively Receding Galerkin Optimal Control for a Nonlinear Boiler-Turbine Unit

The boiler-turbine unit is really a complex system in thermal power engineering due to its large-scale nonlinearity, unmeasured state, unknown disturbances, and constraints imposed on both controls and outputs. To design a controller with appropriate performance in above synthetical cases, this paper intends to propose an adaptively receding Galerkin optimal controller design method, in which, the mathematical dynamics of unit can be directly used as a predictive model without any linearization, and the unmeasured state in the predictive model is adaptively estimated using a predesigned state observer. With the help of a mathematical predictive model, optimal control law is then obtained based on a Galerkin optimization algorithm. Due to the application of the useful information measured at every sampling time instant, the proposed method can deal with the tracking problem with constraints rather than the stabilization problem that can be only done by the traditional Galerkin optimal control. Furthermore, it can also be easily extended to estimate and thus eliminate constant disturbances in an output channel using an independent model strategy. Some simulations suggest that satisfactory tracking performance can be achieved even when the unit experiences wide-range load change.

Stochastic optimal control for sampled‐data system under stochastic sampling

In this study, the problem of designing a stochastic optimal controller for sampled-data systems whose sampling interval is subjected to a certain probability distribution is addressed. To design the controller, the Kronecker product operation and the Vandermonde matrix were introduced. A design method of the stochastic optimal controller is proposed. It is shown that the controller guarantee that the closed-loop system has exponentially mean square stability. Finally, the simulation results illustrate the effectiveness and practicability of the proposed method.

Optimal control of non-minimum phase integrating processes with time delay using disturbance observer-based control scheme

ABSTRACTA systematical design method of optimal control for non-minimum phase integrating processes with time delay using disturbance observer-based (DOB) control scheme is presented. All stabilising controllers and the filter of DOBs for integrating plants are developed. Then the optimal set-point tracking controller and the optimal filter of DOB are systematically derived by minimising the H2 norm performance specifications. The proposed design method has three main advantages. First, the design procedure is systematical and simple. Specified weight functions are chosen for step inputs and inputs similar to steps. The designed set-point tracking controller and the filter of DOB are given in analytical forms. Second, the designed set-point tracking controller and the filter of the DOB are optimal. They are derived from minimising the performance indexes of set-point tracking and input load disturbance rejection (ILDR). Finally, the set-point tracking performance specification and ILDR specification can be quantitatively achieved by conveniently tuning the adjustable parameters. Numerical simulations are given to illustrate the effectiveness of the proposed method.